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GANOT # ELEMENTARY TREATISE ON

PHYSICS

3 T153 00126307 6

GANOT'S PHYSICS.

Sixth Edition, with 34 pages of new matter, 2 Plates,

518 Woodcuts, and an Appendix of Questions.

Crown 8vo. "js. 6d.

NATURAL PHILOSOPHY

FOR GENERAL READERS AND YOUNG PERSONS.

A Course of Physics divested of Mathematical Formula;,
expressed in the language of daily life.

Translated and Edited from Ganot's Cmirs Elcmentaire de
Physiqzic, by E. Atkinson, Ph.D. F.C.S.

London : LONGMANS, GREEN, & CO.

9d7(^

ELEMENTARY TREATISE

PHYSICS ''

EXPERIMENTAL AND APPLIED

FOR THE USE OF COLLEGES AND SCHOOLS.
TRANSLATED AND EDITED FROM

GANOT'S ELEMENTS DE PHYSIQUE

(with the Author's saiiction)
BY

E. ATKINSON, Ph.D., F.C.S.

LATE PROFESSOR OF EXPERIMENTAL SCIENCE IN THE STAFF COLLEGE.

®;i^irte£nt^ (SMtioit, rjfrisfb Hnl» enlargeb.

ILLUSTRATED by g COLOURED PLATES and MAPS and 987 WOODCUTS.

NEW YORK :
WILLIAM WOOD AND CO., PUBLISHERS,

56 & 58 lafayette place.
i8qo.

,.-^p#^

CONTENTS.

BOOK I.
ON MATTER, FORCE, AND MOTION.

Errata

Pages 494 and 513, Figs. 451 and 480 should be interchanged

Ganot's Physics.
iV. rK.urii.Kij.ii-D 1 -r-v^uj^ij-iiv IV.

BOOK III.
ON LIQUIDS.

I. Hydrostatics . . . ' • • • • .86
II. Capillarity, Endosmose, Effusion, and Absorption . .114

III. Hydrodynamics ....... 127

BOOK IV.
ON GASES.

I. Properties of Gases. Atmosphere. Barometers . .136

II. Measurement of the Elastic Force of Gases . . -157

III. Pressure on Bodies in Air. Balloons . . . -173

IV. Apparatus which depend on the Properties of Air . . 178

CONTENTS.

BOOK I.
ON MATTER, FORCE, AND MOTION.

CHAPTER PAGE

I. General Principles ....... i

II. General Properties of Bodies ..... 4

III. On Force, Equilibrium, and Motion . . , .11

BOOK 11.

ON GRAVITATION AND MOLECULAR ATTRACTION.

I. Gravity, Centre of Gravity, the Balance . . .54

II. Laws of Falling Bodies. Intensity of Terrestrial Gravity.

The Pendulum ....... 63

III. Molecular Forces ....... 73

IV. Properties peculiar to Solids ..... 77

BOOK III.

ON LIQUIDS.

I. Hydrostatics . . . ' . . . . .86

II. Capillarity, Endosmose, Effusion, and Absorption . .114

III. Hydrodynamics

II. Measurement of the Elastic Force of Gases .
III. Pressure on Bodies in Air. Balloons .

127

BOOK IV.
ON GASES.
I. Properties of Gases. Atmosphere. Barometers . . 136

157
173

IV. Apparatus which depend on the Properties of Air . .178

Contents.

BOOK V.

ON SOUND.

CHAPTER

I. Production, Propagation, and Reflection of Sound

II. Measurement of the Number of Vibrations .

III. The Physical Theory of Music ....

IV. Vibrations of Stretched Strings, and of Columns of Air
V. Vibrations of Rods, Plates, and Membranes .

VT. Graphical Method of Studying Vibratory Motions

PAGE

199

2X8

224
241
255
259

BOOK VI.

ON HEAT.

I. Preliminary Ideas. Thermometers

II. Expansion of Solids

III. Expansion of Liquids

IV. Expansion and Density of Gases
V. Changes of Condition. Vapours

VI. Hygrometry

VII. Conductivity of Solids, Liquids, and

VIII. Radiation of Heat

IX. Calorimetry

X. Steam Engines

XI. Sources of Heat and Cold

XII. Mechanical Equivalent of Heat

Gases

272
287

295

302

311

365

375
3S3
422
442
457
474

BOOK VII.
ON LIGHT.

I. Transmission, Velocity, and Intensity of Light

II. Reflection of Light. Mirrors .

III. Single Refraction. Lenses

IV. Dispersion and Achromatism

V. Optical Instruments ....

VI. The Eye considered as an Optical Instrument

VII. Sources of Light. Phosphorescence .

VIII. Double Refraction. Interference. Polarisation

4S1
494
512

535
560
587
607
6x1

THE THIRTEENTH EDITION.

In the present edition the additions made have increased by about
fifty-one pages the size of the work as it stood in the last edition.
The new matter contains also fifty-seven additional illustrations.

I have to express my acknowledgments to Dr. G. H. Johnson for
his kindness in revising the chapter on the Eye.

I am further indebted to Mr. F. C. Poynder for having called my
attention to a number of errata.

The continued favour with which the work has been received,

as a Text-book for Colleges and Schools, and also as a book of

reference for the general reader, renders any apology for omissions

perhaps unnecessary ; it may, however, be as well once more to

point out that the book is intended to be a general Elementary

Treatise on. Physics, and that, while it accordingly aims at giving an

account of the most important facts and general laws of all branches

of Physics, an attempt to treat completely and exhaustively of any one

branch would both be inconsistent with the general plan of the book

and impossible within the available space.

E. ATKINSON.

PORTESBERY HiLL, CaMBERLEY : Dcc. 1889.

EXTRACT FROM ADVERTISEMENT TO THE
TWELFTH EDITION.

Some alterations have been made in Book I. : in making these I
have availed myself of an introductory chapter which Prof Nipher, of
the University of Missouri, prepared for the use of his classes, and
which he kindly placed at my disposal.

E. A.

TRANSLATORS PREFACE TO FIRST EDITION.

The Elements de Physique of Professor Ganot, of which the present
work is a translation, has acquired a high reputation as an Introduction
to Physical Science. In France it has passed through Nine large
editions in little more than as many years, and it has been translated
into German and Spanish.

This reputation it doubtless owes to the clearness and conciseness
with which the principal physical laws and phenomena are explained,
to its methodical arrangement, and to the excellence of its illustrations.
In undertaking a translation, I was influenced by the favourable opinion
which a previous use of it in teaching had enabled me to form.

I found that its principal defect consisted in its too close adaptation
to the French systems of instruction ; and accordingly, my chief labour,
beyond that of mere translation, has been expended in making such
alterations and additions as might render it more useful to the English
student.

I have retained throughout the use of the Centigrade thermometer,
and in some cases have expressed the smaller linear measures on the
metrical system. These systems are now everywhere gaining ground,
and an apology is scarcely needed for an innovation which may help to
familiarise the English student with their use in the perusal of the larger
and more complete works on Physical Science to which this work may
serve as an introduction.

E. A.
Royal Military College, Sandhurst :

LIST OF TABLES.

Absorbing powers . . . 394
Absorption of gases . . 166, 170

heat by gases . . 410

liquids . 404

vapours . 406

various bodies

405,411
Atmosphere, composition of . . 139

Barometric variations

Boiling points

Breaking weight of substances

Capillarity in barometers .
Capillary, constant
Combustion, heat of
Conducting powers of solids for
heat

liquids for heat

Conductors of electricity

Densities of gases

vapours

Density of water .
Diamagnetism
Diathermanous power
Diffusion of solutions

,, of heat .
Dulong and Petit's law

Elasticity.
Electrical conductivity .
Electricity, positive and negative
Electromotive force of different
elements ....

series .

Endosmotic equivalents
Expansion, coefficients of solids 290.

liquids

gases

Eye, dimensions of

refractive indices of media of

Freezing mixtures
Fusing points of bodies

150
333

«3

148
122
465

377
380
390

310
364
301

950
404
126
408
432

79
926

693

787

775
124
), 291
298
306
590
590

320
3"

l-AGE

Glaisher's factors . . -371
Gravity, force of, at various places 69

Hardness, scale of . . .84

Latent heat, of evaporation . 341
fusion . .437

Magnetic declination . . . 658

inclination . . . 664

Molecular velocity of gases . , 275

Radiating powers . . 395, 402
Radiation of powders . . . 414
Reflecting powers . . . 393
Refraction, angle of double . .616
Refractive indices . . . 5-2
of media of eye . 590

Sound, transmission of, in tubes
Specific gravity of liquids
solids

[08

heat of solids and liquids 430, 431

gases ._ _ . . 434

inductive capacities , . 716

striking distance . . 757

Tangent galvanometer and volta-
meter, comparison between
Temperatures, various remarkable .

at different latitudes .

thermal springs

measurement of

Tension of aqueous vapour . 325.

vapours of liquids

Thermo-electric series .

Undulations, length of

Velocity of sound in gases

liquids

rock

solids

Vibrations of musical scale

833
286
984
986
307
329
330
911

6x1

208
210
212
211

225

LIST OF PLATES AND MAPS.

Table of Spectra Fyontispieu

Coloured Rings produced by Polarised Light in Double Refract-
ing Crystals To face p. 636

Isogonic Lines for the Year 1882 ,, 659

IsocLiNic Lines for the Year 1882 ,, 664

IsoDYNAMic Lines for the Year 1882 ,, 067

Aurora Borealis ,, 1029

Isothermal Lines for the Year ...... ,, 1031

Isothermal Lines for January ,, 1032

Isothermal Lines for July ,, 1034

Mini

iiliiiiilii

Millimetres

Square
Centi-

Centimetres

The area of the figure within the heavy lines is
that of a square decimetre. A cube, one of whose
sides is this area, is a cubic decimetre or litre. A
htre of water at the temperature of 4° C. weighs a
kilogramme. A litre of air at 0° C. and 760™"
pressure weighs 1*2 93 gramme.

A Htre is i-'jdp'nt ; a pint is 0*568 of a htre.

The smaller figures in dotted lines represent the
areas of a square centimetre and of a square inch.

A cubic centimetre of water at 4° C. weighs a
oramme.

Square Inch

Inches Feet

Millimetre ..... o'o3937 o"oo328i

Centimetre ..... o'3937i o'o328ig

Decimetre ..... 3'937o8 o"328o90

Metre 39 '37079 3 ■280899

Kilometre 3937070000 328o'899i67

A Hectare or 10,000 square metres is equal to 2'47ii4 acres, each of which is 43,560
square feet. A kilometre is o-62i4 of a statute mile. A statute mile is i '609 kilometre.
A knot (in telegraphy) is 2,029 yards or i'iS28 statute mile.

Measures of Capacity.

Cubic Feet

Cubic Inches 1,728 c. in. = 1 c. ft.

Cubic centimetre or millimetre . o'o6io3 o'oooo35

Litre or cubic decimetre . . . 61 '02705 o'C353i7

Kilolitre or cubic metre . . 6i,o27'o5i52 35'3i658i

Measures of Weight.

Avoirdupois Pounds
English Grains of 7,000 grains

Milligramme o"oi543 o"ooooo22

Gramme i5'4323S o'oo22046

Kilogramme 15, 432 '34880 2 '2046213

I grain = 0*064799 gramme ; i pound avoirdupois is o'4S3593 kilogramme.

Contents,

BOOK VIII.
ON MAGNETISM.

CHAPTER

I. Properties of Magnets ....

II. Terrestrial Magnetism. Compasses

III. Laws of Magnetic Attraction and Repulsion

IV, Processes of Magnetisation

PAGE

649
656
669

677

BOOK IX.

ON FRICTIONAL ELECTRICITY.

I. Fundamental Principles ...... 688

II. Quantitative Laws of Electrical Action . . . 696

III. Action of Electrified Bodies on Bodies in the Natural

State. Induced Electricity. Electrical Machines . 709

IV. Condensation or Accumulatio-n of Electricity . . 737

BOOK X.

ON DYNAMICAL ELECTRICITY.

I.
IL

in.

IV.

VI.

VIL

VIIL

IX.

Voltaic Pile. Its Modifications
Detection and Measurement of Voltaic Currents .
Effects of the Current .....
Electrodynamics. Attraction and Repulsion of Currents

BY Currents ......

Magnetisation by Currents. Electromagnets. Electric

Telegraphs ......

Voltaic Induction .....

Optical Effects of Powerful Magnets. Diamagnetism
Thermo-electric Currents ....

Determination of Electrical Constants

Animal Electricity .....

Elementary Outlines of Meteorology and Climatology
Problems and Examples in Physics

770
790

844

S62
8S7
944
952
965
942

993
1039

INDEX

1063

ELEMENTARY TREATISE

PHYSICS.

BOOK I.

ON MATTER, FORCE, AND MOTION.
CHAPTER I.

GENEKAL PRINCIPLES.

1. Object Of Physics. — The object of Physics is the study of the phe-
nomena presented to us by bodies. It should, however, be added, that
changes in the nature of the body itself, such as the decomposition of one
body into others, are phenomena whose study forms the more immediate
object oi clicmistry.

2. Matter. — That which possesses the properties whose existence is
revealed to us by our senses, we call matter or substance.

All substances at present known to us may be considered as chemical
combinations of sixty-seven elementary or simple substances. This number,
however, may hereafter be diminished or increased by the discovery of some
more powerful means of chemical analysis than we at present possess.

3. Atoms, molecules. — From various properties of bodies, we conclude
that the matter of which they are formed is not perfectly continuous, but
consists of an aggregate of an immense number of exceedingly small por-
tions or atoms of matter. These atoms cannot be divided physically ; they
are retained side by side, without touching each other, being separated by
distances which are great in comparison with their supposed dimensions.

A group of two or more atoms forms a molecule., so that a body may be
considered as an aggregate of very small molecules, and these again as
aggregates of still smaller atoms. The smallest masses of matter we e\'er
obtain artificially are particles^ and not molecules or atoms. Molecules
retain their position in virtue of the action of certain forces called molecular
forces.

From considerations based upon various physical phenomena Sir W,
Thomson has calculated that in ordinary solids and liquids, the average

2 On Matter, Force, and Motion. [3-

distance between contiguous molecules is less than the one hundred-millionth
but greater than the one two thousand-millionth of a centimetre.

To form an idea of the degree of the size of the molecules, Sir W.
Thomson gives this illustration : — ' Imagine a drop of rain, or a glass sphere
the size of a pea, magnified to the size of the earth, the molecules in it being
increased in the same proportion. The structure of the mass would then be
coarser than that of a heap of fine shot, but probably not so coarse as that
of a heap of cricket-balls.'

The number of molecules of gas in a cubic centimetre of air is calculated
at twenty-one trillions.

By dissolving in alcohol a known weight of fuchsine, and diluting the
liquid, it was observed that a solution containing not more than 0-00000002
of a gramme in one cubic centimetre had still a distinct colour ; that is, that
a weight of not more than the ^^-;-millionth of a gramme can be perceived by
the naked eye. As the molecular weight of this substance is 2,1)1 times that
of hydrogen, it follows that the weight of an atom of hydrogen cannot be
greater than the one 20,000-millionth of a gramme.

Loschmidt gives the diameter of the molecules of hydrogen at 0-00000004
of a centimetre ; and according to Mousson and Quincke the diameter of
the sphere within which one molecule can act upon an adjacent one, or
what is called the radius of molecular action, is between the 0-00003 and
0-00004 of a millimetre, and is therefore from 5 to 10 times less than the
wave-length of light.

4. Molecular state of bodies. — With respect to the molecules of bodies,
three different stages of aggregation present themseh'es.

First, the solid state, as observed in wood, stone, metals, &c., at the
ordinary temperature. The distinctive character of this state is, that the
relative position of the molecules of the bodies is fixed and cannot be
changed without the expenditure of more or less force. Solid bodies tend,
therefore, to retain whatever form may have been given to them by nature or
by art.

Secondly, the liquid state, as observed in water, alcohol, oil, &c. Here
the relative position of the molecules is no longer fixed, the molecules glide
past each other with the greatest ease, and the body assumes with readiness
the form of any vessel in w hich it may be placed.

Thirdly, the gaseous state, as in air and in hydrogen. In gases the
mobility of the molecules is still greater than in liquids ; but the distinctive
character of a gas is its incessant struggle to occupy a greater space, in con-
sequence of which a gas has neither an independent form nor an independent
volume, for this depends upon the pressure to which it is subject.

The general \(tx\\\ fluid \-i applied to both liquids and gases.

Most simple bodies, and many compound ones, may be made to pass
successively through all the three states. Water presents the most familiar
example of this. Sulphur, iodine, mercury, phosphorus, and zinc are other
instances.

5. Physical phenomena, la-ws, and theories. — E\ ery change which
can happen to a body, actual alteration of its chemical constitution being ex-
cepted, may be regarded as ?^ physical phenomenon. The fall of a stone, the
vibration of a string, and the sound which accompanies it, the attraction of

-6] Physical Agents. 3

light particles by a rod of sealing-wax which has been rubbed by flannel,
the rippling of the surface of a lake, and the freezing of water, are examples
of such phenomena.

K physical law is the constant relation which exists between any pheno-
menon and its cause. As an example, we have the phenomenon of the
diminution of the volume of a gas by the application of pressure ; the cor-
responding law has been discovered, and is expressed by saying that tlie
volume of a gas is inversely proportional to the pressure.

In order to explain the cause of whole classes of phenomena, suppositions,
■or hypotheses., are made use of. The utility and probability of an hypothesis
or theory are the greater the simpler it is, and the more varied and numerous
are the phenomena which are explained by it ; that is to say, are brought
into regular causal connection among themselves and with other natural
phenomena. Thus the adoption of the undulatory theory of Hght is justified
by the simple and unconstrained explanation it gives of all luminous pheno-
mena, and by the connection it reveals with the phenomena of heat.

6. Physical agrents. — In our attempts to ascend from a phenomenon to
its cause, we assume the existence oi physical agents, or ?tatural forces SLCimg
upon matter ; as examples of such we have gravitation, heat, light, magnet-
ism, and electricity.

Since these physical agents are disclosed to us only by their effects, their
intimate nature is completely unknown. In the present state of science, we
cannot say w^hether they are properties inherent in matter, or whether they
result from movements impressed on the mass of subtile and imponderable
forms of matter diffused through the universe. The latter hypothesis is, how-
ever, generally admitted. This being so, it may be further asked, are there
several distinct forms of imponderable matter, or are they in reality but one
and the same ? As the physical sciences extend their limits, the opinion
tends to prevail that there is a subtile, imponderable, and eminently elastic
fluid called the ether distributed through the entire universe ; it pervades
the mass of all bodies, the densest and most opaque, as well as the lightest
or the most transparent. It is also considered that the ultimate particles of
which matter is made up are capable of definite motions varying in character
and velocity, and which can be communicated to the ether. A motion of a
particular kind communicated to the ether can give rise to the phenomenon
of heat ; a motion of the same kind, but of greater velocity, produces light ;
and it may be that a motion different in form or in character is the cause of
electricity. Not merely do the atoms of bodies communicate motion to the
atoms of the ether, but this latter can impart it to the former. Thus the
atoms of bodies are at once the sources and the recipients of the motion.
All physical phenomena, referred thus to a single cause, are but transforma-
tions of motion.

On Matter, Force, and Motion.

CHAPTER II.

GENERAL PROPERTIES OF BODIES.

7. Different kinds of properties. — By the term properties, as applied
to bodies, we understand the different ways in which bodies present them-
selves to our senses. We distinguish general from specific properties. The
former are shared by all bodies, and amongst them the most important are
impenetrability, extension, divisibility, porosity, compressibility, elasticity,^
mobility, and inertia.

Specific properties are such as are observed in certain bodies only, or in
certain states of these bodies ; such are solidity, fluidity, tenacity, ductility,
malleability, hardness, transparency, colour, &c.

With respect to the above general properties, impenetrability and exten-
sion might, perhaps, be more aptly termed essential attributes of matter,
since they suffice to define it ; while divisibility, porosity, compressibility,
and elasticity do not apply to atoms, but only to bodies or aggregates of
atoms (3).

8. Impenetrability. — Impenetrability is the property in virtue of which
two portions of matter cannot at the same time occupy the same portion of
space. Thus, when a stone is placed in a vessel of water the volume of the
water rises by an amount depending on the volume of the stone ; this method,
indeed, is used to determine the bulk of irregularly shaped bodies by means
of graduated measures.

Strictly speaking, this property applies only to the atoms of a body. In
many phenomena bodies appear to penetrate each other ; thus, the volume
of a compound body is always less than the sum of the volumes of its con-
stituents ; for instance, the volume of a mixture of water and sulphuric acid,
or of water and alcohol, is less than the sum of the volumes before mixture.
In all these cases, however, the penetration is merely apparent, and arises
from the fact that in every body there are interstices, or spaces unoccupied
by matter (13).

9. Extension. — Extension or magnitude is the property in virtue of which
every body occupies a limited portion of space.

Many instruments have been invented for measuring linear extension or
lengths with great precision. Two of these, the vernier and micrometer
screw, on account of their great utility, deserve to be here mentioned.

10. Vernier. — The vernier forms a necessary part of all instruments
where lengths or angles have to be estimated with precision ; it derives its
name from its inventor, a French mathematician, who died in 1637, and
consists essentially of a short graduated scale, ab (fig. i), which is made to

-11] Micrometer Screw. 5

slide along a fixed scale, AB, so that the graduations of both may be com-
pared with each other. The fixed scale AB, being divided into equal parts,
the whole length of the vernier, ab, may be taken equal to nine of those parts,
and is itself divided into ten equal parts. Each of the parts of the vernier,
ab, will then be less than a part of the scale by one tenth of the latter.

This being granted, in order to measure the length of any object, ;//;/, let
us suppose that the latter, when placed as in the figure, has a length greater
than four but less than five parts of the fixed scale. In order to determine
by what fraction of a part /nn exceeds four, one of the ends, a, of the vernier,
ab, is placed in contact with one extremity of the object, 7nn, and the
division on the vernier is sought which coincides with a division on the
scale AB. In the figure this coincidence occurs at the eighth division of
the vernier, counting from the end, ti, and indicates that the fraction to be
measured is equal to y^ of a part of the scale, AB. In fact, each of the
parts of the vernier being less than a part of the scale by ~ of the latter, it
is clear that on proceeding towards the left from the point of coincidence
the divisions of the vernier are respectively one, two, three, &c. tenths

Fig. I.

behind the divisions of the scale ; so that the end, n, of the object (that is to
say, the eighth division of the vernier) is ~ behind the division 4 on the
scale ; in other words, the length of mft is equal to 4^*^ of the parts into
which the scale AB is divided. Consequently if the scale AB were divided
into inches, the length of nm would be 4/^ = 4| inches. The divisions on
the scale remaining the same, it would be necessary to increase the length
of the vernier in order to measure the length inn more accurately. For
instance, if the length of the vernier were equal to nineteen of the parts on
the scale, and this length were divided into twenty equal parts, the length nui
could be determined to the twentieth of a part on the scale, and so on. In
instruments like the theodolite, intended for measuring angles, the scale and
vernier have a circular form, and the latter usually carries a magnifier in
order to determine with greater precision the coincident divisions of vernier
and scale.

II. micrometer screw. — Another useful little instrument for measuring-
small lengths with precision is the microineter screw. It is used under various
forms, but the principle is the same in all, and may be conveniently illustrated
by reference to the spher'ometcr. This consists of an accurately turned screw
with a blunt point which works in a companion supported on three steel
points (fig. 2). To one of these is fixed a vertical graduated scale, each
division of which is equal to the distance between two threads of the screw.

On Matter, Force, and Motion.

[11-

Fig. 2.

This distance may be accurately determined by measuring a given length of
the screw by compasses, and counting the number of the threads in this
length. A milled head attached to the screw is graduated at the periphery
into any given number of parts, say 500^
Suppose now the distance between the
threads is r millimetre, when the head has
made a complete turn it will have risen or
sunk through one millimetre, and so on in
proportion for any multiple or fraction of a
turn.

In order to determine the thickness of a
piece of glass for instance, the apparatus is
placed on a perfectly plane polished surface^
and the point of the screw is brought in.
contact with the glass. The division on the
vertical scale immediately abo\e the limb,,
and that on the limb are read off. After
removing the glass plate the point is brought in contact with the plane
surface, and corresponding readings are again made, from which the thick-
ness can be at once deduced.

The same process is obviously applicable to determining the diameter of
a wire.

To ascertain whether a surface is spherical, three points are applied to
the surface, and the screw is also made to touch as described above. It is
then moved along the surface, and if all four points are everywhere in con-
tact the surface is truly spherical. This application is of great value in
ascertaining the exact curvature of lenses.

The diameter of a sphere may also be measured by its means ; for it
can be shown by a simple geometrical construction that the distance of the
movable point from the plane of the fixed points, multiplied by the diameter
of the sphere, is equal to the square of the distance of the movable point
from one of the fixed points. If// is the distance of the movable point from
the plane of the fixed points, c the distance of the movable point from the
fixed point when in the same plane, and which is known once for all, and d
the diameter of the circle, then it can be shown by a simple geometrical con-
struction that (^ = , + /^
h

12. Divisibility. — Divisibility is the property in virtue of which a body
may be separated into distinct parts.

Numerous examples may be cited of the extreme divisibility of matter (3).
The tenth part of a grain of musk will continue for years to fill a room
with its odoriferous particles, and at the end of that time will scarcely be
diminished in weight. Blood is composed of red, flattened globules, floating
in a colourless liquid called seriun. In man the diameter of one of these
globules is less than the 3,500th part of an inch, and the drop of blood which
might be suspended from the point o a needle would contain about a million
of globules.

Again, the microscope has disclosed to us the existence of insects smaller
even than these particles of blood ; the struggle for existence reaches even

-13]

Porosity.

to these little creatures, for they devour still smaller ones. If blood runs in
the veins of these devoured ones, how infinitesimal must be the magnitude
of its component globules !

Although experiment fails to determine whether there be a limit to the
divisibility of matter, many facts in chemistry, such as the invariability in
the relative weights of the elements which combine with each other, would
lead us to believe that such a limit does exist. It is on this account that
bodies are conceived to be composed of extremely minute and indivisible
parts called atoms (3).

13. Porosity. — Porosity is the quality in virtue of which interstices or
pores exist between the molecules of a body.

Two kinds of pores may be distinguished : physical pores., where the
interstices are so small that the surrounding molecules remain within the
sphere of each other's attracting or repelling
forces ; and sensible pores, or actual cavities
across which these molecular forces cannot act.
The contractions and expansions resulting from
variations of temperature are due to the exist-
ence of physical pores, whilst in the organic
world the sensible pores are the seat of the
phenomena of exhalation and absorption.

In wood, sponge, and a great number of
stones^ — for instance, pumice stone — the sensible
pores are apparent ; physical pores never are.
Yet, since the volume of every body may be
diminished, we conclude that all possess physical
pores.

The existence of sensible pores in leather or
wood may be shown by the following experi-
ment : — A long glass tube, A (fig. 3), is provided
with a brass cup at the top, and a brass foot
made to screw on to the plate of an air-pump.
The bottom of the cup consists of a thick piece
of leather. After pouring mercury into the cup
so as entirely to cover the leather, the air-pump
is put in action, and a partial vacuum produced
within the tube. By so doing a shower of mer-
cury is at once produced within the tube, for the
atmospheric pressure on the mercury forces that
liquid through the pores of the leather. In the
same manner water or mercury may be forced
through the pores of wood by replacing the

leather in the above experiment by a disc of wood cut perpendicularly to the
fibres.

When a piece of chalk is thrown into water, air-bubbles at once rise to
the surface, in consequence of the air in the pores of the chalk being expelled
by the water. The chalk will be found to be heavier after immersion than it
was before, and, knowing its volume, the volume of its pores may be easily
determined from the increase of its weight.

8 On Matter, Force, and Motion. [13-

The porosity of agate, flint, marble is evident from the fact that they are
penetrated by liquids such as oil, on which, indeed, the artificial coloration
of these minerals depends.

The porosity of gold was demonstrated by the celebrated Florentine
experiment made in 1661. Some academicians at Florence, wishing to try
whether water was compressible, filled a thin globe of gold with that liquid,
and, after closing the orifice hermetically, they exposed the globe to pressure
with a view of altering its form, knowing that any alteration in form must be
accompanied by a diminution in volume. The consequence was, that the
water forced its way through the pores of the gold, and stood on the outside
of the globe like dew. More than twenty years previously the same fact was
demonstrated by Francis Bacon by means of a leaden sphere ; the experi-
ment has since been repeated with globes of other metals, and similar results
obtained. At a red heat both platinum and iron allow gases to diffuse
through them.

.\ glass tube about a metre long, closed at one end, is half filled with
water, and then pure alcohol poured upon it to a mark near the top ; on
then closing the open end with the thumb and inverting the tube several
times the mixture shrinks so that its level is now nearly an inch below the
mark ; at the same time very minute bubbles are seen to rise, owing to the
water having penetrated into the pores of the alcohol and expelled the air
present.

14. Apparent and real volumes. — In consequence of the porosity of
bodies, it becomes necessary to distinguish between their real and apparent
\olumes. The real volume of a body is the portion of space actually occu-
pied by the matter of which the body is composed ; its apparent volume is
the sum of its real volume and the total volume of its pores. The real
volume of a body is invariable, but its apparent volume can be altered in
\arious wa)-s.

1 5. Applications. — The property of porosity is utilised in filters of paper,
felt, stone, charcoal, &c. The pores of these substances are sufficiently large
to allow liquids to pass, but small enough to arrest the passage of any sub-
stances which these liquids may hold in suspension. Again, large blocks of
stone are often detached in quarries by introducing wedges of dry wood into
grooves cut in the rock. These wedges being moistened, water penetrates
their pores, and causes them to swell with considerable force. Dry cords,
when moistened, increase in diameter and diminish in length — a property of
which advantage has been taken in order to raise great weights.

16. Compressibility.— Cc';;//;-^.y^zW///j is the property in virtue of which
the volume of a body may be diminished by pressure. This property is at
once a consequence and a proof of porosity.

Bodies differ greatly with respect to compressibility. The most com-
pressible bodies are gases ; by sufficient pressure they may be made to
occupy ten, twenty, or even some hundred times less space than they do
under ordinary circumstances. In most cases, howe\'er, there is a limit
beyond which, when the pressure is increased, they become liquids.

The compressibility of sohds is much less than that of gases, and is found
in all degrees. Cloths, paper, cork, woods, are amongst the most compres-
sible. Metals are so also to a great extent, as is proved by the process of

-18] Mobility, Motion, Rest. 9

coining, in which the metal receives the impression from the die. There is,
in most cases, a hmit beyond which, when the pressure is increased, bodies
are fractured or reduced to powder.

The compressibiUty of hquids is so small as to have remained for a long
time undetected : it may, however, be proved by experiment, as will be seen
in the chapter on Hydrostatics.

17. Elasticity. — Elasticity is the property owing to which bodies resume
their original form or volume, when the force which altered that form or
volume ceases to act. Elasticity may be developed in bodies by pressure,
by traction or pulliiig, flexion or bending, and by torsion or twisting. In
treating of the general properties of bodies, the elasticity developed by
pressure alone requires consideration ; the other kinds of elasticity, being
peculiar to solid bodies, will be considered amongst their specific properties
(arts. 89, 90, 91).

Gases and liquids are perfectly elastic ; in other words, after undergoing
a change in volume they regain exactly their original volume when the
pressure becomes what it originally was. Solid bodies present different de-
grees of elasticity, though none present the property in the same perfec-
tion as liquids and gases, and in all it varies according to the time during
which the body has been exposed to pressure. Caoutchouc, ivory, glass,
and marble possess considerable elasticity ; lead, clay, and fats scarcely
any.

There is a limit to the elasticity of solids, beyond which they either break
or are incapable of regaining their original form and volume. This is called
the limit of elasticity ; within this limit all substances are perfectly elastic.
In sprains, for instance, the elasticity of the tendons has been exceeded.
In gases and liquids, on the contrary, no such limit can be reached ; they
always regain their original volume when the original pressure is restored (152).

If a ball of ivory, glass, or marble be allowed to fall upon a slab of polished
marble, which has been previously slightly smeared with oil, it will rebound
and rise to a height nearly equal to that from which it fell. On afterwards
examining the ball a circular blot of oil will be found upon it, more or less
extensive according to the height of the fall. From this we conclude that at
the moment of the shock the ball was flattened, and that its rebound was
caused by the effort to regain its original form.

18. Mobility, motion, rest.^ — Mobility is the property in virtue of which
the position of a body in space may be changed.

Motion and rest may be either relative or absolute. By the relatii'e
motion or rest of a body we mean its change or permanence of position with
respect to surrounding bodies ; by its absolute motion or r-est we mean the
change of permanence of its position with respect to ideal fixed points in
space.

Thus a passenger in a railway carriage may be in a state of relative rest
with respect to the train in which he travels, but he is in a state of relative
motion with respect to the objects, such as trees, houses, &c., past which the
train rushes. These houses, again, enjoy merely a state of relative rest, for
the earth itself which bears them is in a state of incessant relative motion
with respect to the celestial bodies of our solar system, inasmuch as it moves
at the rate of more than eighteen miles in a second. In short, absolute

lo On Matter, Force, and Motion. [18—

motion and rest are unknown to us ; in nature, relative motion and rest are
alone presented to our observation.

19. Inertia. — Inertia is a purely negative though universal property of
matter (26) ; it is the property that matter cannot of itself change its own
state of motion or of rest. If a body is at rest it remains so until some
force acts upon it ; if it is in motion this motion can only be changed by the
application of some force.

This property of inertia is what is expressed by Newton's first law of
motion.

A body, when unsupported in mid-aii', does not fall to the earth in virtue
of any inherent property, but because it is acted upon by the force of gravity.
A billiard ball gently pushed does not move more and more slowly, and
finally stop, because it has any preference for a state of rest, but because its
motion is impeded by the friction on the cloth on which it rolls, and by the
resistance of the air. If all impeding causes were withdrawn, a body once
in motion would continue to move for ever in a straight line with unchanging
velocity.

20. Illustrations. — Numerous phenomena may be explained by the
inertia of matter. For instance, before leaping a ditch we run towards it, in
order that the motion of our bodies at the moment of leaping may add itself
to the muscular efi'ort then made.

On descending carelessly from a carriage in motion, the upper part of the
body retains its motion, whilst the feet are prevented from doing so by fric-
tion against the ground ; the consequence is we fall towards the moving"
carriage. A rider falls over the head of a horse if it suddenly stops. In
striking the handle of a hammer against the ground the handle suddenly
stops, but the head, striving to continue its motion, fixes itself more firmly on
the handle.

By the property of inertia may also be explained the following experi-
ments : — Let a card be placed upon a tumbler, and a shilling on the card ;
if the edge of the card be smartly flicked with the finger the card is driven
away and the coin falls into the tumbler. A gentle push with the finger will
move a door on its hinges ; but if a pistol bullet be fired against the door it
perforates the door without moving it. So, too, a pistol shot fired through a
window-pane produces a sharp round hole, while a less violent shock will
smash the pane. A clay tobacco pipe, which is suspended by two vertical
hairs, may be cut in two by a powerful stroke with a shajp sword without
breaking the hairs.

A string which gently applied will raise a weight snaps at once when a
sudden pull is exerted. Substances which explode with great rapidity, such
as fulminating mercury, chloride of nitrogen, cannot be used with fire-arms,
because there is not sufficient time to transfer the motion to the projectiles^
and hence the weapons are burst.

The terrible accidents on our railways are chiefly due to inertia. When
the motion of the engine is suddenly arrested the carriages strive to continue
the motion they have acquired, and in doing so are shattered against each
other. Hammers, pestles, stampers are applications of inertia. So are also
the enormous iron fly-wheels, by which the motion of steam-engines is
regulated.

-22]

Measure of Spaee.

CHAPTER III.

ON FORCE, EQUILIBRIUM, AND MOTION.

21. Measure of time. — To obtain a proper measure of force it is
necessary, as a preliminary, to define certain conceptions which are pre-
supposed in that measure ; and, in the first place, it is necessary to define
the unit of time. Whenever a second is spoken of without qualification
it is understood to be a second of vieatt solar time. The exact length of
this unit is fixed by the following considerations. The instant when the sun's
centre is on an observer's meridian — in other words, the instant of the transit
of the sun's centre — can be determined with exactitude, and thus the interval
which elapses between two successive transits also admits of exact determina-
tion, and is called an apparent day. The length of this interval differs
slightly from day to day, and therefore does not serve as a convenient
measure of time. Its average length is not open to this objection, and
therefore serves as the required measure, and is called a ineaii solar day.
The short hand of a common clock would go exactly twice round the face
in a mean solar day if it went perfectly. The mean solar day consists of 24
equal parts called hours, these of 60 ec^ual parts called minutes, and these
again of 60 equal parts called seconds. Consec^uently, the second is the
86,400th part of a mean solar day, and is the generally received unit of time.

22. Measure of space. — Space may be either length or distance, which
is space of one dimension ; area, which is space of two dimensions ; or
volume, which is space of three dimensions. In England the standard of
length is the British Imperial Yard, which is the distance between two fixed
points on a certain metal rod, kept in the Tower of London, when the tempera-
ture of the whole rod is 60° F. = i5°-5 C. It is, however,

usual to employ as a unit, a/cc/, which is the third part of a
yard. In France the standard of length is the metre ; this
is approximately equal to the ten-millionth part of a qua-
drant of the earth's meridian, that is of the arc from the
Equator to the North Pole ; it is practically fixed by the
distance between two marks on a certain standard rod. The
standard metre, adopted by an International Committee pig. 4.

for weights and measures, is constructed of an alloy of 90
per cent, platinum and 10 per cent, iridium, which is characterised by great
hardness, and unalterability. Its length is somewhat over a metre, and its
cross section is represented in its natural size in figure 4. This shape has
the advantage of giving the greatest rigidity and of soon acquiring the
temperature of the surrounding medium. The exact length of the metre is

12 On Matter, Force, and Motion. [22-

marked by two fine lines on the surface. The relation between these
standards is as follows :

I yard =0-914401 metre.

I metre = 1-093612 yard.

The unit of length having been fixed, the units of area and volume are
connected with it thus : the uftit of area is the area of a square, one side of
which is the unit of length. The tinit of volume is the volume of a cube, one
edge of which is the unit of length. These units in the case of English mea-
sures are the square yard (or foot) and the cubic yard (or foot) respectively ;
in the case of French measures, the square metre and cubic metre respec-
tively. The length of the seconds pendulum, in lat. 45°, which is about that
of Milan, is o-9935m., and thus only differs from a metre by 6-5 millimetres.

23. IVXeasure of mass. — Two bodies are said to have equal masses when,
if placed in a perfect balance itt vacuo, they counterpoise each other. Suppose
we take lumps of any substance, lead, butter, wood, stone, &c., and suppose
that any one of them when placed on the one pan of a balance will exactly
counterpoise any other of them when placed on the opposite pan — the balance
being perfect and the weighing performed in vacuo ; this being the case,
these lumps are said to have equal masses.

The British unit of mass is the standard pound (avoirdupois), which is a
certain piece of platinum kept in the Exchequer Office in London. This unit
having loeen fixed, the mass of a given substance is expressed as a multiple
or submultiple of the unit.

It need scarcely be mentioned that many distances are ascertained and
expressed in yards which it would be physically impossible to measure
directly by a yard measure. In like manner the masses of bodies are fre-
quently ascertained and expressed numerically which could not be placed in
a balance and subjected to direct weighing.

24. Density and relative density. — If we consider any body or portion
of matter, and if we conceive it to be divided into any number of parts having
equal volumes, then, if the masses of these parts are equal, in whatever
way the division be conceived as taking place, that body is one of uniform
density. The density of such a body is the mass of the tmit of volume. Con-
sequently, if M denote the mass, V the volume, and D the density of the
body, we have

M = VD.

If now we have an equal volume V of any second substance whose mass is
M' and density D', we shall have

M' = VD'.

Consequently, D:D'::M:]\r; that is, the densities of substances are
in the same ratio as the masses of equal volumes of those substances.
If now we take the density of distilled water at 4° C. to be unity, the relative
density of any other substance is the ratio which the mass of any given
volume of that substance at that temperature bears to the mass of an equal
volume of water. Thus it is found that the mass of any volume of platinum
is 22-069 times that of an equal volume of \\ater, consequently the relative
density of platinum is 22-069.

62-42

l-ooo

112-36

I -Boo

449-86

7-207

548-55

8-788

708-59

11-352

269-43

20-332

58-05

0-930

-25] Velocity and its Measure. 1 3

The relative density of a substance is generally called its spccijic gravity.
Methods of determining it are given in Book 111.

In the table below the densities D of various substances, expressed in
pounds to the cubic foot, are given, and column G gives the relative densities
of the same substances.

It is evident that column G is obtained by dividing the values in colunui
D by 62-42.

Water

Anthracite

Cast iron

Cast copper

„ lead .....

„ platinum ....
Melting ice

In the metric system, since the mass of the cubic centimetre of water
is one gramme, it is evident that the density D, in grammes to the cubic
centimetre, has the same numerical value as the relative density referred to
water.

25. Velocity and its measure. — When a material point moves, it de-
scribes a continuous line which may be either straight or curved, and is
called its path and sometimes its trajectory. Motion which takes place
along a straight line is called rectilinear motion ; that which takes place
along a curved line is called curniilijiear motion. The rate of the motion of
a point is called its velocity. Velocity may be either uniform or variable ; it
is uniform when the point describes equal spaces or portions of its path in
all equal times ; it is variable when the point describes unequal portions of
its path in any equal times.

Uniform velocity is measured by the number of units of space described
in a given unit of time. The units commonly employed in this country
are feet and seconds. If, for example, a velocity 5 is spoken of without
qualification, this means a velocity of 5 feet per second. Consequently,
if a body moves for / seconds with a uniform velocity 7/, it will describe
vt feet.

The following are a few examples of different degrees of velocity expressed
in this manner. A snail 0-005 f^^t in a second ; the Rhine between Worms
and Mainz 3-3 ; military quick step 4-6 ; moderate wind 10 ; fast sailing-
vessel 18-0 ; Channel steamer 22-0 ; i-ailway train 36 to 75 feet ; racehorse and
storm 50 feet ; wave in a tempest 72 feet; eagle no feet; carrier pigeon
120 feet ; a hurricane 160 feet ; sound at 0° 1,090 ; a shot from an Armstrong
gun 1,180 ; a Martini-Henry rifle bullet 1,330 ; a point on the Equator in its
rotation about the earth's axis 1,520 ; velocity of the vibratory motion of par-
ticles of air 1,590; maximum tide rate 3,005 ; velocity of the centre of the
earth 101,000 feet ; light, and also electricity in a medium destitute of resist-
ance 192,000 miles.

Variable velocity is measured at any instant by the number of units of
space a body would describe if it continued to move uniformly from that
instant for a unit of time. Thus, suppose a body to run down an inclined
plane, it is a matter of ordinary observation that it mo\'es more and more

14 On Matter, Force, and Motion. [25-

quickly during its descent ; suppose that at any point it has a velocity 15,
this means that at that point it is moving at the rate of 15 ft. per second, or,
in other words, if from that point all increase of velocity ceased, it would de-
scribe 1 5 ft. in the next second.

26. rorce. — Forces manifest themselves to us by the changes which they
produce, or tend to produce, in the motion of matter. The action of forces
in causing motion is best expressed in Newton's laws : The first law is,
Every body continues in its state of rest or of uniform motion in a straight
line, except as it is compelled by forces to change that state.

A body may be at rest, or may be moving uniformly in a straight line,
while acted upon by a system of forces. In this case the forces are said to
balance each other. If a constant unbalanced force act upon a body, it will no
longer move uniformly. The velocity will increase continually, at a uniform
rate. A familiar case of this kind is found in the attraction of the earth for
other bodies. According to Newton's law of gravitation, the attraction
between two masses, one of which contains m and the other m' units of

mass, is , where r is the distance between the centres of the masses

r-
(62). If one of the masses be the unit mass, or one pound, the other
being the earth, the above expression represents the pull which the earth
exerts upon a pound of matter : this pull is the weight of a pound.

It is important to distinguish very carefully between a pound — the unit
of mass — and the weight of a pound, which is a force. Weight is not a
necessary property of matter. If physical conditions were such that we
could visit the centre of the earth, we should find matter without weight,
although its other properties would remain unchanged. A bullet fired from
a gun, although weightless, would ha\'e the same effect as at the surface of
the earth, this effect being dependent, as will be shown, upon the amount of
matter (mass) in the bullet and the velocity imparted, and having no relation
whatever to the weight of the bullet. A pound of sugar at the centre of the
earth would have precisely the same sweetening properties as at the surface.
The commercial value of provisions, drugs, &c., is therefore strictly propor-
tional to the number of units of mass purchased, and has no necessary rela-
tion to the weights of those masses.

It is also to be observed that, if masses are counterpoised on a lever
balance at any one locality, they would remain balanced at any other point,
since the weights of the masses would change in the same ratio. Hence
the lever balance with standard ' weights ' really measures the mass of a
body, and not its weight, and the standard ' weights ' should really be called
masses. A spring balance determines weight and not mass, since its indi-
cations change as the weight of the mass changes.

At the centre of the earth, masses could not be determined by means of
a balance, since they weigh nothing, and any mass would counterpoise any
other mass.

27. XVIeasure of Torce. — In devising a unit in which to measure force, it is
most convenient to make use of the attractive force of the earth. Suppose that
two equal masses, P, are balanced on a pulley with fixed axle, that the string
and pulley are without mass, and that there is no friction or air-resistance.
The masses P are then perfectly inert. The tension on the string is the

-27] Measure of Force. 1 5

pull of the earth on oue of the masses P, or, in other w ords, the weight of P.
If the pulley is started by a force which then ceases to act, the masses will
thereafter move uniformly according to the first law of motion, the tension
on the string being, as before, the weight of P. This will all be
true, whatever may be the amount of matter in the masses P. /"""^
If, now, the masses P being at rest, an additional mass in I
be placed on one side, the system will begin to move. The \.,_^
4:ension on the string is now greater than the weight of P, and
less than the weight of P + m. The force which causes the
motion is the pull of the earth on m, or the weight of the added f^p

mass. The motion is now uniformly accelerated. At the in-
stant of starting, the velocity is zero. At the end of the first Pip
second, the velocity will be — say a ; at the end of the second p-jg .

second, la ; and at the end of / seconds, the velocity will be at.
The increase in the velocity per second is «, which is called the accelera-
tion.

If the mass m be entirely disconnected from the masses P and allowed
to fall freely, it also falls with a uniformly accelerated motion ; but experi-
ment shows that the acceleration is greater than in the former case. This
acceleration of a freely falling body is usually denoted by g. The force
-which causes the motion is, however, the same as before, being the weight
of VI. The difference in the two cases is that, in the latter case, the pull of
the earth on in is employed in setting in motion the mass in only ; while, in
the former case, the two inert masses P are attached to ;«, and are con-
strained to move with it, the mass to be moved being thus increased without
a corresponding increase of the force employed in moving.

It is evident that if the masses P should diminish to zero, or the mass m
should increase until it became very large, or infinite, the weight of m would
impart a greater and greater acceleration, until finally the acceleration
would become g. On the other hand, if the masses P should become very
large, or infinite, or the mass m very small, or zero, the acceleration would
become zero. It is shown by experiment that if the mass in is made n
times as great (so that the moving force is // times as great), and the masses
P are equally diminished — so that zV -r m is unchanged — the acceleration
becomes n times as great, so that, the mass to be moved being unchanged,
the acceleration is directly proportional to the force applied. If, however,
the mass ;;/ be made 11 times as great, and it is desired to have the accelera-
tion remain unchanged, it is found that the masses P must be equally
increased in such a way that 2P + ;« has also become n times as great.
This shows that, the acceleration remaining constant, the force applied must
change in the same ratio as the mass.

From these experiments it follows that if any force F is applied in giving
uniformly accelerated motion to a mass M, the acceleration being ^, then

F = YM.a.

Here M is measured in pounds, and the acceleration a measures the
change in velocity of M in feet per second. K is a constant, the numerical
value of which will depend upon the unit which we now adopt in which to
measure F. If, as is customary, we adopt as the unit force that force which

1 6 Ou Matter, Force, and Motion. [27-

will make a = i when M = i, then we at the same time necessarily niake the
remaining quantity K in the last equation equal to i ; and, measured in these
units,

F = Via.

The unit force is then that force which can impart unit acceleration to
unit mass.

If V represent the initial velocity of a body, and %' its final velocity, the
change in velocity having taken place in / seconds, then the change per
second is

7/-V

a = .

This value of a in the previous equation gives
P_M7'-MV

28. Momentum. — It thus appears that the number of units of force in
any force which, acting for t seconds on a mass M, is capable of changing its
velocity from V to v, is measured by the change per second in the product
M7/. This quantity M?/, being thus an important one, has received a special
name — inoinenhiin. We may now say that the number of units in a force is
measured by the change in momentum which it can produce per second,
which is the substance of Newton's second law of motion.

29. Acceleration of Gravity. — At London, the force with which the
earth attracts a pound of matter is capable of imparting to the pound an
acceleration of 32-1912. At other places, the acceleration is different, and
may be denoted by^. Hence, at London, the weight of a pound, expressed
in the units which we have chosen for measuring forces, will be 32-1912. At
any other point on the earth, or in the interior of the earth, or at any point
outside, where the acceleration of a falling body is g^ the number of units of
force in the weight of a pound is g. The number w of units of force in the
w eight of /;/ pounds is given by the equation

ia = mg.

If at some point where the acceleration is 32 it is found that the weight
of 10 lb., or 320 units of force, is sufficient to serve as the driving-weight to
a certain clock, then at some other point, where the acceleration is 16, it
would be necessary to use the weight of 20 lb. in order to secure the same
effect.

The weight of lb., or 0-49 oz., at London, is a unit of force. At

32-1912

any other point, where the acceleration is g, the weight of - lb. is the unit of

force. Where great accuracy is not required, it is customary to take the
weight of the pound as the unit of force, and then the intensity of the force
is given in pounds weight, a unit which varies slightly for different places on
the earth, as g varies. In like manner, for ordinary purposes, a land
surveyor does not find it necessary to make corrections for the varying
length of his chain due to changes in temperature, although such correc-

-30] Representation of Forces. 17

tions are highly important in the more refined operations of a geodetic
survey.

Pendulum observations (79) show that at any given place the acceleration
of a falling body is constant, but it is found to have different values at dif-
ferent places ; adopting the units of feet and seconds, it is found that very
approximately

^=^'(1-0-00256 cos 2<^),

at a station whose latitude is <^, where g' denotes the number 32-1724, or
the value of^at lat. 45°.

Experience teaches that in all cases where a force is exerted there must
be two bodies, between which the force acts. Newton's third law asserts
that the mutual action of the two bodies is always equal and oppositely
directed.

The attraction" of the earth for in pounds of matter is w^, where ^ is the
acceleration of the body. The attraction of the m pounds for the earth is
M a, where M is the mass of the earth in pounds, and a is the acceleration
with which it moves towards w. According to the third law of motion

M.a = ing.

Um is a small body, like a few thousand pounds, then, since the mass of the
earth is very large, the acceleration of the earth will be inappreciable. If ;;/
and M were equal, a and g would be equal. Remembering that the accele-
ration is the change per second in the velocity, if the two bodies move
towards each other for / seconds, the initial velocities being Vj and V.,, and
the final velocities v^ and v.,, the above expression becomes

M^z/i - M Vj _ mvo — mV^
} " / ^'

As / divides out of this equation, it will follow that the two bodies which
mutually attract each other will suffer equal changes of momenta in the
same time. If the two bodies start from rest at the same instant, so that Vj
and v., are zero, then

Mt'i = ;/i7'.,,

or they will have equal momenta at the same instant. The momenta of a
freely-suspended rifle and of a bullet fired from it will be equal so long as the
ball is in the barrel. If the rifle is supported, the supporting body must be
included with the rifle in the value M.

30. Representation of forces. — Draw any straight line AB (fig. 6), and
fix on any point O in it. We may suppose a force to act on the point O,
along the line AB, either towards A or B : then O is

called the point of application of the force, AB its line g — -; jlj — ^

of action ; if it acts towards A, its direction is OA, if Fig. 6.

towards B, its direction is OB. It is rarely necessary

to make the distinction between the line of action and direction of a force ;
it being very convenient to make the convention that the statement — a force
acts on a point O along the line OA — means that it acts from O to A. Let
us suppose the force which acts on O along OA to contain P units of force ;

1 8 071 Matter, Force, and Motion. [30-

from O towards A measure ON, containing P units of length, the Hne ON is
said to represejit the force. The analogy between the line and the force is
very complete ; the line ON is drawn from O in a given direction OA, and
contains a given number of units P, just as the force acts on O in the direc-
tion OA, and contains a given number of units P. It is scarcely necessary
to add, that if an equal force were to act on O in the opposite direction, it
would be said to act in the direction OB, and would be represented by OM,
equal in magnitude to ON.

When we are considering several forces acting along the same line we
may indicate their directions by the positive and negative signs. Thus the
forces mentioned above would be denoted by the symbols + P and — P
respectively.

31. Forces acting- along- the same line. — If forces act on the point O
in the direction OA equal to P and Q units respectively, they are equivalent
to a single force R containing as many units as P and Q together — that is,

R = P + Q.
If the sign + in the above equation denote algebraical addition, the equation
will continue true whether one or both the forces act along OA or OB. It
is plain that the same rule can be extended to any number of forces, and if
several forces have the same line of action, they are equivalent to one force
containing the same number of units as their algebraical sum. Thus if
forces of 3 and 4 units act on O in the direction OA, and a force of 8 in the
direction OB, they are equivalent to a single force containing R units given
by the equation

R=3+4-8= -i;

that is, R is a force containing one unit acting along OB. This force R is
called their resultant. If the forces are in equilibrium R is equal to zero.
In this case the forces have equal tendencies to move the point O in opposite
directions.

32. Resultant and components. — In the last article we saw that a single
force R could be found equivalent to several others ; this is by no means
peculiar to the case in which all the forces have the same line of action ; in

fact, when a material point, A (fig. 7), remains in equili-
brium under the action of several forces, S, P, Q, it does
so because any one of the forces, as S, is capable of
neutralising the combined effects of all the others. If the
force S, therefore, had its direction reversed, so as to act
along AR, the prolongation of AS, it would produce the
same effect as the system of forces P, Q.

Now, a force whose effect is equivalent to the combined
effects of several other forces is called their resultant, and
with respect to this resultant, the other forces are termed
components.

When the forces P, Q act on a point they can only
have o?ie resultant ; but any single force can be resolved
into components in an indefinite number of ways.
If a point move from rest, under the action of any number of forces, it
will begin to move in the direction of their resultant.

-33] Paralklograui of Forces. 19

2,^. Parallelogram of forces. — When two forces act on a point their
resultant is found by the following theorem, known as the principle of the
parallelogram of forces : — If two forces act on a point., and if lines be drazun
from that poitit representing the forces in magnitude and direction, and a
parallelogram be constructed on these lines as sides, their resultatit will be
represented in magnitude and direction by that diagonal which passes throiigJi
the point. Thus let P and Q (fig. 8) be two forces acting on the point A
along AP and AQ respectively, and let AB and AC be taken containing the
same number of units of length that P and Q contain units of force ; let the
parallelogram ABDC be completed, and the diagonal AD drawn ; then the
theorem states that the resultant, R, of P and Q is represented by AD ; that
is to say, P and Q together are equal to a single force R acting along the
line AD, and containing as many units of force as AD contains units of
length.

Proofs of this theorem are given in treatisfes on Mechanics ; we will here
give an account of a direct experimental verification of its truth ; but before
doing so we must premise an account of a very simple experiment.

Let A (fig. 9) be a small pulley, and let it turn on a smooth, hard, and
thin axle, with little or no friction : let W be a weight tied to the end of a
fine thread which passes over the pulley ; let a spring CD be attached by
one end to the end C of the thread and by the end D to another piece of
thread, the other end of which is fastened to a fixed point B ; a scale CE
can be fastened by one end to the point C and pass inside the spring so that

the -elongation of the spring can be measured. Now it will be found on trial
that with a given weight W the elongation of the spring will be the same
whatever the angle contained between the parts of the string WA and BA.
Also it would be found that if the whole were suspended from a fixed point,
instead of passing over the pulley, the weight would in this case stretch the
string to the same extent as before. This experiment shows that when care
is taken to diminish to the utmost the friction of the axle of the pulley, and
the imperfect flexibility of the thread, the weight of W is transmitted with-
out sensible diminution to B, and exerts on that point a pull or force along
the line BA virtually equal to W.

This being premised, an experimental proof, or illustration of the paral-
lelogram of forces, may be made as follows : —

Suppose H and K (fig. 10) to be two pulleys with axles made as smooth
and fine as possible ; let P and Q be two w^eights suspended from fine and

.c 2

20 On Matter, Fojre, and Motion. [33-

flexible threads which, after passing over H and K, are fastened at A to a
third thread AL, from which hangs a weight R ; let the three weights come
to rest in the positions shown in the figure. Now the point A is acted on by-
three forces in equiHbrium— viz. P from A to H, Q from A to K, and R
from A to L, consequently any one of them must be equal and opposite to
the resultant of the other two. Now if we sup-
pose the apparatus to be arranged immediately
in front of a large slate, we can draw lines upon
it coinciding with AH, AK, and AL. If now we
measure off along AH the part AB containing
as many inches as P contains pounds, and along
AK the part AC containing as many inches as
Q contains pounds, and complete the parallelo-
gram ABCD, it will be found that the diagonal
AD is in the same line as AL, and contains as
many inches as R weighs pounds. Consequently, the resultant of P and Q
is represented by AD. Of course, any other units of length and force might
have been employed. Now it will be found that when P, Q, and R are
changed in any way whatever, consistent with equilibrium, the same con-
struction can be made — the point A will have different positions in the
different cases ; but when equilibrium is established, and the parallelogram
ABCD is constructed, it will be found that AD is vertical, and contains as
many units of length as R contains units of force, and consequently it repre-
sents a force equal and opposite to R — that is, it represents the resultant of
P and Q.

34. Resultant of any number of forces acting; in one plane on a
point — Let the forces P, Q, R, S (fig. ri) act on the point A, and let them

be i-epresented by the lines AB, AC, AD, AE, as
shown in the figure. First, complete the parallelo-
gram ABFC and join AF ; this line represents the
resultant of P and Q. Secondty, complete the
parallelogram AFGD and join AG ; this line re-
presents the resultant of P, Q, R. Thirdly, com-
plete the parallelogram AG HE and join AH ; this
line represents the resultant of P, Q, R, S. It is
manifest that the construction can be extended to
any number of forces. A little consideration will
show that the line AH might be determined by the
following construction :— Through B draw BF
parallel to, equal to, and towards the same part as AC ; through F draw
FG parallel to, equal to, and towards the same part as AD ; through G draw
GH parallel to, equal to, and towards the same part as AE ; join AH, then
AH represents the required resultant.

35. Triang^Ie of Forces. — If the resultant of the forces is zero, they have
no joint tendency to move the point, and consequently are in equilibrium.

The case of three forces acting on a point is of such importance that we
may give a brief statement of it. Let P, Q, R (fig. 12) be three forces in
equilibrium on the point O. From any point B draw BC parallel to and
towards the same part as OP, from C draw CA parallel to and towards the

-37] Composition and Resolution of Parallel Forces. 2 1

same part as OQ, and take CA such that P : Q : : BC : CA ; then, on joining
AB, the third force R must act along OR parallel to and towards the same
part as AB, and must be proportional in magnitude to
AB. This construction is frequently called the Triangle
of Forces. It is evident that while the sides of the
triangle are severally proportional to P, Q, R, the angles
A, B, C are supplementary to QOR, ROP, POQ re-
spectively ; consequently, every trigonometrical relation
existing between the sides and angles of ABC will
equally exist between the forces P, Q, R, and the sup-
plements of the angles between their directions. Thus
in the triangle ABC it is known that the sides are Fig. 12.

proportional to the sines of the opposite angles ; now,
since the sines of the angles are equal to the sines of their supplements, we
at once conclude that when three forces arc in equilibrium., each is propor-
tional to the sine of the angle between the directions of the other two.

36. Moments of Forces. — Let P (fig. 13) denote any force acting from B
to P, take A any point, let fall AN a perpendicular from A on BP. The
product of the number of units of force in P, and the number of units of
length in AN, is called the moment of P with respect to A. Since the force
P can be represented by a straight line, the moment of P can be represented
by an area. In fact, if BC is the line representing P, the moment is properly
represented by twice the area of the triangle ABC. The perpendicular AN
is sometimes called the arm of the pressure. Now if a watch were placed
with its face upwards on the paper, the force P would cause the arm AN to
turn round A in the contrary direction to the hands of the

watch. Under these circumstances, it is usual to con-
sider the moment of P with respect to the point A to be
>positive. If P acted from C to B, it would turn NA in
the same direction as the hands of the watch, and now its
moment is reckoned negative.

It is a simple geometrical consequence of the paral-
lelogram of forces {j)-^ that the moment of the resultant
equals the sum of the moments of the component forces, regard being had to
the signs of the moments.

If the point about which the moments are measured be taken in the direc-
tion of the resultant, its moment with respect to that point will be zero ; and
consequently the sum of the moments with respect to such point will be zero.

37. Composition and resolution of parallel forces. — The case of the
equilibrium of three parallel forces is merely a particular case of the equili-
brium of three forces acting on a point. In fact, let P and Q be two forces
whose directions pass through the points A and B, and intersect in O,
fig. 14 ; let them be balanced by a third force R whose direction produced
intersects the line AB in C. Now suppose the point O to move along AO,
gradually receding from A, the magnitude and direction of R will continually
change, and also the point C will continually change its position, but will
always lie between A and B. In the limit P and Q become parallel forces,
acting towards the same part balanced by a parallel force R acting towards
Ihe contrary part through a point X between A and B. The question is : —

N
Fig.

On Matter, Force, and Motioii.

[37-

Fig. 14.

FU'st, in this limiting case, what is the value of R ; secondly, what is the
position of X ? Now with regard to the first point it is plain that if a triangle
abc be drawn as in art. 35, the angles a and b in the
limit will vanish, and c will become 180°, consequently
ab ultimately equals ac + cb ;

or R = P + Q.

With regard to the second point it follows from last
article (36) that the moments of P and Q about C
are always equal, whence

AX : XB : : Q : P,

a proportion which determines the position of X.
Hence the following rules for the composition of any
two parallel forces, viz. —

I. When two parallel forces P and Q act towards the same part, at rigidly
connected points A and B, their resultant is a parallel force acting towards
the same part, equal to their sum, and its direction divides the line AB
into two parts AC and CB inversely proportional to the forces P and Q.

II. When two parallel forces P and Q act towards contraiy parts
at rigidly connected points A and B, of which P is the greater, their
resultant is a parallel force acting towards the same part as P, equal to the
excess of P over Q, and its direction divides BA produced in a point C such
that CA and CB are inversely proportional to P and Q.

In each of the above cases if we were to apply R at the point C, in
opposite directions to those shown in the figure, it would plainly (by the above
theorem) balance P and Q, and therefore when it acts as shown in figs. 15
and 16 it is the resultant of P and Q in those cases respectively. It will, of
course, follow that the force R acting at C can be resolved into P and Q
acting at A and B respecti\ely.

Fig.

Fig. 16.

If the second of the above theorems be examined, it will be found that
no force R exists equivalent to P and Q when these forces are equal. Two
such forces constitute a couple, which may be defined to be two equal parallel
forces acting towards contrary parts ; they possess the remarkable property
that they are incapable of being balanced by any single force whatsoever.

In the case of more than two parallel forces the resultant of any two caa

-40] TJu Lever. 23

be found, then of that and a third, and so on to any number ; it can be
shown that however great the number of forces they will either be in ecjuili-
brium or will reduce to a single resultant or to a couple.

38. Centre of parallel forces. — On referring to figs. 15 and 16, it will
be remarked that if we conceive the points A and B to be fixed in the
directions AP and BQ of the forces P and Q, and if we suppose those
directions to be turned round A and B, so as to continue parallel and to
make any given angle with their original directions, then the direction of
their resultant will continue to pass through C ; that point is therefore called
the centre of the parallel forces P and Q.

It appears from investigation, that whenever a system of parallel forces
reduces to a single resultant, those forces will have a centre ; that is to say^
if we conceive each of the forces to act at a fixed point, there will be a point
through which the direction of their resultant will pass when the directions
of the forces are turned through any equal angles round their points of
application in such a manner as to retain the parallelism of their dii'ections.

The most familiar example of a centre of parallel forces is the case in
which the forces are the weights of the parts of a body ; in this case the
forces all acting towards the same part will have a resultant, viz. their sum ;
and their centre is called the centre of gravity of the body.

39. Equality of action and reaction. — We will proceed to exemplify
some of the principles now laid down by investigating the conditions of
equilibrium of bodies in a few simple cases ; but before doing so we refer
again to the law stated in art. (29) and which holds good whenever a mutual
action is called into play between two bodies. Reaction is always equal and
contrary to action : that is to say, the mutual actio?ts of two bodies on each
other are always forces equal in amount and opposite in direction., and this is
equally true when the bodies are in motion as well as when they are at rest.
A very instructive example of this law has already been given (j,'^., in which
the action on the spring CD (fig. 8) is the weight W transmitted by the
spring to C, and balanced by the reaction of the ground transmitted from B
to D. Under these circumstances the spring is said to be stretched by a
force W. If the spring were removed, and the thread were continuous from
A to B, it is clear that any part of it s stretched by two equal forces, viz. an
action and reaction, each equal to W, and the thread is said to sustain a
tension W. When a body is urged along a smooth surface, the mutual
action can only take place along the common perpendicular at the point of
contact. If, however, the bodies are rough, this restriction is partially re-
moved, and now the mutual action can take place in any direction not
making an angle greater than some determinate angle with the common
perpendicular. This determinate angle has different values for different
substances, and is sometimes called the limititig angle of resistance, sovi\&-
times the angle of repose.

40. The lever is a name given to any bar straight or curved, AB (fig. 17)
resting on a fixed point or edge c called i\\e fulcrufn. The forces acting on
the lever are the zueight or resistance Q, the power P, and the reaction
of the fulcrum. Since these are in equilibrium, the resultant of P and Q
must act through c, for otherwise thay could not be balanced by the reaction.
Draw cb at right angles to QB and ca to PA produced ; then observing-

24 On Matter, Force, and Motion. [40-

that P X ca, and Q x cb are the moments of P and Q with respect to c, and
that they have contrary signs, we have by (36),

P : ; ca=(:^xcb;

an equation commonly expressed by the rule, that in the lever the power
is to the weight ift the ijtverse ratio of their arms.

Levers are divided into three kinds,
according to the position of the fulcrum
with respect to the points of apphcation of
the power and the weight. In a lever of
the first kind the fulcrum is between the
power and resistance, as in fig. 17, and as
in a poker and in the common steelyard ;
a pair of scissors and a carpenter's pincers
are double levers of this kind. In a lever
of the second kind\h& resistance is between
the power and the fulcrum, as in a wheel-
barrow, or a pair of nutcrackers, or a
door ; in a lever of the third kind the
power is between the fulcrum and the
Fig. 17. resistance, as in a pair of tongs or the

treadle of a lathe.
41. Pulleys. — The pulley is a hard circular disc of wood or of metal, in
the edge of which is a groove, and which can turn freely on an axis in the
centre. Pulleys are either yf.ir^, as in fig. 18, where the stirrup or fork is
rigidly connected with some immovable body, and where the axis rotates in

19, where the axis is fixed to
the fork,and it passes through
a hole in the centre of the
disc. The rope which passes
round the pulley in fig. 18,
supports a weight at one end;
while at the other a pull is
applied to hold this weight
in equilibrium.

We may look upon the
power and the resistance as
acting at the circumference
of the circle ; hence as the
radii are equal, if we consider
the pulley as a lever, the
two arms are equal, and
equilibrium will pre\ail when
the power and the resistance
are equal. The fixed pulley
affords thus no mechanical
appli-

the stirrup ; or it may be movable, as in fi^

Fig. 19.

advantage, but is simply convenient in changing the direction of th
cation of a force.

In the case of the movable pulley one end of the rope is suspended to

-42] JV/iec/ and Axle. 25

fixed point in a beam, and the weight is attached to the hook on which the
pulley acts. The tension of the rope is everywhere the same; one portion
of the weight is supported by the fixed part and the other by the power,
and these are equal to each other, and are together equal to the weight,
including the pulley itself ; hence in this case P = i Q.

If several pulleys are joined together on a common axis in a special
sheath, which is fixed, and a rope passes round all those and also round a
similar but movable combination of pulleys, such an arrangement, which is
represented in fig. 20, is called a block a?id tackle.

If we consider the condition of the rope it will be found to have every-
where the same tension ; the weight Q which is attached to the hook
common to the whole system is supported by the six portions of the rope :
hence each of these portions
will sustain one sixth of the
weight ; the force which is
applied at the free end of the
rope which passes over the
upper pulley, and which de-
termines the tension, will have
the same value ; that is to
say, it will support one sixth
of the weight.

The relation between
power and resistance in a
block and tackle is expressed

by the equation P = — , in

//
which P is the power, Q the
weight, and ;/ the number of
cords by which the weight is
supported.

42. The wheel and axle.
— The older form of this ma-
chine, fig. 21, is that of an
axle, to which is rigidly fixed,
concentric with it, a wheel of
larger diameter. The power
is applied tangentially on the
wheel, and the resistance tan-
gentially to the axle, as for
instance in the treadmill and
water-wheel. Sometimes, as
in the case of the capstan,
the power is applied to spokes fixed in the axle, which represent semi-
diameters of the wheel ; in other cases, as in the windlass, the handle is
rigidly fixed to the axis.

In all its modifications we may regard the wheel and axle as an applica-
tion of the lever, the arms of which are the radii of the wheel and axle re-
spectively ; and in all cases equilibrium exists where the power is to the

Fig. 20,

On Matter, Force, and Mot ion.

[42-

Thus

resistance as the radius of the axle is to the radius of the wheel,
in fig. 21, P : Q = ab : rt^, or P x a^ = Q x ab.

Frequent applications of wheels of different diameters are met with in
which the motion of one wheel is transmitted to another, either by means
of teeth fitting in each other on the circumference of the wheels, as in fig. 22^
or by means of bands passing over the two wheels, as in the illustration of
Ladd's Magneto-Electrical Machine (see Book viii.).

In fig. 22, which represents the essential parts of a crab winch, in order
to raise the weight Q a power p must be applied at the circumference of

the wheel such that ^ = Q =- , in which r and R arc the radii of the axle
R

b and of the toothed wheel a respectively.

The rotation of the wheel a is effected by means of the smaller wheel cor

crab, the teeth of which fit in those of a. But if this wheel c is to exert at

its circumference a power p, the power P which is applied at the end of

r'
the handle must be P = —^p, in which r' is the radius of r, R' the length of

R'
a lever at the end of which P acts, and consequently

RR'^

The radius of the wheel c is to that of the wheel a as their respective circum-
ferences ; and, as the teeth of each are of the same size, the circumferences
will be as the number of teeth.

Trains of wheelwork are used, not only in raising great weights by the
exertion of a small power ; as in screw jacks, cranes, crab winches, &c., but
also in clock and watch works, and in cases in which changes in velocity or
in power or even in direction are required. Numerous examples will be met
with in the various apparatus described in this work.

43. Inclined Plane The properties and laws of the inclined plane may

be conveniently demonstrated by means of the apparatus represented in
fig. 23. RS represents the section of a smooth piece of hard wood hinged at
R ; by means of screw it can be clamped at any angle x against the arc-
shaped support, by which at the
same time the angle can be mea-
sured ; (^? is a cylindrical roller,
to the axis of which is attached
a string passing over a pulley
to a scale-pan P.

It is thus easy to ascertain
by direct experiments what
weights R must be placed in the
pan P in order to balance a roller
of any given weight, or to cause
it to move with a gi\en angle of
inclination.

The line RS represents the
length, ST the height, and RT the base of the inclined plane.

In ascertaining the theoretical conditions of equilibrium we ha\e a useful

-43] Inclined Plane. 27

application of the parallelogram of forces. Let the hne ab, fig. 23, represent
the force which the weight W of the cylinder exerts acting vertically down-
wards ; this may be decomposed into two others ; one, ad, acting at right
angles against the plane, and representing the pressure which the weight
exerts against the plane ; and which is counterbalanced by the reaction of
the plane ; the other, ac, represents the component which tends to move the
weight down the plane, and this component has to be held in equilibrium by
the weight P, equal to it and acting in the opposite direction.

It can be readily shown that the triangle abc is similar to the triangle
SRT, and that the sides ac and ab are in the same proportion as the sides
ST and SR. But the line ac represents the power, and the line ab the
weight ; hence

ST:SR = P:W;

that is, on an inclined plane, equilibrium obtains when the power is to the
weight as the height of the inclined plane to its length.

ST
Since the ratio ^ is the sine of the angle x, we may also state the prm-
SR
ciple thus :

P = \V sin X.

The component da or be, which represents the actual pressure against
the plane, is equal to W cos x ; that is, the pressure against the plane is to
the weight as the base is to the length of the inclined plane.

In the above case it has been considered that the power acts parallel to
the inclined plane. It may be applied so as to act horizontally. It will then
be seen from fig. 24 that the weight W may be decomposed into two forces,
one of which, ab, acts at right angles to the plane, and the other, ac, parallel
to the base. It is this latter which is to be kept in equilibrium by the power.
From the similarity of the two triangles acb and STR, ac : bc='S>T : TR
= h: b ; but be is equal to W, and ac is equal to P, hence the power which
must be applied at b to hold the weight W in equilibrium is as the height
of the inclined plane is to the base, or as the tangent of the angle of inclina-
tion X ; that is, P = W tan x. The pressure upon the plane in this case may

be easily shown to be ab =

cos X

that is = . This is sometimes

cos X

called the relative weight on the

plane.

If the force P which is to
counterbalance W is not parallel to
the plane, but forms an angle, E, with
it, this force can be decomposed into ^'^' ^'^'

one which is parallel to it, and one which is at right angles. Of these onlj-
the first is operative, and is equal to P cos E.

In most cases of the use of the inclined plane, such as in moving carriages
and waggons along roads, in raising casks into waggons or warehouses, the
power is applied parallel to the inclined plane. An instance of a case in
which a force acts parallel to the base is met with in the screw.

On Matter, Force, and Motion.

[43-

Owing to the unevenness of the surfaces in actual use, the laws of equili-
brium and of motion on an inclined plane undergo modification. T\\&fric-
tion, for instance, which comes into play amounts on ordinary roads to from
Is to ^, and on railways to from x|o to 5 jo *^f the relative weight. This must
be looked upon as a hindrance to be continually overcome, and must be
deducted from the force required to keep a body from falling down an
inclined plane, or must be added to it in the case in which a body is to be
moved up the plane. Hence the use of the inclined plane in unloading heavy
casks into cellars, &c.

A body which cannot roll does not move on the inclined plane, provided
the inclination is below a certain amount (39). The determination of this
limiting afigle of resistance, at which a body on an inclined plane just begins
to move, may serve as a rough illustration of a mode of ascertaining the
' coefficient of friction.'

For in the case in which the power is applied parallel to the plane, the
component of the weight which presses against the plane or the actual load,
L, is W cos X ; and the component which tends to move the body down the
plane is equal to W sin x. If the friction, R, is just sufficient to hold this in

equihbrium, the coefficient of friction will be , =^,-, = tan x.

^ L W cos X

Thus if we place on the plane a block of the same material, by gradually
increasing the inclination it will begin to move at a certain angle, which
will depend on the nature of the material ; this angle is the limiting angle
of resistance, and its tangent is the coefficient of friction for that material.

44. The 'Wedge. — The ordinary form of the wedge is that of a three-
sided prism of iron or steel, one of whose angles is very acute. Its most
frequent use is in splitting stone, timber, &c. Fig. 25 represents in section
the application of the wedge to this purpose. The side ab is the back, the
vertex of the angle acb which the two faces ac and
be make with each other represents the edge, and
the faces ac and be the sides of the wedge. The
power P is usually applied at right angles to the
back ; and we may look upon the cohesion be-
tween the fibres of the wood as representing the
resistance to be overcome ; as corresponding to
what in other machines is the weight. Suppose
this to act at right angles to the two faces of
the wedge, and to be represented by the lines
fe and ge ; complete the parallelogram gef, then
the diagonal he will represent the resultant of
the reaction of the fibres tending to force the
wedge out ; the force which must be applied to
hold this wedge in equilibrium must therefore be
equal to eh. Now efh is similar to the triangle
acb, therefore ab: ac^eh: ef; but these lines re-
present the pressure applied at the back of the
wedge, and the pressure on the face ac, hence if P
represent the former and Q the latter, there is equilibrium when ^ :C = ab:bc,
that is, when the power is to the resistance in the same ratio as the back of

Fig. 25-

-45]

TJie Screw.

the wedge bears to one of the sides. The relation between power and re-
sistance is more favourable the sharper the edge, that is, the smaller the
angle which the sides make with each other.

The action of all sharp cutting instruments, such as chisels, knives,
scissors, &c., depends on the principle of the wedge. It is also appUed when
very heavy weights are to be raised through a short distance, as in launching
ships, and in bracing columns and walls to the perpendicular.

45. The Screw. — Let us suppose a piece of paper in the shape of a
rio'ht-angled triangle aee' to be applied with its vertical side ac'e' against a
cylinder, and parallel to the axis, and to be wrapped round the cyhnder ; the
hypotenuse will describe a screw line or helix on the surface of the cylinder
(fig. 26) ; the points ab c de will occupy the positions respectively a b' c' d' e'.
If the dimensions be so chosen that the base of the triangle, cc\ is equal
to the circumference of the cylinder, then the hypotenuse abc becomes an
inclined plane traced on the surface of the cylinder ; the distance ac' being
the height of the plane.

Fig. 27.

Fig. 26.

An ordinary screw consists of an elevation on a solid cylinder ; this
elevation may be either square, as in fig. 27, or acute, and such screws are
called square or sharp screws accordingly.

When a corresponding groove is cut in the
hollow cylinder or nut of the same diameter
as the bolt, this gives rise to an internal or
companion screw or nut^ fig. 28.

The vertical distance between any two
threads of a screw measured parallel to the
axis is called the pitch, and the angle ace' or aee' is called the inclination of
the screw.

In practice, a raised screw is used with its companion in such a manner
that the elevations of the one fit into, and coincide with, the depressions of
the other. The screw is a modification of the inclined plane, and the condi-
tions of equilibrium are those which obtain in the case of the plane. The
resistance, which is either a weight to be raised or a pressure to be exerted,
acts in the direction of the vertical, and the power acts parallel to the base ;
hence we have P : R = // : (5, and the length of the base is the circumference
of the cylinder ; whence P : R = /^ : Ztrr ; r being the radius of the cylinder,
and h the pitch of the screw.

The power is usually applied to the screw by means of a lever, as in the
bookbinders' press, the copying press, &c., and the principle of the screw
may be stated to be generally that the power of the screw is to the resistance
in the same ratio as that of the pitch of the screw to the circumference of the
circle through which the power acts.

On Matter, Force, a)id Motion.

[46-

Fig. 29.

46. Virtual Velocity.^ — If the point of application of a force be slightly

displaced, the resolved part of the displacement in the direction of the force

is termed the virtual velocity of the force, and is' considered as positive or

negative, according as it is in the same direction as the force, or in the

opposite direction. Thus in fig. 29 let the point of

application A of the force P be displaced to A', and

draw A'rt perpendicular to AP. Then A<-? is the virtual

velocity of the force P, and being, in this case, in the

direction of P, is to be considered positive.

The principle of virtual velocities asserts that if any
machine or system be kept in equilibrium by any
number of forces, and the machine or system then re-
ceive any vc7y small displacement, the algebraic sum of the products formed
by multiplying each force by its virtual velocity will be zero. Of course, the
displacement of the machine is supposed to be such as not to break the
connection of its parts ; thus in the wheel and axle the only possible dis-
placement is to turn it round the fixed axle ; in the inclined plane the weight
must still continue to rest on the plane : in the various systems of pulleys
the strings must still continue stretched, and must not alter in length, &c.

The complete proof of this principle is beyond the scope of the present
work, but we may easily establish its truth in any of the machines we have
already considered. It will be found in eveiy case that, if the machine
receive a small displacement, the virtual velocities of P and W will be of
opposite signs, and that, neglecting the signs, P x P's virtual velocity = W x
W's virtual velocity. Thus, to take the case of a bent lever, let P and Q be
the forces acting at the extremities of the arms of the bent lever AFB (fig. 30),
and let the lever be turned slightly round its fulcrum F, bringing A to A', and
B to B'. Draw A'^and B'^ perpendicular to P and Q respectively ; then Ka
is the virtual velocity of P, and V>b that of Q, the former being positive and
the latter negative. Let Yp, Yq be the perpendiculars from the fulcrum
upon P and Q, or what we have called (art. 40) the arms of P and Q. Now,
as the displacement is very small, the angles FAA', FBB' will be very nearly
right angles ; and, therefore, the right-angled triangles A«A', B^B' will
ultimately be similar to the triangles F^A, F^B respectively, whence

.\a Yp , Bb

= ^and —

AA' FA' BB'

AA' , Bl? BB'

FA-' "'"^ Y, ^ FB-

triangles FAA', FBB' are similar,

^? or ^^ -
FB' Yp -

But the

if the lever be in equilibrium (art. 40).

and ^,
Iq

jles FAA'

as they are both isosceles, and

their vertical angles are equal, so

„ , AA' BB' , Art Bb

that :^-- = ^^-- ; whence - = =^

FA FB ' Yp Yg

P X Aa

or, as we may put it, - — =
' B xYp

Qj< Bb

q.Yq-

these two equal fractions are equal,
Hence the numerators are equal, or

Now the denominators of ,^

-46a] Machines. 3 1

P X P"s virtual velocity = Q x Q's virtual velocity.

As a further and simpler example, take the case of the block and tackle
described in article 41. Suppose the weight to be raised through a space// ;
then the virtual velocity of the weight is k, and is negative. Now, as the
distance between the block and tackle is less than before by the space //, and
as the rope passes over this space 71 times, in order to keep the rope still
tight the power will have to move through a space equal to 7ih. This is the
virtual velocity of P, and is positive, and as W = «P, we see that
W X W's virtual velocity = P x P's virtual velocity.

46a. niacblnes. — In many machines in common use, two forces can readily
be distinguished. One is a force applied in order to drive the machine, and the
■other is a force overcome, and is called the resistance. The force applied is
usually, though improperly, called the power. In general these forces are un-
equal. If the machine moved without friction these forces might be exactly
balanced, in such a way that if either of them were increased in the slightest
degree, the machine would begin to move with a uniformly accelerated motion.
If such a machine thus balanced were to be started by an impulse which
should the7t cease to act, the machine would move continuously at a uniform
rate until acted upon by some other external force. If we imagine a balanced
frictionless machine to become a machine with friction, then either of the two
forces might be varied between certain limits, without setting the machine
into motion. Hence, if the machine is to move uniformly, the force applied
in driving it must be greater than would be necessary to give uniform motion
to a frictionless machine. The force applied, P, and the resistance overcome,
R, may be expressed in pounds weight, which may be converted into absolute
units by multiplying by the value of_^at the place. While P moves over a
certain distance p, R moves over a distance r. These distances can be deter-
mined by measurement. The ratio of r to p can often be seen by simple in-
spection, since its value depends upon the gearing or construction of the
machine.

If the force P is exerted over a distance/, the work applied is Vp foot-
pounds. While this work is being applied to the machine, a certain amount
of work, Rr, is transmitted through the machine, and is done upon the resist-
ance. Experiment shows that the work applied Vp is always greater than
the work Rr transmitted through the machine. This difference represents
the work which is required to move the parts of the machine upon each
other, and is called internal work. If the internal work is represented by I,
the condition for uniform action of a machine is given by the equation
P/=Rr+I.

It will be assumed that a small force V" is applied, sufficient to move
the machine uniformly when unloaded. This value of V" is not included
in P. In this case, the work of friction is due wholly to the load which the
machine carries, and I becomes zero when R = o. The quantity I is of the
same nature as the other two quantities n the equation, being the product of
a certain force of friction into a certain distance, but in general these factors
cannot be determined separately. It is found that I diminishes in value as
the parts of the machine in contact are made smoother, and is further

32 On Matter, Force, and Motion. [46a-

diminished by oiling the bearings — that is to say, the quantities Vp and Rr^
which can be easily determined, become more nearly equal.
The equation may also be put into the following form : —

P r I

— = - + z where / = — .
R i^ R^

It is evident that the ratio - is a constant quantity, for a given machine.,
P

P
geared in a definite manner. Experiment shows that the ratio -— is also-

practically constant, so that the quantity i may also be considered constant
for a given machine in a definite condition. It would, however, be changed
by oiling the bearings, as this would make it necessary to diminish P in
order to preserve uniform motion, and it also depends upon the arrangement
of the machine, as will be pointed out further on.

47. Friction. — In the cases of the actions of machines which have hitherto-
been described, the resistances which are offered to motion have not been
at all considered. The surfaces of bodies in contact are never perfectly
smooth ; even the smoothest present inequalities which can neither be
detected by the touch nor by ordinary sight ; hence when one body moves
over the surface of another, the elevations of one sink into the depressions
of the other, like the teeth of wheels, and thus offer a certain resistance to-
motion ; this is what is called y^zV/Zw;. It must be regarded as a force which,
continually acts in opposition to actual or possible motion.

Friction is of two kinds : sliding, as when one body glides over another ;
this is least when the two surfaces in contact remain the same, as in the
motion of an axle in its bearing ; and rolli)7g friction, which occurs when one
body rolls over another, as in the case of an ordinary wheel. The latter is
less than the former, for by the rolling the inequalities of one body are raised
over those of the other. As rolling friction is considerably less than sliding
friction, it is a great saving of power to convert the latter into the former ; as
is done in the case of the casters of chairs and other furniture, and also in
that of friction wheels. This, however, is not always the case ; thus a sledge
experiences less friction on snow than a carriage, for in this case the wheels
sink and friction on the sides results. On the other hand, it is sometimes
useful to change rolling into sliding friction, as when drags are placed on
carriage wheels.

Friction is directly proportional to the pressure of the two surfaces
against each other. That fraction of the pressure which must act as moving
force merely to overcome friction is called the coefficient of friction.

Friction is independent of the extent of the surfaces in contact if the pres-
sui'e is the same. Thus, suppose a board with a surface of a square deci-
metre resting on another board to be loaded with a weight of a kilogramme.
If this load be distributed over a similar board of two square decimetres
surface, the total friction will be the same, while the friction per square
centimetre is one-half, for the pressure on each square centimetre is one-half
of what it was before. So, too, a rectangular stone experiences the same
friction whether it is laid on the narrow or on the broad side. Friction is
diminished by polishing and by smearing, but is increased by heat. It is

48]

Resistance to Motion in a Fluid Medium.

greater as a body passes from the state of rest to that of motion than during
motion, but seems independent of the velocity. The coefficient of friction
depends on the nature of the substance in contact ; similar bodies experience
in general greater friction than dissimilar ones, for with the former the in-
equalities fit more into one another ; thus for oak upon oak it is 0*4 1 8 when
the fibres are parallel, and o'293 when they cross ; for beech upon beech it
is 0-36. Greasy substances, which are not absorbed by the body, diminish
friction, but increase it if they are absorbed. Thus moisture and oil increase,
while tallow, soap, and graphite diminish, the friction of wooden surfaces.
In the sliding friction of cast iron upon bronze the coefficient was found to
be 0-25 without grease ; with oil it was 0-17, fat o-ii, soap 0-03, and with a
mixture of fat and graphite 0-02. The coefficient of rolling friction for cast-
iron wheels on iron rails as in railways is about 0-004 j for ordinary wheels
on an ordinary road it is 0-04, hence a horse can draw ten times as great a
load on rails as on an ordinary road, and this is indeed a main use of rail and
tram ways. The coefficient of steel upon smooth ice has been determined
by a skater holding in his hand a spring balance (88) attached to a cord by
which he was drawn along by a second skater. At starting the spiral showed
a pull of 5 to 6 kilos, but during the motion this varied between i and 2 kilos.
As the weight of the skater was 62 kilos, the coefficient of friction during
the motion was -^ to ---, or i'6 to 3*2 per cent.

Without friction on the ground, neither man nor animals, neither ordinary
carriages nor railway carriages, could move. Friction is necessary for the
transmission of power from one wheel to another by means of loands or
ropes ; and without friction we could hold nothing in the hands.

48. Resistance to IVSotion in a Fluid Medium. — A body in moving
through any medium such as air or water experiences a certain resistance ;
for the moving body sets in motion those parts of the medium with which it
is in contact, whereby it loses an equivalent amount
of its own motion.

This resistance increases with the surface of the
moving body ; thus a soap-bubble or a snow-flake
falls more slowly than does a drop of water of the
same weight. It also increases with the density of
the medium ; thus in rarefied air it is less than in air
under the ordinary pressure ; and in this again it is
less than in water.

The influence of this resistance may be illustrated
by means of the apparatus represented in fig. 31,
which consists of two vanes, ww, fixed to a horizontal
axis, xx\ to which is also attached a bobbin s. The
rotation of the vanes is effected by means of the falling
of a weight attached to the string coiled round the
bobbin. The vanes can be adjusted either at right
angles or parallel to the axis. In the rormer position
the vanes rotate rapidly when the weight is allowed to
act ; in the latter, however, where they press with their
entire surface against the air, the resistance greatly lessens the rapidity of
rotation.

34 On Matter, Force, and Motion. [48-

The resistance increases with the velocity of the moving body, and for
moderate velocities is proportional to the square ; for, supposing the velo-
cities of a body made twice as great, it must displace twice as much matter,
and must also impart to the displaced particles twice the velocity. For
high velocities the resistance in a medium increases in a more rapid ratio
than that of the square, for some of the medium i^ carried along with the
moving body, and this, by its friction against the other portions of the
medium, causes a loss of velocity.

It is this resistance which so greatly increases the difficulty and cost of
attaining very high speeds in steam- vessels. Use is made, on the other hand,
of this resistance in parachutes (fig. 175) and in the windvanes for dimi-
nishing the velocity of falling bodies (fig. 55), the principle of which is
illustrated by the apparatus, fig. 31. Light bodies fall more slowly in air
than heavy ones of the same surface, for the moving force is smaller com-
pared with the resistance. The resistance to a falling body may ultimately
equal its weight ; it then moves uniformly forward with the velocity which
it has acquired. Thus, a rain-drop falling from a height of 3,000 feet
should, when near the ground, have a velocity of nearly 440 feet, or that
of a musket-shot ; owing, however, to the resistance of the air, its actual
velocity is probably not more than 30 feet in a second. On railways the
resistance of the air is appreciable ; with a carriage exposing a surface of
22 square feet, it amounts to 16 or 17 pounds when the speed of the train
is 16 feet a second, or 11 miles an hour.

By observing the rate of diminution in the number of oscillations of a
horizontal disc suspended by a thread when immersed in water, Meyer de-
termined the coefficient of the frictional or internal resistance of water, and
found that at 10° it was equal to o'oi567 gramme on a square centimetre ;
and for air it was about I- as much.

49. Uniformly Accelerated Rectilinear IVSotion. — Let us suppose a
body containing ;// units of mass to move from rest under the action of a
force of F units, the body will move in the line of action of the force, and
will acquire in each second an additional velocity y given by the equation

F = mf;
consequently, if 7/ is its velocity at the end of / seconds, we have

v=ff. (I)

To determine the space it will describe in t seconds, we may reason as
follows : — The velocity at the time / being//, that at a time t + t will be /
(/ + t). If the body moved uniformly during the time r with the former
velocity, it would describe a space s equal to ftr ; if with the latter velocity
a space s^ equal to /(/ + T)r. Consequently,

s\:s::t + T:f;

therefore, when r is indefinitely small, the limiting values of s and j-j are
equal. Now, since the body's velocity is continually increasing during the
time r, the space actually described is greater thim or and less than Sy But
since the limiting values of s and s^ are equal, the limiting value of the space
described is the same as that oi s or s^ In other words, if we suppose the

-49] Uniformly Accelerated Rectilinear Motion. 35

whole time of the body's motion to be divided into any number of equal

parts, if we determine the velocity of the body at the beginning of each of

these parts, and if we ascertain the spaces described on the supposition that

the body moves uniformly during each portion

of time, the limiting value of the sum of these

spaces will be the space actually described by

the body. Draw a line AC (fig. 32), and at A

construct an angle CAB, whose tangent equals

/"; divide AC into any number of equal parts in .

D, E, F,...and draw PD, QE, RF,...BC at /-^P"'

right angles to AC ; then since PD = AD x yj ■^^ — K ^ G H
QE = AE X / RF = AF x / EC = AC x/ &c.. Fig. 3,.

PD will represent the velocity of the body at the

end of the time represented by AD, and similarly QE, RF,...BC, will represent
the velocity at the end of the times AE, AF,...AC. Complete the rectangles
D^, Ey^ F^. . . These rectangles represent the space described by the body on
the alDove supposition during the second, third, fourth, ...portions of the time.
Consequently, the space actually described during the time AC is the limit
of the sum of the rectangles ; the limit being continually approached as the
number of parts into which AC is divided is continually increased. But this
limit is the area of the triangle ABC : that is ^AC x CB or iAC x AC x /
Therefore, if AC represents the time / during which the body describes a
space .?, we have

s = \ft\ (2)

Since this equation can be written

2/. = PP
we find, on comparison with equation (i), that

v- = 2fs. (3)

To illustrate these equations, let us suppose the accelerative effect of the
force to be 6 ; that is to say that, in virtue of the action of the force, the body
acquires in each successive second an additional velocity of 6 feet per second,
and let it be asked what, on the supposition of the body moving from rest,
will be the velocity acquired, and the space described, at the end of 12
seconds ; equations i and 2 enable us to answer that at that instant it will be
mo\'ing at the rate of 72 feet per second, and will have described 432 feet.

The following important result follows from equation 2. At the end of
the first, second, third, fourth, &c., second of the motion, the body will have
described \f, \f^ 4, f /"x 9, f_/"x 16, &c., feet ; and consequently during the
first, second, third, fourth, &c., second of the motion will have described hf^
\'f '^ 3) i/x 5) 2/^ 7j &c., feet, namely spaces in arithmetical progression.

The results of the above article can be stated in the form of laws which
apply to the state of a body moving from a state of rest under the action of
a constant force :—

I. TJie velocities arc proportional to the times during lukich the motion
has lasted.

II. The spaces described are proportional to the squares of the times em.'
ployed in their description.

D 2

36 On Matter, Force, and Motion. [49-

III. The spaces described are proportioial to t/ie squares of tJie velocities
acquired during their description.

IV. The spaces described in equal successive periods of time increase by a
constafit quantity.

Instead of supposing the body to begin to move from a state of rest, we
may suppose it to have an initial velocity V, in the direction of the force. In
this case equations i, 2, and 3 can be easily shown to take the following
forms, respectively : —

v = Y -^ft,
^ = V/ + hft\
ir = V- 4 2fs.

If the body move in a direction opposite to that of the force,/ must be
reckoned negative.

The most important exemplification of the laws stated in the present
article is in the case of a body falling freely in vacuo. Here the force causing
the acceleration is that of gravity, and the acceleration produced is denoted
by the letter g : it has already been stated (29) that the numerical value of
_^is 32-1912 at London, when the unit of time is a second and the unit of
length a foot. Adopting the metre as unit of length, the value of _c^at London
is 9-8117.

50. Motion on an Inclined Plane. — Referring to (43), suppose the force
P not to act ; then the mass M is acted on by an unbalanced force M g sin x,
in the direction SR, consequently the acceleration down the plane is g
sin X, and the motion becomes a particular case of that discussed in the
last article. If it begins to move from rest, it will at the end of / seconds
acquire a velocity v given by the equation

V =gt sin X,
and will describe a length ^ of the plane given by the equation

.y = hgt' sin X.

Also, if V is the velocity acquired while describing s feet of the plane,

v"- = 2gs sin X.

Hence (fig. 23) if a body slides down the plane from S to R the velocity
which it acquires at R is equal to ^/-g- RS sin R or •f2g. ST ; that is to say,
the velocity which the body has at R does not depend on the angle x, but
only on the perpendicular height ST. The same would be true if for RS
we substituted any smooth curve ; and hence we may state generally, that
when a body moves along any smooth line under the action of gravity, the
change of velocity it experiences in moving from one point to another is that
due to the vertical height of the former point above the latter.

51. Motion of Projectiles. — The equations given in the above article
apply to the case of a body thrown vertically upwards or downwards with a
certain initial velocit)'. We will now consider the case of a heavy body
thrown in a horizontal direction. Let a, fig. ^2ii be such a body thrown with
an initial velocity of v feet in a second, and let the line ab represent the space
described in any interval ; then at the end of the 2, 3, 4... equal interval,

-51]

Motion of Projectiles.

the body, in virtue of its inertia, will have reached the points c d e, &c.
But during- all this time the body is under the influence of gravity, which,
if it alone acted, would cause the body to fall through the distances repre-
sented on the vertical line ; these are determined
by the successive values of hgt', which is the
formula for the space described by a freely
falling body (50). The effect of the combined
action of the two forces is that at the end of the
first interval, &c., the body will be at b', at the
end of the second interval at c', of the third at
d', Sec, the spaces t>d', cc\ dd'... being propor-
tional to the squares of ab, ac, ad, respectively,
and the line joining these points represents the
path of the body. By taking the intervals of
time sufficiently small we get a regularly curved
line of the form known as \h& parabola.

If the direction in which the body is thrown
makes an angle of a with the horizon (fig. 34),
then after / seconds it would have travelled a
distance ab = vt,^\\&x& 7' is the original velo-
city ; during this time, however, it will have
fallen through a distance bc = \gt''- ; the height which it will have actually
reached is =bd -bc = vt sin a-hgt"' \ and the horizontal distance will be

Fig- 33

Fig. 34.

ad=ab cos a = vt cos a. The range of the body, or the greatest distance
through which it is thrown, will be reached when the height is again = o ; that

is, when 7'/ sin a - ^ £r^ = o, from which / = ?'^:iA^5Jf. Introducing this value

^ . , • r 1 T . J \. J 27'- sin a cos a , • ,
of / mto the equation for the distance d, we have d= , which

by a trigonometrical transformation = '_Lli!L^. The greatest height is

attained in half the time of flight, or when t = ", from which we get

2^
It follows from the formula that the height is greatest when sin a is
greatest, which is the case when it = 90°, or when the body is thrown vertically
upwards ; the range is greatest where sin 2a is a maximum, that is, when
2a = 90° or a = 45°.

38 On Matter, Force, and Motion. [51-

In these formulae- it has been assumed that the air offers no resistance.
This is, however, far from the case, and in practice, particularly if the velo-
city of projection is very great, the path differs from that of a parabola.
Fig. 34 approximately represents the path, allowing for the resistance of the
air. The divergence from the true theoretical path is affected by the fact
that in the modern rifled arms the projectiles are not spherical in shape ;
and also because, along with their motion of translation, they have, in con-
sequence of the rifling, a rotatory motion about their axis.

52. Composition of Velocities. — The principle for the composition of
velocities is the same as that for the composition of forces : this follows evi-
dently from the fact that forces are measured by the momentum they com-
municate, and are therefore to one another in the same ratio as the velocities
they communicate to the same body. Thus (fig. 7, art. 32), if the point has
at any instant a velocity AB in the direction AP, and there is communicated
to it a velocity AC in the direction AQ, it will move in the direction AR with
a velocity represented by AD. And conversely, the velocity of a body re-
presented by AD can be resolved into two component velocities AB and AC.
This suggests the method of determining the motion of a body when acted
on by a force in a direction transverse to the direction of its velocity ; namely,
suppose the time to be divided into a great number of intervals, and suppose
the velocity actually communicated by the force to be communicated at once;
then by the composition of velocities we can determine the motion during
each interval, and therefore during the whole time ; the actual motion is the
limit to which the motion, thus determined, approaches when the number of
intervals is increased.

53. IVIotion in a Circle — Centrifugal Force. — When a body is once in
motion, unless it be acted upon by some force, it will move uniformly
forward in a straight line with unchanged velocity (26). If, therefore, a body
moves uniformly in any other path than a straight line — in a circle, for
instance — this must be because some force is constantly at work which
continuously deviates it from this straight line.

We have already seen an example of this in the case of the motion of
projectiles (51), and will now consider it in the case of central motion or
motion in a circle, of which we have an example in the motion of the
celestial bodies, or in the motion of a sling.

In the latter case, if the string is cut, the stone, ceasing to be acted upon
by the tension of the string, will move in a straight line with the velocity
which it already possesses — that is, in the direction of the tangent to the
curve at the point where the stone was when the string was cut. The tension
of the string, the effect of which is to pull the stone towards the centre of
the circle and to cause the stone to move in its circular path, is called the
ceiitripetal or coitral force ; the reaction of the stone upon the string, which
is equal and opposite to this force, is called the centj'ifiigal force. The
amount of the forces may be arrived at as follows : —

Let us suppose a body moving in a circle with given uniform velocity
to be at the point a (fig. 35) ; then, had it not been acted on by a force
in the direction ac, it would, in a small succeeding interval of time /, have
continued to move in the direction of the tangent at a, and have passed
through a distance which we will represent by ab. In consequence, however.

53]

Motion in a Circle- Centrifugal Force.

of this force, it has not followed this direction, but has arrived at the point d
on the curve ; hence the force has made it traverse the distance bd=ac in
this interval. If / be the acceleration with which the body is drawn to-
wards the centre ae = k/t'-, and if ad be very small, it
may be taken as equal to ad or vt, where v is the
velocity of the moving body. Now if an is the dia-
meter of the circle, the triangle adn is inscribed in a
semicircle and is right-angled, whence ad^ -aex an =
ae X 2r. Substituting their values for ad and ae in
this equation, we find that v't'- = h ft' x 2r, from which

/ =

that is, in order that a body with a certain

velocity may move in a circle, it must be drawn to
the centre by a force which is directly as the square
of the velocity with which the body moves, and which
is inversely as the radius of the circle. In order to
express this in the ordinary units of weight, we must
multiply the above expression by the mass, which

gives F = ^~ — or . To keep the body in a circle,

an attraction towards the centre is needed, which is

constantly equal to

and this attraction is con-

stantly neutralised by the centrifugal force.

The above expression may be put in a form which
is sometimes more convenient. If T be the time in
seconds required to traverse the circumference 2nr

with the velocity v, then v'- = '^^- , from which

P ^4W7rV^4W7rV Fig. 35.

If a rigid body rotates about a fixed axis, all parts of the body describe
circumferences of various diameters, but all in the same time. The velocity
of the motion of individual particles increases with the distance from the axis
of rotation. By angular velocity is understood the velocity of a point at unit
distance from the axis of rotation. If this is denoted by «, the velocity v of a

point at a distance from the axis is wr, from which » =— = -^ and F= rar.

The existence of centrifugal force may be demonstrated by means of
numerous instructive experiments, such as the centrifugal railway. If a small
can of water hung by the handle to a string be rapidly rotated in a vertical
circle, no water will fall out, for, at a suitable velocity, the liquid will press
against the bottom of the vessel with a force at right angles to the circle and
greater than its own weight.

Centrifugal force has been used in chemical laboratories to separate
•crystals from the mother liquors, and also to promote the deposition of fine
precipitates which under ordinary circumstances settle very slowly ; it is also
applied industrially in sugar factories to purify sugar from syrup, in dye works
to dry yarn and cloth rapidly, and in laundries.

On Matter, Force, and Motion.

[54

54. Motion in a Vertical Circle. — Let ACBD (fig. 36) be a circle whose
plane is vertical and radius denoted by r. Suppose a point placed at A, and
allowed to slide down the curve, what velocity will it
have acquired on reaching any given point P ? Draw
the vertical diameter CD, join CA, CP, and draw the
horizontal lines AMB and PNP'. Now, assuming the
curve to be smooth, the velocity acquired in falling
from A to P is that due to MN, the vertical height of
A above P (51) ; if, therefore, v denote the velocity of
the point at P, we shall have

we have

Fig. 36.

Now by similar triangles DCP, PCN,
DC : CP: :CP : CN
consequently, if we denote by j- the chord CP,

2rNC = y-.
In like manner if cz denote the chord CA,

2rMC = rt',
therefore 2rM N = ^r — j'-,

and

^{cv-f).

Now V will have equal values when j has the same value, whether positive
or negative, and for any one value of j' there are two equal values of 7/, one
positive and one negative. That is to say, since CP' is equal to CP, the
body will have the same velocity at P' that it has at P, and at any point the
body will have the same velocity whether it is going up the curve or down
the curve. Of course it is included in this statement that if the body begins
to move from A it will just ascend to a point B on the other side of C, such
that A and B are in the same horizontal line. It will also be seen that at C
the value of s is zero ; consequently, if V is the velocity acquired by the
body in falling from A to C, we have

and, on the other hand, if the body begins to move from C with a velocity V,
it will reach a point A such that the chord AC or a is given by the same
equation. In other words, the velocity at the lowest point is proportional to
the chord of the arc described.

55. Itlotion of a Simple Pendulum. — By a simple pendulum is meant a
heavy particle suspended b)' a fine thread from a fixed point, about which it
oscillates without friction. So far as its changes of velocity are concerned
they will be the same as those of the point in the previous article, for the
tension of the thread, acting at each position in a direction at right angles to
that of the motion of the point, will no more affect its motion than the re-
action of the smooth curve affects that of the point in the last article. The
time of an oscillation — that is, the time in which the point moves from A to
B — can be easily ascertained when the arc of vibration is small ; that is, when
the chord and the arc do not sensibly differ.

Fig. 37-

-56] Motion of a Simple Penduluiii. 41

Thus, let AB (fig. yj) equal the arc or chord ACB (fig. 36) ; with centre
C and radius AC or a describe a circle, and suppose a point to describe the
circumference of that circle with a uniform velocity

V or c? A /^. At any instant let the point be at Q,

join CQ, draw the tangent QT, also draw QP at
right angles and QN parallel to AB, then the angles
NQT and CQP are equal. Now the velocity of Q

resolved parallel to AB is V cos TQN or «a/-.

cos CQP ; that is, if CP equals s, the velocity of Q
parallel to AB is

^/^PQor,^/'^(.r-.^).

But if we suppose a point to move along AB in such a manner that its
velocity in each position is the same as that of the oscillating body, its

velocity at P would also equal j^ f S (a- - s") ; and, therefore, this point

would describe AB in the same time that Q describes the semicircumference
AQB. If then / be the required time of an oscillation, we have

This result is independent of the length of the arc of vibration, provided its
aiiiplitiaic, that is AB, be small— not exceeding 4 or 5 degrees, for instance.
It is evident from the formula that the time of a vibration is directly pro-
portional to the square root of the length of the pendulum, and inversely
proportional to the square root of the accelerating force of gravity.

As an example of the use of the formula we may take the following : — It
has been found that 39-13983 inches is the length of a simple pendulum
whose time of oscillation at Greenwich is one second ; the formula at once
leads to an accurate determination of the accelerating force of gravity g ; for
using feet and seconds as our units we have /= i, r= 3-26165, and rr stands
for the known number 3-14159, therefore the formula gives us
.^=(3-14159)' X 3-26165 = 32-1912.

This is the value employed in (29).

Other examples will be met with in the Appendix.

56. Crapnic Representation of the Changes of Velocity of an Oscil-
lating- Body.— The changes which the velocity of a vibrating body under-
goes may be graphically represented as follows : — Draw a line of indefinite
length and mark off AH (fig. 38) to represent the time of one vibration, HH'

P H

-<" ^ A

'^ >~

Fig. 38.

to represent the time of the second vibration, and so on. During the first
vibration the velocity increases from zero to a maximum at the half-vibration,
and then decreases during the second half-vibration from the maximum to

42 On Matter, Force, and Motion. [56-

zero. Consequently, a curved line or arc AQH may be drawn, whose
ordinate QM at any point Q will represent the velocity of the body at the
time represented by AM. If a similar curved line or arc HPH' be drawn,
the ordinate PN of any point P will represent the velocity at a time denoted
by AN. But since the direction of the velocity in the second oscillation is
contrary to that of the velocity in the first oscillation, the ordinate NP must
be drawn in the contrary direction to that of MQ. If, then, the curve be
continued by a succession of equal arcs alternately on opposite sides of AD,
the variations of the velocity of the vibrating body will be completely repre-
sented by the varying magnitudes of the ordinates of successive points of the
curve. The last article shows this to be the curve of sines for a pendulum.

57. Impulsive Forces. — When a force acts on a body for an inappre-
ciably short time, and yet sensibly changes its velocity, it is termed an instan-
taneous ox impulsive {oxcq. Such a force is called into play when one body
strikes against another. A force of this character is nothing but a finite
though very large force, acting for a time so short that its duration is nearly,
or quite, insensible. In fact, if M is the mass of the body, and the force
contains M/ units, it will, in a time t, communicate a velocity ft ; now, how-
ever small / may be, M/and therefore f may be so large that // may be of
sensible or even considerable magnitude. Thus if M contains a pound of
matter, and if the force contains ten thousand units, though t were so short
as to be only the —^ of a second, the velocity communicated by the force
would be one of 10 feet per second. It is also to be remarked that the body
will not sensibly move while this velocity is being communicated ; thus, in
the case supposed, the body would only move through \ft' or the 5^5 of a
foot while the force acts upon it.

When one body impinges on another, it follows from the law of the
equality of action and reaction (39) that whatever force the first body exerts
upon the second, the second will exert an equal force upon the first in the
opposite direction. Now forces are proportional to the momenta generated
in the same time ; consequently, these forces generate, during the whole or
any part of the time of impact, in the bodies respectively, equal momenta
with contrary signs ; and therefore the sum of the momenta of the two bodies
will remain constant during and at the end of the impact. It is of course
understood that if the two bodies move in contrary directions their momenta
have opposite signs, and the sum is an algebraical sum. In order to test

the physical validity of this conclusion,
Newton made a series of experiments,
which may be thus briefly described —
Two balls A and B (fig. 39) are hung
from points C, D in the same horizontal
line by threads in such a manner that
their centres A and B are in the same
horizontal line. With centre C and ra-
Pig 3g_ dius CA describe a semicircle EAF,

and with centre D and radius DB
describe a semicircle GBH, on the wall in front of which the balls hang.
Let A be moved back to R, and be allowed to descend to A ; it there im-
pinges on B ; both A and B will now move along the arcs AF and BH

-58] Direct Collision of Tivo Bodies. 43

respectively ; let A and B come to their highest points at r and k respectively.
Now if V denote the velocity with which A reaches the lowest point, v and ii
the velocities with which A and B leave the lowest points after impact, and
r the radius AC, it follows from (54) that

V = chd AR ^ A, 7' = chd Ar ., A and // = chd ^k ,^f

y-J,,.. = cnaAry

therefore if A and B are the masses of the two balls, the momentum at the
instant before impact was proportional to A x chd AR, and the momentum
after impact was proportional to A x chd Ar+ B x chd B/&. Now when the
positions of the points R, r, and k had been properly corrected for the
resistance of the air, it was found that these two expressions were equal to
within quantities so small that they could be pi'operly referred to errors of
observation. The experiment succeeded ec[ually under every modification,
whether x\ impinged on B at rest or in motion, and whatever the materials of
A and B might be.

58. Direct Collision of Two Bodies. — Let A and B be two bodies
moving with velocities V and U respectively, along the same line, and let their
mutual action take place in that line ; if the one overtake the other, what
will be their respective velocities at the instant after impact ? We will answer
this question in two extreme cases.

i. Let us suppose the bodies to be quite inelastic. In this case, when A
touches B, it will continue to press against B until their velocities are
equalised, when the mutual action ceases. For whatever deformation the
bodies may have undei'gone, they have no tendency to recover their shapes.
If, therefore, x is their common velocity after impact, we shall have Kx -v 'Qx
their joint momentum at the end of impact, but their momentum before
impact was AV + BU. Whence

(A+B).r=AV + BU,
an equation which determines x.

ii. Let us suppose the hodA&s perfectly elastic. In this case they recover
their shapes, with a force exactly equal to that with which they were com-
pressed. Consequently the whole momentum lost by the one, and gained by
the other, must be exactly double of that lost while compression took place ;
that is, up to the instant at which their velocities were equalised. But these
are respectively A\^ - A.t- and Bar- BU ; therefore, if v and u are the required
final velocities,

At/ = AV - 2(AV - Ax) or 2/ = - V + 2x

Bzi = BU + 2(B.r- BU) or u = 2x- U,

hence (A + B)7' = 2BU + (A- B)V

and (AhB)«-2AV-(A-B)U.

The following conclusion from these equations may be noticed : suppose a
ball A, moving with a velocity V, to strike directly an equal ball B at rest.
In this case A = B and U = o, consequently v = o and te = V ; that is, the
former ball A is brought to rest, and the latter B moves on with a velocity V.
If now B strike on a third equal ball C at rest, B will in turn be brought
to rest, and C will acquire the velocity V. And the same is true if there is

44 On Matter, Force, and Motion. [58-

a fourth, or fifth, or indeed any number of balls. This result may be shown
with ivory balls, and is a very remai-kable experiment.

59. Work: Meaning- of the Term.— It has been pointed out (ig, 26)
that a moving- body has no power of itself to change either the direction or
the speed of its motion, and that, if any such change takes place, it is a proof
that the body is acted upon by some external force. But although change of
motion thus always implies the action of force, forces are often exerted with-
out causing any change in the motion of the bodies on which they act. For
instance, when a ship is sailing at a uniform speed, the force exerted on it by
the wind causes no change in its motion, but simply prevents such a change
being produced by the resistance of the water ; or, when a railway-train is
running with uniform velocity, the force of the engine does not change, but
only maintains its motion in opposition to the forces, such as friction and the
resistance of the air, which tend to destroy it.

These two classes of cases— namely, first, those in which forces cause a
change of motion ; and secondly, those in which they prevent, wholly or in
part, such a change being produced by other forces — include all the effects
to which the action of forces can give rise. When acting in either of these
ways, a force is said to do work : an expression which is used scientifically
in a sense somewhat more precise, but closely accordant with that in which
it is used in common language. A little reflection will make it evident that,
in all cases in which we are accustomed to speak of work being done —
whether by men, horse-power, or steam-power, and however various the pro-
ducts may be in different cases — the physical part of the process consists
solely in producing or changing motion, or in keeping up motion in opposition
to resistance, or in a combination of these actions. The reader will easily
convince himself of this by calling to mind what the definite actions are which
constitute the work done by (say) a navvy, a joiner, a mechanic, a weaver ; that
done by a horse, whether employed in drawing a vehicle, or in turning a gin ;
or that of a steam-engine, whether it be used to drag a railway-train or to
drive machinery. In all cases the work done is reducible, from a mechanical
point of view, to the elements that have been mentioned, although it may be
performed on different materials, with different tools, and with different
degrees of skill.

It is, moreover, easy to see (comp. 53) that any possible change or
motion may be represented as a gain by the moving body of an additional
(positive or negative) velocity either in the direction of its previous motion,
or at right angles to it ; but a body which gains velocity is (27) said to be
accelerated. Hence, what has been said above may be summed up as
follows : — When a force produces acceleration, or when it maintains inoiion
unchanged in opposition to resistattce, it is said to do WORK.

60. ivxcasure of Work. — In considering how work is to be measured, or
how the relation between different cjuantities of work is to be expressed
numerically, we have, in accordance with the above, to consider first, wt>r>^<?/"
acceleration ; and secondly, work against resistance. But in order to make
the evaluation of the two kinds of work consistent, we must bear in mind
that one and the same exertion of force will result in work- of either kind
according to the conditions under which it takes place ; thus, the force of
gravity acting on a weight let fall from the hand causes it to move with a

-60] Measure of Work. 45

continually accelerated velocity until it strikes the ground ; but if the same
weight, instead of being allowed to fall freely through the air, be hung to a
cord passing round a cylinder by means of which various degrees of friction
can be applied to hinder its descent, it can be made to fall with a very small
and practically uniform velocity. Hence, speaking broadly, it may be said
that, in the former case, the work done by gravity upon the weight is work of
acceleration only, while in the latter case it is work against resistance (friction)
only. But it is very important to note that an essential condition, without
which a force, however great, cannot do work either of one kind or the other,
is that the thing acted on by it shall move while the force continues to act.
This is obvious, for if no motion takes place it clearly cannot be either
accelerated or maintained against resistance. The motion of the body on
which a force acts being thus necessarily involved in our notion of work
being done by the force, it naturally follows that, in estimating how much
work is done, we should consider how much — that is to say, how far — the
body moves while the force acts upon it. This agrees with the mode of
estimating quantities of work in common life, as will be evident if we consider
a veiy simple case— for instance, that of a labourer employed to carry bricks
up to a scaffold : in such a case a double number of bricks carried would
represent a double quantity of work done, but so also would a double height
of the scaffold, for whatever amount of work is done in raising a certain
number to a height of twenty feet, the same amount must be done again to
raise them another twenty feet, or the amount of work done in raising the
bricks forty feet is twice as great as that done when they are raised only
twenty feet. It is also to be noted that no direct reference to ///;/£■ enters into
the conception of a quantity of work : if we want to know how much work a
labourer has done, we do not ask how long he has been at work, but what he
has done — for instance, how many bricks he has carried, and to what height ;
and our estimate of the total amount of work is the same whether the man
has spent hours or days in doing it.

The foregoing relations between force and work may be put into definite
mathematical languag'e as follows : — If the point of application of a force
moves in a straight line, and if the part of the force resolved along this line
acts in the direction of the motion, the product of that component and the
length of the line is the work done by the force. If the component acts in
the opposite direction to the motion, the component may be considered as
a resistance, and the product is work done against the resistance. Thus, in
(43), if we suppose a to move up the plane from R to S, the work done by P
is P X RS : the work done against the resistance W is W sin x x RS. It
will be observed that if the forces are in equilibrium during the motion, so
that the velocity of a is uniform, P equals W sin x, and consequently the
work done by the power equals that done against the resistance. Also, since
RS sin X equals ST, the work done against the resistance equals W x ST.
In other words, to raise W from R to S requires the same amount of work
as to raise it from T to S.

If, however, the forces are not in equilibrium, the motion of a will not be
uniform, but accelerated ; the work done upon it will nevertheless still be
represented by the product of the resultant force resohed along the direction
of motion into the distance through which it moves.

46 On Matter, Force, and Motion. [60-

In order to ascertain the relation between the amount of work done
and the change produced by it in the velocity of the moving mass, we must
recall one or two elementary mechanical principles. Let F be the resultant
force resolved along the direction of motion, and S the distance through
which its point of application moves : then, according to what has been said,
the work done by the force = FS. Further, it has been pointed out (29) that
a constant force is measured by the momentum produced by it in a unit of
time : hence, if T be the time during which the force acts, V the velocity of
the mass M at the beginning of this period, and Vj the velocity at the end,
the momentum produced during the time T is MVj - MV, and consequently
the momentum produced m a unit of time, or, in other words, the measure
of the force, is

M(V,-V)
T

The distance S through which the mass M moves while its velocity
changes from the value V to the value V, is the same as if it had moved
during the whole period T with a velocity equal to the average value of the
varying velocity which it actually possesses. But a constant force acting
upon a constant mass causes its velocity to change at a uniform rate ; hence,
in the present case, the average velocity is simply the arithmetical mean of
the actual and final velocities :

S = KV. + V)T.

Combining this with the last equation, we get as the expression for the
work done by the force F :

FS = ^M(V,--V-);

or, in words, when a co7ista7it force acts on a mass so as to change its velocity^
the work done by the force is equal to half the product of the mass into the
change of the square of the velocity.

The foregoing conclusion has been arrived at by supposing the force F
to be constant, but it is easy to show that it holds good equally if F is the
average magnitude of a force which varies from one part to another of the
total distance through which it acts. To prove this, let the distance S be
subdivided into a very great number n of very small parts, each equal to s,
so that ns = S. Then, by supposing ^ to be sufficiently small, we may with-
out any appreciable error consider the force as constant within each of these
intervals, and as changing suddenly as its point of application passes from
one interval to the next. Let F,, F.,, F., . . . . F,i, be the forces acting
throughout the ist, 2nd, 3rd .... ;7th interval respectively, and let the
velocity at the end of the same intervals be 7/,, 7/., ta, .... v^^ ( = V,).
respectively ; then, for the work done in the successive intervals, we have :

F,.y = iM(7/;'-V'')

F.j = iM(7/.,2-7/,^)

F,>=iM(7A;--7'„^)

Yj = iM(7/,;- - 7',, - ;-) = ^M(v,- - 7'^- ;-),

-61j Unit of Work. Power. 47

or, for the total work,

(F, + F, + F3+ +F„> = iM(\V-V^);

where the quantity of the left-hand side of the equation may also be

written l1 - "^ ' ' n. «j' = FS, if we put F to stand for the average (or

n
arithmetical mean) of the forces F,, F.,, &c.

An important special case of the application of the above formula arises
when either the initial or the final velocity of the mass M is nothing ; that
is to say, when the effect of the force is to make a body pass from a state
of rest into one of motion, or from a state of motion into one of rest. The
general expression then assumes one of the following forms, namely : —

FS = iMVi-or,
-FS = |MV-;

the first of which denotes the quantity of work which must be done on a body
of mass M in order to give to it the velocity Vj, while the second expresses
the work that must be done in order to bring the same mass to rest when it
is moving with the velocity V, the negative sign in the latter case showing
that the force here acts in opposition to the actual motion, and is therefore
to be regarded as a resistance.

In practice, the case which most frecjuently occurs is where work of ac-
celeration and work against resistance are performed simultaneously. Thus,
recurring to the inclined plane already referred to in art. 43 ; if the force P
(where P is the constant force with which the string pulls W up the plane)
be greater than W sin x, the body W will move up the incline with a con-
tinually increasing velocity, and if the point of application of P be displaced
from R to S, the total amount of work done, namely, P x RS, consists of a
portion = W sin x RS, done against the resistance of the weight W, and of a
portion = (P - W sin x) RS expended in accelerating the weight. Hence, to
determine the velocity v with which W arrives at the top of the incline, we
have the ecjuation

(P-Wsin,r) RS = iW-./"-;

for the portion of P which is in excess of what is required to produce equili-
brium with the weight W, namely, P-W sin x, corresponds to the resultant
force F supposed in the foregoing discussion, and RS to the distance through
which this resultant force acts.

61. Unit of "Work. Power. — For strictly scientific purposes a unit of
work is taken to be the work done by a unit offeree when its point of appli-
cation moves through one foot in the direction of its action ; but, as a con-
venient and sufficiently accurate standard for practical purposes, the quantity
of work which is done in lifting i pound through the height of i foot is
commonly adopted as the unit, and this quantity of work is spoken of as one
' foot-pound.' It is, however, important to observe that the foot-pound is not
perfectly invariable, since the weight of a pound, and therefore the work done
in lifting it through a given height, differs at different places, being a little
greater near the Poles than near the Equator.

On the metrical system the kilograniuietre is the unit ; it is the work

48 On Matter, Force, and Motion. [61-

done when a weight of a kilogramme is raised through a heig"ht of a
metre. This is equal to 7-24 foot-pounds, and one foot-pound = -1381 of a
kilogrammetre.

In estimating the usefulness of an)^ motor it becomes necessary to know
the time required by it for doing a given amount of work. The amount of
work per second is the power of the motor. The unit of power is the
power required to do a unit of work in a unit of time. For measuring the
power of engines the unit used is the horse-power., which represents a rate
of work of 33,000 foot-pounds per minute.

It is to be observed that in every case the unit is of the same denomina-
tion as the thing or quantity measured. The unit of length must be a length ;
the unit of value must be a definite quantity of some valuable commodity.
The numbers, to determine which is one of the objects of physical research,
are to be considered as abstract numbers, representing how many times the
unit is taken.

bia. Systems of Units. — The units of mass, length, and time are said
to be fiindamcntal units, as all other units, such as those of area, velocity,
acceleration, power, &c., are referred to them. These latter units are there-
fore called derived units. The magnitudes of the fundamental units are,
however, arbitrary. A large class of writers use the centimetre, gramme,
and second, and this system is usually called the C.G.S. system ; others
use the foot, pound, and second. It thus becomes important to have a
systematic method of reducing measurements from one system of units to
another.

Let L, M, T represent respectively the magnitude or dimensio7is of the
centimetre, the gramme, and the second, and L', M', T' represent the
dimensions of the foot, the pound, and the minute. Then, if a wire is found
to be / cm. or /' ft. in length, its length may be represented either by /L or
/'L', and hence

/L = /'L', or/=f^V.

The ratio is the length of a foot in centimetres, and has been found

by direct comparison to be 30'4797. Hence any measurement, /' in feet, is
converted into centimetres by multiplying i' by this number.

In a similar manner, if /// and ///' represent the number of units of mass
in a piece of matter in the two systems,

M' ,

ni = ^, III ,

M '

where the unit ratio is the number of grammes in a pound, or 453'59.
For converting a volume v' into the equivalent 7',

(/'L')^ = (/L)", or F' = {^^ /'3

/LV ,

For Density, ^

-61a] Systems of Units 49

m M. ^m' M'
p' i}- in • L'3'

M Vl7

Here the ratio - is said to be a measure of the magnitude or dimensions

of the unit of density, in terms of the dimensions of the fundamental units

of mass and length. If a substance is said to have a unit density, then if M

is the gramme and L^ the cubic centimetre, the density of the substance

would be that ^of water. If, however, M were the kilogramme and L^ the

cubic centimetre, the density would be a thousand times that of water.

If, again, L^ represents a cubic decimetre, and M the kilogramme, the

density would again be that of water. It appears, then, that the magnitude

of the unit of density is directly proportional to the magnitude of the unit

of mass, and mversely as the magnitude of the unit of volume or the cube of

the unit of length. As the unit density is the density of a unit mass to the

M
unit volume, it is clear that „ measures the dimensions of the unit of density.

Similar explanations apply in the succeeding cases.
/

For Velocity^ v--

~, ^- T second i
i he ratio — - ■■

/ ' T / ■ T'

L' T

')=■■- — .11

L T'

T' minute 60

If the units of time were the same, the unit factor — = i, and the velo-
city in centimetres would be

L' ,
v= -- V,

where v' is the velocity in feet per second.
vil

For Momentum^ inv =

iiii
t

nd
t

ML in' I' M'L'
T t' ' T'

VIV--

^^•--

For Acceleration, <z = -

_ I

/' L'

• yx

t" ' T^^'

1/
L

ar-'

where a' is the acceleration in

feet

per minute.

On Matter, Force, and Motion.

For Force ^ F =

-- ma = — J

ml ML m'V WL'
M L W)

In the C.G.S.

system the unit is called the Dyne.

For Work,W^Yl==^'^^

mP MU m'l'"- M'L'2

In the C.G.S.

system the unit of work is called the Erg.

Rale 0) Work

^,orPower,Y = ^l='^
t /3

mP M.U m'l'^ M'L'2

[61a-

-l'(D'©'

If work is expressed in foot-pounds or kilogramme-metres, the unit of
force being the weight of a pound or kilogramme, then to convert a certain
number of foot-pounds into kilogramme-metres we have

wl . WL = w'l' WU.
Work (kgT.-m.) = (~— . — j work, foot-pounds,

L' foot o

T- = = 0-3048,

L metre
the unit factor being thus 0-1383.

Similarly, to convert foot-pounds per minute mto kilogr. -metres per second,

p /W'L'TW
VW L TV '
where the conversion factor becomes 0-00230. '

The units commonly used for measuring the power ot engmes are the
horse-power, which is 33,000 times as great as the unit in which P' of the
last equation was measured, and the force de cheval, which is 75 times as
great as the unit in which P was measured. Hence, if P' is to be in horse-
power, and P \\\fo7-ce de cheval, the equation will become

P = 0-00230 X 33^52?p/
75
= 1-0139 P',
and hence one British horse-power = I'oi'^c) force de cheval.

-63] Varieties of Energy. 5 1

These examples will be sufficient to indicate the method of converting
measurements from one system of units to any other, and the treatment of
other derived units may be deferred until they are needed.

62. Energ^y. — The fact that any agent is capable of doing work is usually
expressed by saying that it possesses Ene^'gy, and the quantity of energy it
possesses is measured by the amount of work it can do. For example, in
the case of the inclined plane above referred to, the working power or energy
of the force P is P x RS ; and if this force acts under the conditions last
supposed, by the time its own energy is exhausted (in consec[uence of its
point of application having arrived at S, the limit of the range through which
it is supposed able to act), it has conferred upon the weight W a quantity of
energy equal to that which has been expended ; for, in the first place, W
has been raised through a vertical height equal to ST, and could by falling
again through the same height do an amount of work represented by W x ST ;
and in the second place W can do work by virtue of the velocity that has
been imparted to it, and can continue moving in opposition to any given
resistance R through a distance s, such that

The energy possessed by the mass M in consequence of having been raised
from the ground is commonly distinguished as energy oj positio?t or potential
energy, and is measured by the product of the force tending to cause motion,
into the distance through which the point of application of the force is
capable of being displaced in the direction in which the force acts. The
energy possessed by a body in consequence of its velocity is commonly dis-
tinguished as e?tergy of motion, or kinetic energy: it is measured by half the
product of the moving mass into the square of its velocity.

63. Varieties of energry. — It will be seen, on considering the definition
oiivork gi\'en above, that a force is said to do work when it produces any
change in the condition of bodies ; for the only changes which, according to
the definition oi force given previously (26), a force is capable of producing,
are changes in the state of rest or motion of bodies and changes of their
place, in opposition to resistances tending to prevent motion or to produce
motion in an opposite direction. There are, however, many other kinds of
physical changes which can be produced under appropriate conditions, and
the recent progress of investigation has shown that the conditions under
which changes of all kinds occur are so far analogous to those required for
the production of work by mechanical forces that the term work has come
to be used in a more extended sense than formerly, and is now often used to
signify the production of any sort of physical change.

Thus work is said to be done when a body at a low temperature is raised
to a higher temperature, just as much as when a weight is raised from a
lower to a higher level ; or, again, work is done when an electrical, magnetic,
or chemical change is produced. This extension of the meaning of the
term work involves a similar extension of the meaning of energy, which in
this wider sense may be defined as the capacity for producing physical
change.

As examples of energy in this more general sense, the following may be
mentioned : — {a) the energy possessed by gunpowder in virtue of the mutual

52 On Matter, Force, and Motion. [63-

chemical affinities of its constituents, whereby it is capable of doing work by
generating heat or by acting on a cannon-ball so as to change its state of
rest into one of rapid motion ; {b) the energy of a charged Leyden jar, which,
according to the way in which the jar is discharged, can give rise to changes
of temperature, to changes of chemical composition, to mechanical changes,
or to changes of magnetic or electrical condition ; (c) the energy of a red-hot
ball, which, amongst other effects it is capable of producing, can raise the
temperature and increase the volume of bodies colder than itself, or can
change ice into water or water into steam ; the energy of the stretched
string of a bow : here work has been consumed in stretching the string ;
when it is released the work reappears in the velocity imparted to the
arrow.

64. Transformation of energ-y. — It has been found by experiment
that when one kind of energy disappears or is expended, energy of some
other kind is produced, and that, under proper conditions, the disappearance
of any one of the known kinds of energy can be made to give rise to a greater
or less amount of any other kind. One of the simplest illustrations that can
be given of this transformation of energy is afforded by the oscillations of a
pendulum. When the pendulum is at rest in its lowest position it does not
possess any energy, for it has no power of setting either itself or other bodies
in motion, or of producing in them any kind of change. In order to set the
pendulum oscillating, work must be done upon it, and it thereafter possesses
an amount of energy corresponding to the work that has been expended.
When it has reached either end of its path, the pendulum is for an instant at
rest ; but it possesses energy by virtue of its position, and can do an amount of
work while falling to its lowest position, which is represented by the product
of its weight into the vertical height through which its centre of gravity de-
scends. When at the middle of its path the pendulum is passing through its
position of equilibrium, and has no power of doing work by falling lower ; but
it now possesses energy by virtue of the velocity which it has gained, and
this energy is able to carry it up on the second side of its lowest position to
a height equal to that from which it has descended on the first side. By
the time it reaches this position the pendulum has lost all its velocity, but it
has regained the power of falling : this, in its turn, is lost as the pendulum
returns again to its lowest position, but at the same time it regains its pre-
vious velocity. Thus, during every quarter of an oscillation the energy of
the pendulum changes from potential energy of position into actual energy
or energy of motion, or vice versa.

A more complex case of the transformation of energy is afforded by a
thermo-electric pile, the terminals of which are connected by a conducting
wire : the application of energy in the form of heat to one face of the pile
gives rise to an electric current in the wire, which, in its turn, reproduces
heat, or by proper arrangements can be made to produce chemical, magnetic,
or mechanical effects, such as those described below in the chapters on
Electricity.

It has also been found that the transformations of energy always take
place according to fixed proportions. For instance, when coal or any other
combustible is burned, its chemical energy, or power of combining with
oxygen, vanishes, and heat or thermal energy is produced, and the quantity

-65] Conservation of Energy. 53

of heat produced by the combustion of a given amount of coal is fixed and
invariable. If the combustion take place under the boiler of a steam-engine,
mechanical work can be obtained by the expenditure of part of the heat pro-
duced, and here again the cjuantitative relation between the heat expended
and the work gained in place of it is perfectly constant.

65. Conservation of energ-y. — Another result of great importance, which
has been arrived at by experiment, is that the total amount of enei'gy possessed
by any system of bodies is unaltered by any transformations arising from the
action of one part of the system upon another, and can only be increased or
dmiinished by effects produced on the system by external agents. In this
statement it is of course understood that in reckoning the sum of the energy
of various kinds which the system may possess, those amounts of the
different forms of energy which are mutually convertible into each other are
taken as being numerically equal ; or, what comes virtually to the same
thing, the total energy of the system is supposed to be reduced — either ac-
tually, or by calculation from the known ratio of transformation of the various
forms of energy — to energy of some one kind ; then the statement is equivalent
to this : that the total energy of any one form to which the energy of a given
system of bodies is reducible is unalterable so long as the system is not acted
on from without. Practically it is always possible, in one way or another, to
convert the whole of the energy possessed by any body or system of bodies
into heat, but it cannot be all converted without loss into any other form of
energy ; hence the principle stated at the beginning of this article can be
enunciated in the closest conformity with the direct results of experiment by
saying that, so long as any system of bodies is not acted on from without,
the total quantity of heat that can be obtained from it is unalterable by any
changes. which may go on within the system itself. For instance, a quantity
of air compressed into the i-eservoir of an air-gun possesses energy which is
represented partly by the heat which gives to it its actual temperature above
the absolute zero (460), and partly by the work which the air can do in expand-
ing. This latter portion can be converted into heat in various ways, as, for
example, by allowing the air to escape through a system of capillary tubes
so fine that the air issues from them without any sensible velocity ; if, how-
ever, the expanding air be employed to propel a bullet from the gun, it
produces considerably less heat than in the case previously supposed, the
deficiency being represented for a time by the energy of the moving bullet,
but reappearing in the form of heat in the friction of the bullet against the
air, and, when the motion of the bullet is destroyed, by striking against an
inelastic obstacle at the same level as the gun. But whatever the mode and
however numerous the intermediate steps by which the energy of the com-
pressed air is converted into heat, the total quantity of heat finally obtainable
from it is the same.

54 Gravitation and Molecular Attraction. [66-

BOOK II.

GRAVITATION AND MOLECULAR ATTRACTION.

CHAPTER L
GRAVITY. CENTRE OF GRAVITY. THE BALANCE,

66. Universal attraction: its laws. — Uiiiversal attractiofi is a force
in virtue of which the material particles of all bodies tend incessantly to
approach each other ; it is a mutual action, however, which all bodies, at
rest or in motion, exert upon one another, no matter how great or how small
the space between them may be, or whether this space be occupied or un-
occupied by other matter.

A vague hypothesis of the tendency of the matter of the earth and stars
to a common centre was adopted even byDemocritus and Epicurus. Kepler
assumed the existence of a mutual attraction between the sun, the earth, and
the other planets. Bacon, Galileo, and Hooke also recognised the existence
of universal attraction. But Newton was the first who established the law,
and the universality of gravitation.

Since Newton's time the attraction of matter by matter was experimentally
established by Cavendish. This eminent English physicist succeeded, by
means of a delicate torsion balance (89), in rendering visible the attraction
between a large leaden and a small copper ball.

The attraction between any two bodies is the resultant of the attractions
of each molecule of the one upon every molecule of the other according to
the law of Newton, which may be thus expressed : the attraction between
two material particles is directly proportional to the p?'odzict of their masses
and inversely proportional to the square of their distances asunder. To
illustrate this, we may take the case of two spheres, which, owing to their
symmetry, attract each other just as if their masses were concentrated in
their centres. If without other alteration the mass of one sphere were
doubled, tripled, &c., the attraction between them would be doubled, tripled,
&c. If, however, the mass of one sphere being doubled, that of the other
were increased three times, the distance between their centres remaining the
same, the attraction would be increased six times. Lastly, if, without alter-
ing their masses, the distance between their centres were increased from i
to 2, 3, 4 ... . units, the attraction would be diminished to the 4th, 9th,

-67j Terrestrial Gravitation. 55

1 6th .... part of its former intensity. In short, if we define the unit of
attraction as that which would exist between two units of mass whose
distance asunder was the unit of length, the attraction of two molecules,
having the masses vi and ni' , at the distance r, would be expressed by

67. Terrestrial gravitation. — The tendency of any body to fall towards
the earth is due to the mutual attraction of that body and the earth, or to
terrestrial gravitation, and is, in fact, merely a particular case of universal
attraction.

At any point of the earth's surface, the direction of gravity — that is, the
line which a falling body describes — is called the vertical line. The vertical
lines drawn at different points of the earth's surface converge very nearly to
the earth's centre. For points situated on the same meridian the angle con-
tained between the vertical lines equals the difference between the latitudes
of those points.

The directions of the earth's attraction upon neighbouring bodies, or upon
different molecules of one and the same body, must, therefore, be considered
as parallel, for the two vertical lines form the sides of a triangle whose vertex
is near the earth's centre, about 4,000 miles distant, and whose base is the
small distance between the molecules under consideration.

A plane or line is said to be horisontat when it is perpendicular to the
vertical line.

The vertical line at any point of the globe is generally determined by the
plui)ib-li)ie (fig. 40), which consists of a weight attached to the end of a string.
It is evident that the weight cannot be in equiUbrium un-
less the direction of the earth's attraction upon it passes
through the point of support, and therefore coincides with
that of the string.

The horizontal plane is also determined with great
ease, since it coincides, as will be afterwards shown, with
the level surface of every liquid when in a state of equili-
brium.

When the mean figure of the earth has been approxi-
mately determined, it becomes possible to compare the
direction of the plumb-line at any place with that of the
normal to the mean figure at that place. When any differ-
ence in these directions can be detected, it constitutes a
deviation of the plumb-line, and is due to the attraction of ^p-

some great mass of matter in the neighbourhood, such as
a mountain. Thus, in the case of the mountain of Schehallien, in Perthshire,
it was found by Dr. Maskelyne that the angle between the directions of two
plumb-lines, one at a station to the north, and the other to the south, of the
mountain was greater by 11'^ -6 than the angle between the normals of the
mean surface of the earth at those points ; in other words, each plumb-line
was deflected by about 6" towards the mountain. By calculating the volume
and mass of the mountain, it was inferred from this observation that the
mean density of the mountain was to that of the earth in the ratio of 5 : 9,
and that the mean density of the earth is about five times that of water— a

Gravitation and Molecular Attraction.

[67-

result agreeing pretty closely with that deduced from Cavendish's experiment
referred to in the last article.

68. Centre of gravity, its experimental determination. — Into what-
ever position a body may be turned with respect to the earth, there is a
certain point, invariably situated with respect to the body, through which
the resultant of the attracting forces between the earth and its several mole-
cules always passes. This point is called the centre of gravity ; it may be
within or without the body, according to the form of the latter ; its existence,
however, is easily established by the following considerations : let vi m' m"
m'". . . . (fig. 41) be molecules of any body. The earth's attraction upon
these molecules will constitute a system of parallel forces, having a common
vertical direction, whose resultant will be found by seeking first the resultant
of the forces which act on any two molecules, m and in\ then that of this
resultant and a third force acting on in'\ and so on until we arrive at the
final resultant W, representing the weight of the body and applied at a
certain point G. If the body be now turned into the position shown in
fig. 42, the molecules ;;/, ;//', in". . . . will continue to be acted on by the

Fig. 41.

same forces as before, the resultant of the forces on ;// and w' will pass
through the same point 0 in the line mm\ the following resultant will again
pass through the same point o' in om", and so on up to the final resultant
P, which will still pass through the same point C, which is the centre of
gravity.

To find the centre of gravity of a body is a purely geometrical problem ;
in many cases, however, it can be at once determined. For instance, the
centre of gravity of a right line of uniform density is the point which bisects
its length ; in the circle and sphere it coincides with the geometrical centre ;
in cylindrical bars it is the middle point of the axis. The centre of gravity
of a plane triangle is in the line which joins any vertex with the middle of
the opposite side, and at a distance from the vertex equal to two-thirds of
this line : in a cone or pyramid it is in the line which joins the vertex with
the centre of gravity of the base, and at a distance from the vertex equal to
three-fourths of this line. These rules, it must be remembered, presuppose
that the several bodies are of uniform density.

In order to determine experimentally the centre of gravity of a body, it
is suspended by a string in two different positions, as shown in figs. 43 and
44 ; the point where the directions AB and CD of the string in the two ex-

70]

Different States of EquilibriuDi.

Fig. 43

Fig. 44.

periments intersect each other is the centre of gravity required. For, the
resultant of the earth's attraction being a vertical force applied at the centre
of gravity, the body can only be in equilibrium when the point lies vertically
under the point of suspension ; that is, in the prolongation of the suspended
string. But the centre of gravity,
being in AB as well as in CD, must
coincide with the point of intersec-
tion of these two lines.

The centre of gravity of a thin
piece of cardboard of irregular
shape, for instance, may be found
by balancing it in two positions on
a knife-edge ; the centre of gravity
will then lie in the intersection of
the two lines.

69. Equilibrium of heavy
bodies. — Since the action of gravity
upon a body reduces itself to a
single vertical force applied at the
centre of gravity and directed to-
wards the earth's centre, equili-
brium will be established only when this resuhant is balanced by the
resultant of other forces and resistances acting on the body at the fixed point
through which it passes.

When only one point of the body is fixed, it will be in equilibrium if the
vertical line through its centre of gravity passes through the fixed point. If
more than one point is supported, the body will be in equilibrium if a vertical
line through the centre of gra\'ity passes through a point within the polygon
formed by joining the points of support.

The Leaning Tower of Pisa continues to stand because the vertical line
drawn through its centre of gravity passes within its base.

It is easier to stand on our feet than on stilts, because in the latter case
the smallest motion is sufficient to cause the vertical line through the centre
of gravity of our bodies to pass outside the supporting base, which is here
reduced to a mere line joining the feet of the stilts. A man carrying a load
on his back must lean forward : if he carries it in the left hand he must incline
the upper part of his body to the right, for otherwise the centre of gravity of
the body and of the load would fall outside the line joining the feet and he
would fall. Again, it is impossible to stand on one leg if we keep one side
of the foot and head close to a vertical wall, because the latter prevents
us from throwing the body's centre of gravity vertically above the supporting
base.

70. Sifferent states of equilibrium. — Although a body supported by a
fixed point is in equilibrium whenever its centre of gravity is in the vertical
line through that point, the fact that the centre of gravity tends incessantly
to occupy the lowest possible position leads us to distinguish between three
states of equilibrium — stable, unstable, neutral.

A body is said to be in stable equilibrium if it tends to return to its first
position after the equilibrium has been slightly disturbed. Every body is in

Gravitation and Molecular Attraction.

[70-

this state when its position is such that the sHghtest alteration of the same
elevates its centre of gravity ; for the centre of gravity will descend again
when permitted, and after a few oscillations the body will return to its
original position.

The pendulum of a clock continually oscillates about its position of stable
equilibrium, and an t.gg on a level table is in this state when its long axis
is horizontal. We have another illustration in the toy represented in the
adjoining fig. 45. A small figure cut in ivory is made to stand on one foot
at the top of a pedestal by being loaded with two leaden balls, «, b, placed
sufficiently low to throw the centre of gravity, g, of
the whole compound body below the foot of the
figure. After being disturbed, the httle figure oscil-
lates like a pendulum, having its point of suspen-
sion at the toe, and its centre of gravity at a lower
point, g.

A body is said to be in imstable equilibrium when,
after the slightest disturbance, it tends to depart still
more from its original position. A body is in this state
when its centre of gravity is vertically above the point
of support, or higher than it would be in any adjacent
position of the body. An egg standing on its end, or a
stick balanced upright on the finger, is in this state.

Lastly, if in any adjacent position a body still
remains in equilibrium, its state of equilibrium is
said to be jieutral. In this case an alteration in the
Fis- 45- position of the body neither raises nor lowers its

centre of gravity. A perfect sphere resting on a horizontal plane is in this

Fig. 46 represents three cones. A, B, C, placed respectively in stable,
unstable and neutral equilibrium upon a horizontal plane. The letter g in

each shows the position
of the centre of gravity.
71. The balance. —
The balance is an in-
strument for determi-
ning the relative weights
or masses of bodies.
There are many varie-
ties.

The ordinary balance (fig. 47) consists of a lever of the first kind, called
the beam, AB, with its fulcrum in the middle ; at the extremities of the beam
are suspended two scale-pans, C and D, one intended to receive the object
to be weighed, and the other the counterpoise. The fulcrum consists of a
steel prism, n, commonly called a knife-edge, which passes through the beam,
and rests with its sharp edge, or axis of suspension, upon two supports ; these
are formed of agate, in order to diminish the friction. A needle or pointer
is fixed to the beam, and oscillates with it in front of a graduated arc, a :
when the beam is perfectly horizontal the needle points to the zero of the
graduated arc.

-72]

Conditions to be satisfied by a Balance.

Since by (40) two equal forces in a lever of the first kind cannot be in
equilibrium unless their leverages are equal, the length of the arms «A and
«B ought to remain equal during the process of weighing. To secure this
the scales are suspended from hooks, whose curved parts have sharp edges,
and rest on similar edges at the ends of the beam. In this manner the
scales are in effect supported on mere points, which remain unmoved during
the oscillations of the beam. This mode of suspension is represented in

fig- 47-

72. Conditions to be satisfied by a balance. — A good balance ought
to satisfy the following conditiQns : —

i. The two arms of the beam ought to be precisely equal, otherwise,
according to the principle of the lever, unequal weights will be required to
produce equilibrium. To test whether the arms of the beam are equal,

ihi'iiiiiiiaiiiiiiiiiii'iiiiriHiiiiniiiiiriiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

iiiiiiiiiimiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

iiiiiiiiiiiiiiiiii

Fig. 47.

weights are placed in the two scales, until the beam becomes horizontal ;
the contents of the scales being then interchanged, the beam will remain
horizontal if its arms are equal, but if not, it will descend on the side of the
longer arm.

ii. The balance ought to be z?t equilibrium whefi the scales are empty., for
otherwise unequal weights must be placed in the scales in order to produce
equilibrium. It must be borne in mind, however, that the arms are not
necessarily equal, even if the beam remains horizontal when the scales are
empty ; for this result might also be produced by giving to the longer arm
the lighter scale.

iii. The beam being horizo7ttal., its centre of gravity ought to be i?t the ■
same vertical line with the edge of the fulcrum, and a little below the latter,
for otherwise the beam would not be in stable equilibrium (70).

Gravitation and Molecular' Attraction.

[72-

The effect of changing the position of the centre of gravity may be shown
by means of a beam (fig. 48), whose fulcrum, being the nut of a screw, a, can
be raised or lowered by turning the screw-head, b.

When the fulcrum is at the top of the groove c, in which it slides, the
centre of gravity of the beam is below its edge, and the latter oscillates

■ -^

Fig. 48.

freely about a position of stable equilibrium. By gradually lowering the
fulcrum its edge may be made to pass through the centre of gravity of the
beam when the latter is in neutral equilibrium ; that is to say, it no longer
oscillates, but remains in equilibrium in all positions. When the fulcrum
is lowered still more, the centre of gravity passes above its edge, the
beam is in a state of unstable equilibrium, and is overturned by the least
displacement.

"JT). Belicacy of the balance. — A balance is said to be delicate when a
very small difference between the weights in the scales causes a perceptible
deflection of the pointer.

Let A and B (figs. 49 and 50) be the points from which the scale-pans
are suspended, and C the axis of suspension of the beam. A, B, and C are

Fig. 49. Fig. 50.

assumed to be in the same sti'aight line, according to the usual arrangement.
Suppose weights P and Q to be in the pans, suspended from A and B re-
spectively, and let G be the centre of gravity of the beam ; then the beam
will come to rest in the position shown in the figure, where the line DCN is
vertical, and ECG is the direction of the pointer. According to the above
statement, the greater the angle ECD for a given difference between P and
Q, the greater is the delicacy of the balance. Draw ON at right angles
to CO.

Let W be the weight of the beam, then from the properties of the lever (40)
it follows that measuring moments with respect to C, the moment of P equals
the sum of the moments of Q and W, a condition which at once leads to the
relation

(P-Q)AC = WxGN

74]

Physical and Chejnical Balances.

Now it is clear that for a given value of CG the angle GCN (that is ECD,
which measures the delicacy) is greater as ON is greater ; and from the
formula it is clear that for a given value of P — Q we shall have GN greater
as AC is greater, and as W is less. Again, for a given value of GN the
angle GCN is greater as GC is less. Hence the means of rendering a
balance delicate are —

i. To make the arms of the balance long.

ii. To 7nake the weight of the beam as small as is consistent with its
rigidity.

iii. To brifi^ the coitre of gravity of the beam a very little below the point
of support.

Moreover, since friction will always oppose the action of the force that
tends to preponderate, the balance will be rendered more delicate by diminish-
ing friction. To secure this advantage the edges from which the beam and
scales are suspended are made as sharp and as hard as possible, and the
supports on which they rest are very smooth and hard. This is effected by
the use of agate knife-edges. And, further, the pointer is made long, since
its elongation renders a given deflection more perceptible by increasing the
arc which its end describes.

The sensitiveness of a balance is expressed by the ratio of the smallest
weight, which will produce a measurable deflection of the pointer, to the load.

74. Physical and chemical balances. — Fig. 51 represents one of the
accurate balances ordinarily used for chemical analysis. Its sensitiveness is

Fig. 5

such that when charged with a kilogramme (1,000 grms.) in each scale an
excess of a tenth of a milligramme (jo^o of ^ bi™-) i" either scale produces
a very perceptible deflection of the index.

62 Gravitatio7t and Molecular Attraction. [74-

In order to protect the balance from air-currents, dust, and moisture,
it is always, even when weighing, surrounded by a glass case, Avhose front
slides up and down, to enable the operator to introduce the objects to be
weighed. Where extreme accuracy is desired the case is constructed so
that the space may be exhausted, and the weighing made in vacuo.

In order to preserve the edge of the fulcrum as much as possible, the
whole beam, BB, with its fulcrum K, can be raised from the support on
which the latter rests by simply turning the button O outside the case.

The horizontality of the beam is determined by means of a long index,
which points downwards to a graduated arc near the foot of the supporting
pillar. Lastly, the button C serves to alter the sensitiveness of the balance ;
by turning it, the centre of gravity of the beam can be made to approach or
recede from the fulcrum (6g).

75. iviethod of double weighing-. — Even if a balance be not perfectly
accurate, the true weight of a body may still be determined by its means. To
do so, the body to be weighed is placed in one scale, and shot or sand poured
into the other until equilibrium is produced ; the body is then replaced
by known weights until equilibrium is re-established. The sum of these
weights will necessarily be equal to the weight of the body, for, acting under
precisely the same circumstances, both have produced precisely the same
effect.

The exact weight of a body may also be determined by placing it suc-
cessively in the two pans of a balance, and then deducing its true weight.

For having placed in one pan the body to be weighed, whose true weight
is X, and in the other the weight /, required to laalance it, let a and b be
the arms of levers corresponding to jir and /. Then from the principle of
the lever (40) we have ax=pb. Similarly, if/j is the weight when the body
is placed in the other pan, then bx = ap^. Hence abx'^ = abpp^^ from which
x=^^ppy This method was invented by Pere Amiot, but is ordinarily
known as Bordds MetJwd.

Jolly made use of a very delicate balance to determine the constant of
gravity. The balance was placed in a room in the tower of the University
of Munich, and to each of the scale-pans was attached, by a wire 21 metres
in length, a second scale-pan. A mass of mercury of 5 kilogrammes contained
in a glass vessel was first counterpoised in the upper scale-pans ; it was then
moved to the lower one, and it was found necessary to add 31 "683 mgr. to
the upper pan in order to counterbalance the increase in attractiveness due
to the greater force in the lower pan.

Taking the radius of the earth at Munich at 6,365,722 metres, the number
calculated from the formula in (82) is 33 mgr. ; a sufficiently close result
when the difficulties of the experiments are taken into account.

A large lead sphere was then placed immediately below the mass in the
lower pan, and produced a measurable attraction. From the attraction thus
produced by the known mass of the lead it was possible to deduce the mass
and the mean density of the earth (67) ; the number obtained was 5-69.
Similar experiments' have been made by Prof Poynting and have led to the
same number.

-76]

Laivs of Falling Bodies.

CHAPTER II.

LAWS OF FALLING BODIES. INTENSITY OF TERRESTRIAL GRAVITY.
THE PENDULUM.

76. Xiaws of falling- bodies. — Since a body
falls to the ground in consequence of the earth's
attraction on eacJi of its molecules, it follows that,
everything else being the same, all bodies, great
and small, light and heavy, ought to fall with equal
rapidity, and a lump of sand without cohesion should,
during its fall, retain its original form as perfectly
as if it were compact stone. The fact that a stone
falls more rapidly than a feather is due solely to the
unequal resistances opposed by the air to the descent
of these bodies ; in a •vacuum all bodies fall with
eqtial rapidity. To demonstrate this by experiment
a glass tube about two yards long (fig. 52) may be
taken, having one of its ends completely closed,
and a brass cock fixed to the other. After having
introduced bodies of different weights and densities
(pieces of lead, paper, feather, &c.) into the tube,
the air is withdrawn from it by an air-pump,, and
the cock closed. If the tube be now suddenly re-
versed, all the bodies will fall equally quickly. On
introducing a little air and again inverting ^he tube,
the lighter bodies become slightly retarded, and
this retardation increases with the quantity of air
introduced.

The resistance opposed by the air to falling
bodies is especially remarkable in the case of
liquids. The Staubbach in Switzerland is a good
illustration ; an immense mass of water is seen fall-
ing over a high precipice, but before reaching the
bottom it is shattered by the air into the finest
mist. In a vacuum, however, liquids fall like
solids without separation of their molecules. The
ivater-hamme}' illustrates this : the instrument con-
sists of a thick glass tube about a foot long, half
filled with water, the air having been expelled by
ebullition previous to closing one extremity with the
blow-pipe. When such a tube is suddenly inverted,
the water falls in one undivided mass against the

Gravitation and Molecular Attraction.

[76-

other extremity of the tube, and produces a sharp dry sound, resembhng that

which accompanies the shock of two solid bodies.

From Newton's law (66) it
follows that when a body falls
to the earth the force of attrac-
tion which causes it to do
so increases as the body ap-
proaches the earth. Unless the
height from which the body
falls, however, be very great,
this increase will be altogether
inappreciable, and the force in
question may be considered as
constant and continuous. If
the resistance of the air were
removed, therefore, the motion
of all bodies falling to the earth
would be uniformly accelerated,
and would ol^ey the laws already
explained (49).

TT. Atwood's macbine. —
Several instruments have been
invented for illustrating and
experimentally verifying the
laws of falling bodies. Galileo,
who discovered these laws in
the early part of the seven-
teenth century, illustrated them
by means of bodies falling down
inclined planes. The great
object of all such instruments
is to diminish the rapidity of
the fall of bodies without
altering the character of their
motion, for by this means
their motion may not only be
better observed, but it will be
less modified by the resistance
of the air (48).

The most convenient instru-
ment of this kind is that invented
by Atwood at the end of the
last century, and represented in
fig. 53. It consists of a stout
pillar of wood, about 2| yards
high, at the top of which is a
brass pulley, whose axle rests and
turns upon four other wheels, called jtiction wheels, inasmuch as they serve
to diminish friction. Two equal weights, M and M', are attached to the ex-

Fig. S3-

-77] Atlvood's Machine. ' 65

tremities of a fine silk thread, which passes round the pulley ; a timepiece,
H, fixed to the pillar, is regulated by a seconds pendulum, P, in the usual
way ; that is to say, the oscillations of the pendulum are communicated to a
ratchet, whose two teeth, as seen in the figure, fit into those of the ratchet
wheel. The axle of this wheel gives motion to the seconds hand of the dial,
and also to an eccentric behind the dial, as shown at E by a separate figure.
This eccentric plays against the extremity of a lever D, which it pushes
until the latter no longer supports the small plate i ; and thus the weight M,
which at first rested on this plate, is suddenly exposed to the free action of
gravity. The eccentric is so constructed that the little plate / falls precisely
when the hand of the dial points to zero.

The weights M and M', being equal, hold each other in equilibrium ;
the weight M, however, is made to descend slowly by putting a small bar or
overweight jh upon it ; and, to measure the spaces which it describes, the rod
or scale Q is divided into feet and inches, commencing from the plate i.
To complete the instrument there are a number of plates, A, A', C, <Z\ and
a number of rings, B, B', which may be fixed by screws at any part of the
scale. The plates arrest the descending weight M, the rings only arrest the
bar or overweight ;;/, which was the cause of motion, so that after passing
through them, the weight M, in consequence of its inertia, will move on
uniformly with the velocity it had acquired on reaching the ring. The
several parts of the apparatus being described, a few words will suffice to
explain the method of experimenting.

Let the hand of the dial be placed behind the zero point, the lever D
adjusted to support the plate /, on which the weight M with its o\erweight
HI rests, and the pendulum put in motion. As soon as the hand of the dial
points to zero the plate z will fall, the weights M and w will descend, and by
a little attention and a few trials it will be easy to place a plate A so that M
may reach it exactly as the dial indicates the expiration of one second. To
make a second experiment let the weights M and ;;/, the plate /, and the
lever D be placed as at first ; remove the plate A, and in its place put a ring,
B, so as to arrest the overweight m just when the weight M would have
reached A ; on putting the pendulum in motion again it will be easy, after a
few trials, to put a plate, C, so that the weight M may fall upon it precisely
when the hands of the dial point to two seconds. Since the overweight Jii
in this experiment was arrested by the ring B at the expiration of one second,
the space BC was described by M in one second purely in virtue of its own
inertia, and consequently by (24) BC will indicate the velocity of the falling-
mass at the expiration of one second.

Proceeding in the same manner as before, let a third experiment be made
in order to ascertain the point B' at which the weights M and in arrive after
the lapse of two seconds, and putting a ring at B', ascertain by a fourth
experiment the point C at which M arrives alone, three seconds after the
descent commenced ; WC will then express the velocity acquired after a
descent of two seconds. In a similar manner, by a fifth and sixth experiment,
we may determine the space OB" described in three seconds, and the velo-
city B"C" acquired during those three seconds, and so on ; we shall find
that B'C is twice, and B''C" three times as great as BC — in other words,
that the velocities BC, B'C, B"C" increase in the same proportion as the

66 Gravitation and Molecular Attraction. [77-

times (i, 2, 3, . . . seconds) employed in their acquirement. By the defi-
nition (49), therefore, the motion is uniformly accelerated. The same ex-
periments will also serve to verify and illustrate the four laws of uniformly
accelerated motion as enunciated in (49). For example, the spaces OB,
OB', OB", .... described from a state of rest in i, 2, 3, ... . seconds,
will be found to be proportional to the numbers i, 4, 9 . . . ; that is to say,
to the squares of those numbers of seconds, as stated in the third law.

Lastly, if the overweight in be changed, the acceleration or velocity BC
acquired per second will also be changed, and we may easily verify the
assertion in (27), that force is proportional to the product of the mass moved,
into the acceleration produced in a given time. For instance, assuming the
pulley to be so light that its inertia can be neglected, then if m weighed half
an ounce, and M and M' each 15I ounces, the acceleration BC would be found
to be six inches ; whilst if m weighed one ounce, and M and M' each 63.3
ounces, the acceleration BC would be found to be three inches.

Now in these cases the forces producing motion, that is the overweights,
are in the ratio of i : 2 ; while the products of the masses and the accelera-
tions are in the ratio of (|+ 15I -1- 15I) x 6 to (i + 63^ + 63^) x 3 ; that is, they
are also in the ratio i : 2. Now the same result is obtained in whatever
way the magnitudes of ;/;, M, and M' are varied, and consequently in all
cases the ratio of the forces producing motion equals the ratio of the mo-
menta generated.

78. nXorin's apparatus. — The principle of this apparatus, the original
idea of which is due to General Poncelet, is to make the falling body trace
its own path. Fig. 54 gives a view of the whole apparatus, and fig. 55
gives the details. The apparatus consists of a wooden framework, about
7 feet high, which holds in a vertical position a very light wooden cylinder,
M, which can turn freely about its axis. This cylinder is coated with
paper divided into squares by equidistant horizontal and vertical lines. The
latter measure the path traversed by the body falling along the cylinder,
while the horizontal lines are intended to divide the duration of the fall into
equal parts.

The falling body is a mass of iron, P, provided with a pencil which is
pressed against the paper by a small spring. The iron is guided in its fall
by two light iron wires which pass through guide-holes on the two sides
The top of this mass is provided with a tipper which catches against the end
of a bent lever, AC. This being pulled by the string K attached at A, the
weight falls. If the cylinder M were fixed, the pencil would trace a straight
line on it ; but if the cylinder moves uniformly, the pencil traces the line
w;/, which serves to deduce the law of the fall.

The cylinder is rotated by means of a weight, Q, suspended to a cord
which passes round the axle G. At the end of this is a toothed wheel, r,
which turns two endless screws, a and b, one of which turns the cylinder,
and the other two vanes, .rand x' (fig. 55). At the other end is a ratchet
wheel, in which fits the end of a lever, B ; by pulling at a cord fixed to the
other end of B, the wheel is liberated, the weight Q descends, and the whole
system begins to turn. The motion is at first accelerated, but as the air
offers a resistance to the vanes (48), which increases as the rotation becomes
more rapid, the resistance finally equals the acceleration which gravity tends

-78]

Marines Apparatus.

to impart. From this time the motion becomes uniform. This is the case
■when the weight Q has traversed about three-quarters of its course ; at this
moment the weight P is detached by pulling the cord K, and the pencil then
traces the curve »ui.

If, by means of this curve, we examine the double motion of the pencil
on the small squares which divide the paper, we see that, for displacements

I-^'g- 55-

f ig- 54-

I, 2, 3 .... in a horizontal direction, the displacements are i, 4, 9 . . . .
in a vertical direction. This shows that the paths traversed in the direction
of the fall are directly as the squares of the lines in the direction of the
rotation, which verifies the second law of falling bodies.

From the relation which exists between the two dimensions of the curve
w«, it is concluded that this curve is 2, parabola.

Y 2

Gravitation and Molecular Attraction.

[79-

79. The lengrtb of tlie compound pendulum. — The formula deduced in
article (55), and the conclusions which follow therefrom, refer to the case of the
simple or mathematical pendulum ; that is, to a single heavy point suspended
by a thread without weight. Such a pendulum has only an imaginary
existence, and any pendulum which does not realise these conditions is
called a compound or physical pendulum. The laws for the time of vibra-
tion of a compound pendulum are the same as those which regulate the
motion of the simple pendulum, though it will be necessary to define ac-
curately what is meant by the letigth of such a pendulum. A compound
pendulum being formed of a heavy rod terminated by a greater or less mass,
it follows that the several material points of the whole system will
strive to perform their oscillations in different times, their distances
from the axis of suspension being different, and the more distant
points requiring a longer time to complete an oscillation. From
this, and from the fact that being points of the same body they
must all oscillate together, it follows that the motion of the points
near the axis of suspension will be retarded, whilst that of the more
distant points will be accelerated, and between the two extremities
there will necessarily be a series of points whose motion will be
neither accelerated nor retarded, but which will oscillate precisely
as if they were perfectly free and unconnected with the other points
of the system. These points, being equidistant from the axis of
suspension, constitute a parallel axis known as the axis of oscil-
lation ; and it is to the distance between these two axes that the
term length of the coinpoitnd pendulum is applied : we may say,
therefore, that the leitgth of a compound pendulum is that of the
simple penduhnn which would describe its oscillations in the same
time.

Huyghens, the celebrated Dutch physicist, discovered that the
axes of suspension and oscillation are mutually convertible ; that
is to say, the time of oscillation will remain unaltered when the
pendulum is suspended from its axis of oscillation. This enables us
to determine experimentally the length of the compound pendulum.
P"or this purpose the reversible pendulum devised by Bohnenberger
and Kater may be used. One form of this (fig. 56) is a rod with
the knife-edges a and b turned towards each other. W and V are
lens-shaped masses the relative positions of which may be varied.
By a series of trials a position can be found such that the number
of oscillations of the pendulum in a given time is the same whether
it oscillates about the axis a or the axis b. This being so, the dis-
tance ab represents the length / of a simple pendulum which has
the same time of oscillation. From the value of /, thus obtained,
it is easy to determine the length of the seconds pendulum.
The length of the seconds pendulum — that is to say, of the pendulum
which makes one oscillation in a second — varies, of course, with the
force of gravity. The following table gives its value at the sea-level at
\-arious places as determined by observation. The accelerative effect of
gravity at these places, according to formula (55), is obtained in feet and

Fig. 56.

-80] Verification of the Laws of the Pendulum. 69

metres, by multiplying the length of the seconds pendulum, reduced to feet
and metres respectively, by the square of 3-14159 or 9-87.

Acceleration of Gravity in |

Latitude

Length of Pen-
dulum in inches

Feet

Metres

Hammerfest .

70°.4o'N.

39-1948

32-2364

9-8258

Aberdeen

39-1550

32-2066

9-8164

Konigsberg

39-1507

32-2002

9-8142

Manchester

39-1466

32-1968

9-8134

Dublin .

39-1461

32-1968

9-8132

Berlin .

39-1439

32-1945

9-8124

Greenwich

39-1398

32-1912

9-8115

Paris

39-1285

32-1819

9-8039

Rome

39-1145

32-1712

9-8053

New York

39-1012

32-1594

9-8019

Washington

39-0968

32-1558

9-8006

Madras .

39-0268

32-0992

9-7836

Ascension

39-0242

32-0939

9-7817

St. Thomas

39-0207

32-0957

9-7826

Cape of Good Hope

2,1>

55 s.

39-0780

32-1404

9-7962

Consequently, \g or the space described in the first second of its motion
by a body falling in vacuo from a state of rest (49) is

16-0478 feet or 4-891 metres at St. Thomas,
16-0956 „ „ 4-905 „ at London, and
16-1182 „ „ 4-913 „ at Hammerfest.

In all calculations which are merely used for the sake of illustration we
may take 32 feet, or 9-8 metres, as the accelerative effect due to gravity.

From observations of this kind, after applying the necessary corrections,
and taking into account the effect of rotation (82), the form of the earth can
be deduced.

80. Verification of the laws of the pendulum. — In order to verify the
laws of the simple pendulum (55) we are compelled to employ a compound
one, whose construction differs as little as possible from that of the former.
For this purpose a small sphere of a very dense substance, such as lead or
platinum, is suspended from a fixed point by means of a very fine metal wire.
A pendulum thus formed oscillates almost like a simple pendulum, whose
length is equal to the distance of the centre of the sphere from the point of
suspension.

In order to verify the isochronism of small oscillations, it is merely necessary
to count the number of oscillations made in equal times, as the amplitudes of
these oscillations diminish from 3 degrees to a fraction of a degree ; this
number is found to be constant.

That the time of vibration is proportional to the square root of the length
is verified by causing pendulums, whose lengths are as the numbers i, 4,
9, .... to oscillate simultaneously. The corresponding numbers of oscil-
lations in a given time are then found to be proportional to the fractions

Gravitation and UTo/eadar Attraction.

[80-

I, i, f, &c., .... which shows that the tunes of oscillation increase as the
numbers i, 2, 3, . . . . &c.

By taking several pendulums of exactly ecjual length, B, C, D (fig. 57),
but with spheres of different substances — lead,
copper, ivory — it is found that, neglecting the
resistance of the air, these pendulums oscillate
in equal times, thereby showing that the acce-
lerative effect of gravity on all bodies is the
same at the same place.

By means of an arrangement resembling the
above, Newton verified the fact that the masses
of bodies are determined by the balance ; which,
it will be remarked, lies at the foundation of
the measure of force (28). For it will be seen
on comparing (54) and (55) with (49) that the
law of the time of a small oscillation is obtained
on the supposition that the force of gravity on
all bodies is represented by M.g, in which M is
determined by the balance. In order to verify
this, he had made two round equal wooden
boxes ; he filled one with wood, and as nearly
as possible in the centre of oscillation of the
other he placed an ecjual weight of gold. He
then suspended the boxes by threads eleven
feet long, so that they formed pendulums exactly
equal so far as weight, figure, and resistance of
the air were concerned. Their oscillations were
performed in exactly the same time. The same
results were obtained when other substances
were used, such as silver, lead, glass, sand, salt, wood, water, corn. Now all
these bodies had equal weights, and being contained in the same boxes they
experienced the same resistance by the air, and if the inference, that therefore
they had equal masses, had been erroneous, by as little as the one-thou-
sandth part of the whole, the experiment would have detected it.

81. Application of the pendulum to Clocks. — The regulation of the
motion of clocks is effected by means of pendulums, that of watches by
balaiice-springs. Pendulums were first applied to this purpose by Huyghens
in 1658, and in the same year Hooke applied a spiral spring to the balance
of a watch. The manner of employing the pendulum is shown in fig. 58.
The pendulum rod passing between the prongs of a fork a communicates its
motion to a rod i^, which oscillates on a horizontal axis 0. To this axis is
fixed a piece ;;/;;, called an escapei/ietit or crutch., terminated by two projec-
tions or pallets., which work alternately with the teeth of the escapemeiif
ivheel R. This wheel being acted on by the weight tends to move con-
tinuously, let us say, in the direction indicated by the arrow-head. Now, if
the pendulum is at rest, the wheel is held at rest by the pallet w, and with it
the whole of the clockwork and the weight. If, however, the pendulum
moves and takes the position shown by the dotted line, vi is raised, the
wheel escapes from the confinement in which it \\as held by the pallet, the

Fig. 57-

82]

Causes which modify Terrestrial Graviiatioii.

weight descends, and causes the wheel to turn until its motion is arrested by
the other pallet ;/ ; which, in consequence of the motion of the pendulum,
will be brought into contact with another tooth of the escapement wheel. In
this manner the descent of the weight is alternately permitted and arrested
— or, in a word, regulated— hy the pendulum. By
means of a proper train of wheelwork the motion of
the escapement is communicated to the hands of the
clock : and consecjuently their motion, also, is regu-
lated by the pendulum. In watches the watch spring-
plays the part of the weight in clocks.

The pendulum has also been used for measuring
great velocities. A large wooden box filled with sand
and weighing from 3 to 5 tons is coated with iron ;
against this arrangement, which is known as a ballistic
pendulum^ a shot is fired, and the deflection thereby
produced is observed. From the laws of the impact
of inelastic bodies, and from those of the pendulum,
the velocity of the ball may be calculated from the
amount of this deflection.

The gun may also be fastened to a pendulum ar-
rangement ; and, when fired, the reaction causes an
angular velocity,from which the pressure of the enclosed
gases can be deduced, and therefrom the initial velocity
of the shot,

82. Causes 'whicb modify tbe intensity of
terrestrial gravitation. — The intensity of the force
of gravity — that is, the value of ^ — is not the same in
all parts of the earth. It is modified by several causes,
of which the form of the earth and its rotation are the
most important.

i. The attraction which the earth exerts upon a
body at its surface is the sum of the partial attractions
w hich each part of the earth exerts upon that body,
and the resultant of all these attractions may be considered to act from a
single point — the centre. Hence, if the earth were a perfect sphere, a given
body would be equally attracted at any part of the earth's surface. The
attraction would, however, vaiy with the height above the surface. For small
alterations of level the differences would be inappreciable ; but for greater
heights and in accurate measurements observations of the value of g must
be reduced to the sea-level. The attraction of gravitation being inversel)'
as the square of the distance from the centre (66), we shall have

g : g^ = : ^— — -~ where g is the value of the acceleration of gravity at
K' (R + /i)

the sea level, g^ its value at any height //, and R is the radius of the earth.

From this, seeing that h is very small compared with R, and that therefore

its square may be neglected, we get by simple algebraical transformation

? p-R

Fig. 5S.

72 Gravitation and Molecular Attraction. [82-

But even at the sea-level the force of gravity varies in different parts in
consequence of the form of the earth. The earth is not a true sphere, but
an ellipsoid, the major axis of which is 12,754,796 metres, and the minor
12,712,160 metres. The distance, therefore, from the centre being greater at
the Equator than at the Poles, and as the attraction on a body is inversely
as the square of these distances, calculation shows that the attraction due to
this cause is gi,, greater at the Poles than at the Equator. This is what
would be true if, other things being the same, the earth were at rest.

ii. In consequence of the earth's rotation, the force of gravity is further
modified. If we imagine a body relatively at rest on the Equator, it really
shares the earth's rotation, and describes, in the course of one day, a circle
whose centre and radius are the centre and radius of the earth. Now, since
a body in motion tends by reason of its inertia to move in a straight line, it
follo\\s that to make it move in a circle, a force must be employed at each
instant to deflect it from the tangent (53). Consequently, a certain portion
of the earth's attraction must be employed in keeping the above body on the
surface of the earth, and only the remainder is sensible as weight or accele-
rating force. It appears from calculation that at the Equator the ^'Ca. part
of the earth's attraction on any body is thus employed, so that the magnitude
of^at the Equator is less by the jigth part of what it would be were the
earth at rest.

iii. As the body goes nearer the Poles the force of gravity is less and less
diminished by the effect of centrifugal force. For in any given latitude it
will describe a circle coinciding with the parallel of latitude in which it is
placed ; but as the radii of these circles diminish,
so does the centrifugal force until the Pole, where
the radius is null. Further, on the Equator the
centrifugal force is directly opposed to gravitation ;
in any other latitude only a component of the whole
force is thus employed. This is seen in fig. 59, in
which PP' represents the axis of rotation of the
earth, and EE' the Equator. At any given point
E on the Equator the centrifugal force is directed
along CE, and acts wholly in diminishing the
intensity of gravitation ; but on any other point, a,
nearer the Pole, the centrifugal force acting on a
right line ab at right angles to the axis PP', while gravity acts along c?C,
gravity is no longer directly diminished by centrifugal force, but only by its
component ad., which is less the nearer a is to the Pole.

The combined effect of these two causes — the flattening of the earth at
the Poles, and the centrifugal force — is to make the attraction of gravitation
at the Equator less by about the jjo^d part of its value at the Poles.

-84] Cohesion. 7S

CHAPTER III.

MOLECULAR FORCES.

83. ITature of molecular forces. — The various phenomena which bodies
present show that their molecules are under the influence of two contrary
forces, one of which tends to bring them together, and the other to separate
them from each other. The fii'st force, which is called molecular attraction.,
varies in one and the same body with the distance only. The second force
is due to the vis viva., or moving force, which the molecules possess. It is
the mutual relation between these forces, the preponderance of the one or the
other, which determines the molecular state of a body (4) — whether it be
solid, liquid, or gaseous.

Molecular attraction is only exerted at infinitely small distances. Its
effect is inappreciable when the distance between the molecules becomes
appreciable.

According to the manner in which it is regarded, molecular attraction is
designated by the terms cohesion, affinity, or adhesion.

84. Cohesion. — Cohesion is the force which unites adjacent molecules of
the same nature ; for example, two molecules of water, or two molecules of
iron. Cohesion is strongly exerted in solids, less strongly in liquids, and
scarcely at all in gases. Its strength decreases as the temperature mcreases,
because then the vis viva of the molecules increases. Hence it is that when
solid bodies are heated they first liquefy, and are ultimately converted into
the gaseous state, provided that heat produces in them no chemical change.

Cohesion varies not only with the nature of bodies, but also with the
arrangement of their molecules ; thus, the difference between tempered and
untempered steel (94) is due to a difference in the molecular arrangement
produced by tempering. Many of the properties of bodies, such as
tenacity, hardness, and ductility, are due to the modifications which this
force undergoes.

In large masses of liquids the force of gravity overcomes that of cohesion.
Hence liquids acted upon by the former force have no special shape ; they
take that of the vessel in which they are contained. But in smaller masses
cohesion gets the upper hand, and liquids assume then the spheroidal form.
This is seen in the drops of dew on the leaves of plants. It is also seen when
a liquid is placed on a solid which it does not moisten ; as, for example,
mercury upon wood. The experiment may also be made with water, by
sprinkling upon the surface of the wood some light powder, such as lyco-
podium or lampblack, and then dropping a little water on it. The following
experiment is an illustration of the force of cohesion causing a liquid to assume
the spheroidal form. A saturated solution of zinc sulphate is placed in a

74 Gravitation and Molecular Attraction. [84-

narrow-necked bottle (fig. 60), and a few drops of bisulphide of carbon, coloured
with iodine, made to float on the surface. If pure water be now carefiilly added,
so as to rest on the surface of the sulphate of zinc solution>
the bisulphide collects in the form of a flattened spheroid,
which presents the appearance of blown coloured glass, and
is larger than the neck of the bottle, provided a sufficient
quantity has been taken.
'|| 1^ j The force of cohesion of liquids may be illustrated and

Ij '<^p' I qx^vl measured as follows. A plane, perfectly smooth disc, D

l| (fig. 61), is suspended horizontally to one scale-pan ^ of a

delicate balance, and is accurately equipoised. A some-
what wide vessel of liquid is placed below, and the position
!• ig. DO. ^^ ^^ ^jg^ regulated by means of the sliding screw S until

it just touches the liquid. Weights are then carefully added to the other
scale-pan until the disc is detached from the liquid. In this way it has been
found that the weights required to detach the disc vary with the nature of
the liquid ; with a disc of 118 mm. diameter the numbers for waters, alcohol,
and turpentine were 59-4, 31, and 34 grammes respectively.

The results were the same whether the disc was of glass, of copper, or of
other metals, and they thus only depend on the nature of the Uquid. It is
a measure of the cohesion of the liquid, for a layer remains adhering to the
disc ; hence the weight on the other side does not separate the disc from
the liquid, but separates the particles of liquid from each other.

85. Affinity. — Chemical affinity, or ciionical attraction, is the force which
is exerted between molecules not of the same kind. Thus, in water, which
is composed of oxygen and hydrogen, it is affinity which unites these ele-
ments, but it is cohesion which binds together two molecules of water. In
compound bodies cohesion and affinity operate simultaneously, while in
simple bodies or elements cohesion has alone to be considered.

To affinity are due all the phenomena of combustion, and of chemical
combination and decomposition.

Those causes which tend to weaken cohesion are most favourable to affinity;
for instance, the action of affinity between substances is facilitated by their
division, and still more by reducing them to a liquid or gaseous state. It is
most powerfully exerted by a body in its nascent state — that is, the state in
which the body exists at the moment it is disengaged from a compound ; the
l)ody is then free and ready to obey the feeblest affinity. An increase of
temperature modifies affinity differently under different circumstances. In
some cases by diminishing cohesion, and increasing the distance between
the molecules, heat promotes combination. Sulphur and oxygen, which at
the ordinary temperature are without action on each other, combine to form
sulphur dioxide when the temperature is raised : in other cases heat tends
to decompose compounds by imparting to their elements an unequal expan-
sibility. Thus it is that many metallic oxides — as, for example, those of silver
and mercury — are decomposed, by the action of heat, into gas and metal.

86. Adhesion. — The molecular attraction exerted between \\\fisin-facesoi
bodies in contact is called adhesion.

i. Adhesion takes place between solids. If two leaden bullets are cut
with a penknife so as to form two equal and brightly polished surfaces, and

-86] Adhesion. 75

the two faces are pressed and turned against each other, until the^- are in the
closest contact, they adhere so strongly as to require a force of more than
100 grammes to separate them. The same experiment may be made with
two equal pieces of glass which are polished and made perfectly plane.
When they are pressed one against the other, the adhesion is so powerful
that they cannot be separated without breaking. As the experiment succeeds
in vacuo, it cannot be due to atmospheric pressure, but must be attributed to
a reciprocal action between the two surfaces. The attraction also increases
as the contact is prolonged, and is greater in proportion as the contact is
closer.

In the operation of glueing the adhesion is complete, for the pores and
crevices of the fresh surfaces being filled with liquid glue, so that there is no
empty space on drying, wood and glue form one
compact whole. In some cases the adhesion of
cemented objects is so powerful that the mass
breaks more readily at other places than at the
cemented parts. Both in glueing and cementing
the layer should be thin.

Soldering is due to cohesion ; the surface of
the metals must be quite clean, which is effected
by removing the layer of oxide, with which they
are usually coated, by acid or by borax. The
solder when it solidifies only adheres to clean
metal surfaces.

There is no real difference between adhesion
and cohesion ; thus when two freshly cut surfaces
of caoutchouc are pressed together, they adhere
with considerable force, and ultimately form one
compact solid mass.

ii. Adhesion also takes place between solids
and liquids. If we dip a glass rod into water, on
withdrawing it a drop will be found to collect at
its lower extremity, and remain suspended there.
As the weight of the drop tends to detach it, there
must necessarily be some force superior to this
weight which maintains it there ; this force is the
force of adhesion.

This is the cause why liquids when poured out
of a vessel so easily run down the outside ; it is prevented by greasing the
outer edge, and thus doing away with the adhesion.

The adhesion between liquids and solids is more powerful than that
between solids. Thus, if in the above experiment a thin layer of oil is inter-
posed between the plates they adhere firmly, but when pulled asunder each
plate is moistened by the oil, thus showing that in separating the plates the
cohesion of the plates is overcome, but not the adhesion of the oil to the
metal.

In the above case the solid is wetted by the liquid ; that is, some remains
adhering even when the drop falls. But liquids adhere to solids even when
they are not wetted. Thus if a smooth glass plate be suspended horizontally

Fig. 61

yG Gravitation and Moleadar Attraction. [86-

from one arm of a balance, and be counterpoised as in fig. 6i ; on sliding a
mercuiy level under the plate, so that they touch, a considerable weight must
be placed in the other pan so as to detach the plate from the mercury. Small
drops of mercury, too, adhere to the under side of a glass or porcelain plate.

iii. The force of adhesion operates, lastly, between solids and gases.
If a glass or metal plate be immersed in water, bubbles will be found to
appear on the surface. As air cannot penetrate into the pores of the plate,
the bubbles could not arise from the air which has been expelled. It is
solely due to the layer of air which covered the plate, and moistened it like
a liquid. In many cases when gases are separated in the nascent state
on the surface of metals — as in electrolysis — the layer of gas which covers
the plate has such a density that it can produce chemical actions more power-
ful than those which it can bring about in the free state.

The collection of dust on walls, writing and drawing with chalks and
pencils, depend on the adhesion of solids. Yet these are easily rubbed out,
for the adhesion is only to the surface layer. In writing with ink, and in
water-colour painting, the liquid penetrates into the pores, taking the solid
with it, which is left behind as the liquid evaporates, and hence the adhesion
of such writing and painting is far more complete.

88]

Elasticitv of Traction.

CHAPTER IV.

PROPERTIES PECULIAR TO SOLIDS,

87. Various special properties. — After having described the principal
properties common to soHds, hquids, and gases, we shall discuss the properties
peculiar to solids. They are elasticity of tfactio/7, elasticity of tordoiu elas-
ticity offlexit7-c, tenacity., ductility., and hardness.

88. Elasticity of traction. — Elasticity, as a general property of matter,
has been already mentioned (17), but simply in reference to the elasticity
developed by pressure ; in solids it may also be called into play by traction,
by torsion, and by flexure. The definitions there given require some exten-
sion. In ordinary life we consider
those bodies as highly elastic
which, like caoutchouc, imdergo
considerable change on the appli-
cation of only a small force. Yet
the force of elasticity is greatest in
many bodies, such as iron, which
do not seem to be very elastic. For
hy force of elasticity \?, understood
the force with which the displaced
particles tend to revert to their
original position, and which force is
equivalent to that which has brought
about the change. Considered from
this point of view, gases have the
least force of elasticity ; that of
liquids is considerably greater, and
is, indeed, greater than that of many
solids. Thus the force of elasticity
of mercury is greater than that of
caoutchouc, glass, wood, and stone.
It is, however, less than that of the
other metals, with the exception of
lead.

This seems discordant with or-
dinary ideas about elasticity ; but
it must be remembered that those
bodies which, by the exertion of a small force, undergo a considerable
change, generally have also the property- of undergoing this change without

Fig. 62.

78 Gravitation and Molecular Attraction. [88-

losing the property of reverting completely to their original state. They
have a wide limit of elasticity (17). Those bodies which require great force
to effect a change are also, for the most part, those on which the exertion
of a force produces a permanent alteration ; when the force is no longer
exerted, they do not completely revert to their original state.

In order to study the laws of the elasticity of traction, Savart used the
apparatus repi-esented in fig. 62. It consists of a wooden support from which
are suspended the rods or wires taken for experiment. At the lower ex-
tremity there is a scale-pan, and on the wire two points, A and B, are marked,
the distance between which is measured by means of the catJietonieter before
the weights are added.

The cathetometer consists of a strong upright brass support, K, divided
into millimetres, and which can be adjusted in an exactly vertical position
by means of levelling screws and the plumb-line. A small telescope, exactly
at right angles to the scale, can be moved up and down, and is provided with
a vernier which measures fiftieths of a millimetre. By adjusting the telescope
successively on the two points A and B, as represented in the figure, the
distance between these points is obtained on the graduated scale. Placing,
then, weights in the pan, and measuring again the distance from A to B, the
elongation is obtained.

By experiments of this kind it has been ascertained that for elasticity of
traction or pressure —

The alteration in length within the limits of elasticity is in proportion to
the length and to the load acting on the body., and is inversely as the cross
section.

It depends, moreover, on the specific elasticity; that is, on a special
property of the material of the body. If this coefficient be denoted by E,
and if the length, cross section, and load be respectively designated by /, s,
and P, then for the alteration in length, ^, we have

T^/P

^ = E — •

If in the above expression the sectional area be a square millimetre, and
P iDe one kilogramme, then

^ = E/, from which E = -'

which expresses by what fraction the length of a bar a square millimetre in
section is altered by a load of a kilogramme. This is called the coefficient of
elasticity ; it is a very small fraction, and it is therefore desirable to use its

reciprocal, that is - or ^, as the modulus of elasticity ; or the weight in

kilogrammes which applied to a bar would elongate it by its own length,
assuming it to be perfectly elastic. This coefficient is known as Yoiing^s
modulus. This cannot be observed, for no body is perfectly elastic, but it
may be calculated from any accurate observations by means of the above
formula.

-88] Elasticity of Traction. 79

The following are the best values for some of the principal substances : —

Wrought-iron
Steel-iron
Platinum
Copper
Slate .
Zinc
Brass .
Crown Glass
Plate Glass .
Rock Salt .
Marble
Lead .
Bone .
Acacia .
Pine .
Oak .
Whalebone .
Sandstone .
Fir

Gypsum
Ice

20,869

0-000048

18,809

0-000053

17,044

0-000058

12,500

0-000080

11,035

0-000090

8,734

0-000114

8,543

0-000117

7,917

0-000126

7,015

0-000142

4,230

0-000236

2,309

0-000382

1,803

0-000555

1,635

0-000612

1,262

0-000792

1,113

0-000890

921

0-001085

700

0-001428

631

0-001521

564

0-001768

400

0-002500

236

0-004236

Thus, to double the length of a wrought-iron wire a square millimetre in
section, would (if these were possible) require a weight of 19,000 kilogrammes ;
but a weight of 15 kilogrammes produces a permanent alteration in length
of jg^^th, and this is the limit of elasticity. The weight, which when applied
to a body of unit section, just brings about an appreciable permanent change,
is a measure of the //;;/// of elasticity. Whalebone has only a modulus of 700,
and experiences a permanent elongation by a weight of 5 kilogrammes ; its
limit is, therefore, relatively greater than that of iron. Steel has a high
modulus, along with a wide limit.

Longitudinal stretching is accompanied by a lateral contraction, and
the ratio of the contraction to the proportional stretching is known as
Poissoiis coefficiejit. It was taken by him to be |, but later experiments
have found the ratio to be about \. When a wire is stretched by a load to
within the limit of elasticity, some time often elapses before the full effect is
produced, and conversely when the load is removed, it does not at once
wholly resume its original condition, but a small portion of the deformation
remains, and it only reverts to its initial state after the lapse of some time.
This phenomenon which is met with in most elastic changes of form is
-called the clastic after action or effect., or the elastic fatigue.

Both calculation and experiment show that when bodies are lengthened
by traction their volume increases.

When weights are placed on a bar, the amount by which it is shortened,
or the coefficient of contraction., is equal to the elongation which it would
experience if the same weights were suspended to it, and is represented by
the above numbers.

8o Gravitation and Molecular Attraction. [88-

The influence of temperature on the elasticity of iron, copper, and brass
was investigated by Kohlrausch and Loomis. They found that the altera-
tion in the coefficient of elasticity by heat is the same as that which heat
produces in the coefficient of expansion and in the refractive power ; it is
also much the same as the change in the permanent magnetism, and in the
specific heat, while it is less than the alteration in the conductivity for elec-
tricity.

As an application may be mentioned Jolly's spriiig balance. This con-
sists of a long steel wire ab., wound in the form of a spiral, which is suspended
in front of an accurately graduated scale. To the
lower end of the spiral two scale-pans, c and d., are
hung by a thread, the lower one, d., dipping in a small
vessel of water on an adjustable support. The insti-u-
ment is graduated empirically by observing what dis-
placement of the mark in is produced by putting a
known weight in the scale-pan d. Knowing then once
for all the constant of the instrument, it is easy to
determine the weight of a body by reading the dis-
placement which it produces along the scale.

89. Elasticity of torsion. — The laws of the torsion
of wires were determined by Coulomb, by means of an
apparatus called the torsion balance (fig. 64). It consists
essentially of a metal wire, clamped at one end in a
support. A, and holding at the other a metal sphere, B,
to which is affixed an index, C. Immediately below this
there is a graduated circle, CD. If the needle is
turned from its position of equilibrium through a cer-
tain angle, which is the angle of torsio?!, the force
necessary to produce this effect is the force of torsion.
When, after this deflection, the sphere is left to itself,
the reaction of torsion produces its effect, the wire un-
twists itself, and the sphere rotates about its vertical
axis with increasing rapidity until it reaches its position
of equilibrium. It does not however, rest there ; in
virtue of its inertia it passes this position, and the wire
undergoes a torsion in the opposite direction. The
equilibrium being again destroyed, the wire again tends
to untwist itself, the same alterations are again pro-
duced, and the needle does not rest at zero of the scale
until after a certain number of oscillations about this
point have been completed.
By means of this'apparatus Coulomb found that when the amplitude of
the oscillations is within certain limits, the oscillations arc subject to the
following laws :

I. The oscillations arc very nearly isochronous.

II. For the same wire., the angle of torsion is proportional to the moment
of the force of torsion.

III. With the same force of torsion, and with wires of the same diameter,
the angles of torsion are proportional to the length of the wires.

Fig. 63.

-90]

Elasticity of Flexure.

IV. Tlic same force of /orsion being applied to wires of the savie length,
the angles of torsion are ijiversely proportio7tal to the fourth powers of the
diameters.

Wertheim examined the elasticity of torsion in the case of stout rods
by means of a different apparatus, and found that it is also subject to these
laws. He further found that, all dimensions being the same, different sub-
stances undergo different degrees of torsion for the
same force, and each substance has its own coefficient

of torsion, which is usually denoted by — or by r.

The value of this coefficient is about | that of the
modulus of elasticity.

The laws of torsion may be enunciated in the

I F/ •
formula '^'^ = „ i ; in which w is the angle of tor-
sion, F the moment of the force of torsion, / the
length of the wire, r its radius, and — the specific

torsion-coefficient.

As the angle of torsion is inversely proportional
to the fourth power of the radius, rods of some
thickness require very great force to produce even
small twists. With very small diameters, such as
those of a cocoon or glass thread, the proportionality
between the angle of torsion and the twisting force
holds even for several complete turns. We may
here mention a very ingenious method of obtaining Fig. 64.

very fine threads of glass and even of cjuartz and

other minerals which has been devised by Mr. Boys. It consists in attaching
a stout thread of the substance in question to a small arrow of straw, melting
the end so as to form a small drop. When the arrow is shot from a small
cross-bow, the drop remains behind in virtue of its inertia (17), and a thread
practically uniform but of excessive tenuity is spun out from it and carried
along with the arrow. In this way glass threads 90 feet in length and jouoo^h
of an inch in diameter have been produced. By the same method melting
quartz with the oxyhydrogen blowpipe, threads of this substance have been
produced which are not more than o-ooooi inch in diameter. Such threads
are of great value in torsion experiments, for, while they possess great
tenacity, they are almost destitute of the property of elastic fatigue.

90. Elasticity of flexure. — A solid, when cut into a rod or thin plate,
and fixed at one end, after having been more or less bent, strives to return
to its original position when left to itself This property is known as the
elasticity of flexure, and is very distinct in steel, caoutchouc, wood, and
paper.

If a rectangular bar A B be clamped at one end and loaded at the other
end by a weight W (fig. 65), a flexure will be produced which may be observed
by the cathetometer. The amount of this flexure e is represented by the
formula

6^^

Gravitation aftd Molecular Attraction.

[90

where P is the load, / the length of the bar, b its breadth, h its depth or
thickness, all in mm., and ^ the modulus of elasticity.
If the section of the bar is a circle of radius r, then

3 TrrV ■
It is clear that an accurate measurement of the flexure of a bar furnishes
a means of determining its modulus of elasticity.

The elasticity of flexure is applied in a vast variety of instances— for
example, in bows, watch-springs, carriage-springs ; in spring balances it is

used to determine weights,
in dynamometers to de-
termine the force of agents
in prune movers ; and, as a
property of wool, hair, and
feathers, it is applied to
domestic uses in cushions
and mattresses.

Whatever be the kind
of elasticity, there is, as
has been already said (88),
a limit to it — that is, there
is a molecular displace-
ment, beyond which
bodies are broken, or at
any rate do not regain their primitive form. This limit is affected by
various causes. The elasticity of many metals is increased by hardening,
whether by cold, by means of the draw-plate, by rolling, or by hammering.
Some substances, such as steel, cast iron, and glass, become both harder
and more elastic by tempering (94).

Elasticity, on the other hand, is diminished by annealing, which consists
in raising the body to a temperature lower than that necessary for tempering,
and allowing it to cool slowly. By this means the elasticity of springs
may be regulated at pleasure. Glass, when it is heated, undergoes a
true tempering in being rapidly cooled, and hence, in order to lessen the
fragility of glass objects, they are reheated in a furnace, and are carefully
allowed to cool slowly, so that the particles have time to assume their most
stable position (94).

9 1. Tenacity. — Tenacity is the resistance which a body opposes to the
total separation of its parts. According to the manner in which the external
force acts, we may have various kinds of tenacity : tenacity in the ordinary
sense, or resistance to traction ; 7'etative tenacity, or resistance to fracture ;
reactive tenacity, or resistance to crushing ; sheerifig tenacity, or resistance
to displacement of particles in a lateral direction ; and torsional tenacity, or
resistance to twisting. Ordinary tenacity is determined in different bodies
by forming them into cylindrical or prismatic wires, and ascertaining the
weight necessary to break them.

-91] Tenacity. S3

Mere increase in length does not influence the breaking weight, for the
weight acts in the direction of the length, and stretches all parts as if it had
been directly applied to them.

Tenacity is directly proportional to the breaking weight., and inversely
proportional to the area of a transz'erse section of the wire.

Tenacity diminishes with the duration of the traction. A small force
continuously applied for a long time will often break a wire, which would not
at once be broken by a larger weight.

Not only does tenacity vary with different substances, but it also varies
with the form of the body. Thus, with the same sectional area, a cylinder
has greater tenacity than a prism. The cjuantity of matter being the same,
a hollow cylinder has greater tenacity than a solid one ; and the tenacity of
this hollow cylinder is greatest when the external radius is to the internal
one in the ratio of 1 1 to 5. The shape has also the same influence on the
resistance to crushing as it has on the resistance to traction. A hollow
cylinder with the same mass, and the same weight, offers a greater resistance
than a solid cylinder. Thus it is that the bones of animals, the feathers of
birds, the stems of corn and other plants, offer greater resistance than if they
were solid, the mass remaining the same.

Tenacity, like elasticity, is different in different directions in bodies. In
wood, for example, both the tenacity and the elasticity are greater in the direc-
tion of the fibres than in a transverse direction. And this difference obtains
in general in all bodies, the texture of which is not the same in all directions.

Wires by being worked acquire greater tenacity on the surface, and have
therefore a higher coefficient, than even somewhat thicker rods of the same
material ; and, according to some physicists, solids have a surface tension
analogous to that of liquids (134). A strand of wires is stronger than a rod
whose section is equal to the sum of the sections of the wires.

Wertheim found the following numbers representing the weight in kilo-
grammes for the limit of elasticity, and for the tenacity of wires, imm. in
diameter.

Lead.
Tin .
Silver
Copper
Platinum
Iron .
Steel .
Cast steel

( drawn
1 annealed
I drawn
I annealed
f drawn
( annealed
f drawn
[ annealed
( drawn
[ annealed
( drawn
\ annealed
( drawn
I annealed
f drawn
I annealed

Limit of Elasticity.
Kilogrammes
. 0-25
0-20

Tenacity.

Kilogrammes

2 -07

I -So

• 0-45
0-20

2-45
170

. 11-25

29-00

275

1 6 -02

. I2-00

3-00

. 2600

40-30

30-54
34-10

• 14-50

• 32-3

23-50
61-10
46-88
70-00

. 5r-6
• 5-0

40-00
8o-oo

65-75

84 Gravitation and Molecular Attraction. [91-

The table shows that of all metals cast steel has the greatest tenacity.
Yet it is exceeded by fibres of unspun silk, a thread of which i square milli-
metre in section can carry a load of 500 kilogrammes. Single fibres of cotton
can support a weight of 100 to 300 grammes ; that is, millions of times their
own weight.

In this table the bodies are supposed to be at the ordinary temperature.
At higher temperatures the tenacity rapidly decreases. Seguin made some
experiments on this point with iron and copper, and obtained the following
values for the tenacity, in kilogrammes, of millimetre wire at different tem-
peratures : —

Iron . . at 10°, 60 ; at 370°, 54 ; at 500°, yj ;
Copper . . „ 21 ; „ 77 ; „ o.

92. Ductility. — Ductility is the property in virtue of which a great num-
ber of bodies change their forms by the action of traction or pressure.

With certain bodies, such as clay, wax, &c., the application of a very
little force is sufficient to produce a change ; with others, such as the resins
and glass, the aid of heat is needed, while with the metals more powerful
agents must be used, such as percussion, the draw-plate, or the rolling-mill.

Malleability is that modification of ductility which is exhibited by ham-
mering. The most malleable metal is gold, which has been beaten into
leaves about the ^,^^055^^ of an inch thick.

The most ductile metal is platinum. Wollaston obtained a wire of it
o'oooo3 of an inch in diameter. This he effected by covering with silver a
platinum wire O'oi of an inch in diameter, so as to obtain a cylinder 0-2 inch
in diameter only, the axis of which was of platinum. This was then drawn
out in the form of wire as fine as possible ; the two metals were ecjually ex-
tended. When this wire was afterwards boiled with dilute nitric acid the
silver was dissolved, and the platinum wire left intact. The wire was so fine
that a mile of it would have weighed only 1-25 of a grain.

The glass threads drawn by Mr. Boys' method (89) are so fine, being
under the nioootl'^ °f ^" "'"^^' ^^^* ^ ""'^^ would not weigh more than one-third
of a grain. Threads of quartz have a tenacity approaching that of steel wire.

93. Hardness. — Hardness is the resistance which bodies offer to being
scratched or worn by others. It is only a relative property, for a body which
is hard in reference to one body may be soft in reference to others. The re-
lative hardness of two bodies is ascertained by trying which of them will
scatch the other. Diamond is the hardest of all bodies, for it scratches all,
and is not scratched by any. The hardness of a body is expressed by re-
ferring it to a scale of hardness : that usually adopted is —

1. Talc 5. Apatite 8. To])a/.

2. Rock salt 6. Felspar 9. Coruntlum

3. Calcspar 7. Quartz 10. Diamond

4. Fluorspar

Thus, the hardness of a body which would scratch felspar, but would be
scratched by quartz, would be expressed by the number 6'5.

Huegenay determined the weight necessary to force a steel point to a
depth of 10 mm., and found the order of the metals as follows : lead, tin,
aluminium, gold, silver, platinum, zinc, copper, iron, steel.

-94] rcmpcr. 85

The pure metals are softer than their alloys. Hence it is that, for jevrel-
leiy and coinage, gold and silver are alloyed with copper to increase their
hardness.

The hardness of a body has no relation to its resistance to compression.
Glass and diamond are much harder than wood, but the latter offers far
greater resistance to the blow of a hammer. Hard bodies are often used
for polishing powders; for example, emery, pumice, and tripoli. Diamond,
being the hardest of all bodies, can only be ground by means of its own
powder.

A body which moves with great velocity can cut into bodies which are
harder than itself Thus a disc of wrought iron rotating with a velocity
of 1 1 metres in a second was cut by a steel graver ; while when it rotated
with a velocity of 20 metres, the edge of the disc could cut the graver, and
with a velocity of 50 to 100 metres it could even cut into agate and quartz.

A brittle body is one in which the connection between the parts is
destroyed by the application of a small force. Arsenic, bismuth, and heated
zinc are examples of brittle metals ; they are easily reduced to powder.

94. Temper. — By sudden cooling after they have been raised to a high
temperature, many bodies, more especially steel, become hard and brittle.
By reheating and cooling slowly, which is called anitealing^ hard and brittle
steel may be converted into a soft, flexible material, and in general, by varying
the limits of temperature within which the change takes place, almost any
degree of elasticity and flexibility may be given to it. This operation is
called tetnperifig. All cutting instruments are made of tempered steel.
There are, however, some few bodies upon which tempering produces quite
a contrary- effect. An alloy of one part of tin and four parts of copper, called
tantaiii metal, is ductile and malleable when rapidly cooled, but hard and
brittle as glass when cooled slowly.

86 On Liquids. [95-

BOOK III.

ON LIQUIDS.

CHAPTER I.
HYDROSTATICS.

95. Province of Hydrostatics. — The science of Jiydrosfatics treats of the
conditions of the equilibrium of hquids, and of the pressures they exert,
whether within their own mass or on the sides of the vessels in which they
are contained.

96. General characters of liquids.— It has been already seen (4) that
liquids are bodies whose molecules are displaced by the slightest force.
Their fluidity, however, is not perfect ; their particles always adhere slightly
to each other, and when a thread of liquid moves, it attempts to drag the
adjacent stationaiy particles with it, and conversely is held back by them.
This property is called viscosity (147), and bodies which possess this property
in a high degree are said to be viscous.

Gases also possess fluidity, but in a higher degree than liquids. The
distinction between the two forms of matter is that liquids are almost incom-
pressible and are comparatively inexpansible, while gases are eminently
compressible and expand spontaneously.

The fluidity of liquids is seen in the readiness with which the}' take all
sorts of shapes. Their compressibility is established by the following experi-
ment.

97. Compressibility of liquids. — From the experiment of the Florentine
Academicians (13), liquids were for a long time regarded as being completely
incompressible. Since then researches have been made on this subject by
various physicists, which have shown that liquids are really compressible.

The apparatus used for measuring the compressibility of liquids has been
named \he pieso^neter {ttu(o), I compress ; ^trpov, measure). That shown in
fig. 66 consists of a strong glass cylinder, with very thick sides, and an
internal diameter of about 3^ inches. The base of the cylinder is firmly
cemented into a wooden foot, and on its upper part is fitted a metal cylin-
der closed by a cap which can be unscrewed. In this cap there is a funnel,
R, for introducing water into the cylinder, and a small barrel hermetically
closed by a piston, which is moved by a screw, P.

97]

Compressibility of Liquids.

In the inside of the apparatus there is a glass vessel, A, containing the
liquid to be compressed. The upper part of this vessel terminates in a
capillary tube, which dips under mercury, O. This tube has been previously
divided into parts of equal capacity, and it has been determined how many
of these parts the vessel A contains. The latter is ascertained by finding the
weight, P, of the mercury which the reservoir
A, contains, and the weight, ^, of the mercury
contained in a certain number of divisions, /z,
of the capillary tube. If N be the number of
divisions of the small tube contained in the

whole reservoir, we ha\'e . = — , from which the

;/ p

value of N is obtained. There is further a
manometer. This is a glass tube, B, containing
air, closed at one end, and the other end ot
which dips under mercury. When there is no
pressure on the water in the cylinder, the tube
B is completely full of air ; but when the water
within the cylinder is compressed by means of
the screw P, the pressure is transmitted to the
mercury, which rises in the tube, compressing
the air which it contains. A graduated scale
fixed on the side of the tube shows the reduction
of volume, and this reduction of volume indicates
the pressure exerted on the liquid in the cylin-
der, as will be seen in speaking of the mano-
meter (184).

In making the experiment, the vessel A is
filled with the liquid to be compressed, and the
end dipped under the mercury. By means of
the funnel R the cylinder is entirely filled with
water. The screw P being then turned, the

piston moves downwards, and the pressure exerted upon the water is trans-
mitted to the mercury and the air ; in consequence of which the mercury
rises in the tube B, and also in the capillary tube. The ascent of mercury
in the capillary tube shows that the liquid in the vessel A has diminished in
volume, and gives the amount of its compression, for the capacity of the
whole vessel A in terms of the graduated divisions on the capillary tube has
been previously determined.

In his first experiments. Oersted assumed that the capacity of the vessel
A remained the same, its sides being compressed both internally and ex-
ternally by the liquid. But this capacity diminishes in consequence of the
external and internal pressures. Colladon and Sturm made some experiments
allowing for this change of capacity, and found that for a pressure equal to
that of the atmosphere, mercury experiences a compression of 0-000003 part
of its original volume, water a compression of 0-00005, 'irid ether a compression
of 0-000133 part of its original bulk. The compressibility of sea water is only
about 0-000044 : it is not materially denser even at great depths ; thus at
the depth of a mile its density would be only about i\^t\i the greater. The

On Liquids.

[97-

compressibility is greater the higher the temperature ; thus that of ether at
14° is one-fourth greater than its compressibihty at 0°.

It appears from recent researches that the comi^ressibiHty of water
diminishes with increase of temperature up to a certain hmit, beyond which
it increases again. This hmit seems to be at about 63° C.

As the pressure increases, the average compressibihty for each atmo-
sphere diminishes.

Whatever be the pressure to which a hquid has been subjected, experi-
ment shows that as soon as the pressure is removed the hquid regains
its original vokuiie. from which it is conchided that hquids are perfectly
elastic.

98. Equality of pressures. Pascal's law. — By considering liquids as
perfectly fluid, and assuming them to be uninfluenced by the action of gravity,
the following law has been established. It is often called Pascal's law, for
it was first enunciated by him.

Pressure exerted anywhere upon a mass of liquid is transmitted undi-
minished iti all directions., and acts with the same force on all equal surfaces.,
and in a direction at right angles to those surfaces.

To get a clearer idea of the truth of this principle, let us conceive a vessel
of any given form in the sides of which are placed various cylindrical aper-
tures, all of the same size, and closed by movable
pistons. Let us, further, imagine this vessel to be
filled with liquid and unaffected by the action of
gravity ; the pistons will, obviously, have no ten-
dency to move. If now a weight of P pounds be
ITT^ '^'^\ placed upon the piston A (fig. 67), which has a

^'^ - ^ ^ ^ surface «, it will be pressed inwards, and the

pressure will be transmitted to the internal faces
of each of the pistons B, C, D, and E, which will
each be forced outwards by a pressure P, their
surfaces being equal to that of the first piston.
Since each of the pistons undergoes a pressure P,
equal to that on A, let us suppose two of the pis-
tons united so as to constitute a surface 2a, it will have to support a pres-
sure 2 P. Similarly, if the piston were equal to 3^, it would experience a

pressure of 3P ; and if its area
were 100 or 1,000 times that of
a, it would sustain a pressure of
100 or 1,000 times P. In other
words, the pressure on any part
of the internal walls of the
vessel would be proportional to
the surface.

The principle of the equality
of pressure is assumed as a
consequence of the constitution
of fluids. By the following ex-
it can be shown that pressure is transmitted in all directions,
it cannot be shown that it is equally transmitted. P^ cylinder

Fig. 67.

permient
although

i-l4'

-99] Vertical Dozumvard Pressure : its Laivs. 89

provided with a piston is fitted into a hollow sphere (fig. 68), in which
small cylindrical jets are placed perpendicular to the sides. The sphere
and the cylinder being both filled with water, when the piston is moved the
liquid spouts forth from all the orifices, and not merely from that which is
opposite to the piston.

The reason why a satisfactory cjuantitative experimental demonstration
of the principle of tiie equality of pressure cannot be given is, that the in-
fluence of the weight of the liciuid and of the friction of the pistons cannot be
altogether eliminated.

Yet an approximate verification may be effected by the experiment
represented in fig. 69. Two cylinders of different diameters are joined by a
tube and filled with water. On the surface of the liquid are two pistons P
and /, which hermetically close the cylinders, but move without friction.
Let the area of the large piston be,
for instance, thirty times that of the
smaller one. That being assumed, let
a weight, say of two pounds, be placed
upon the small piston ; this pressure
will be transmitted to the water and
to the large piston, and as this pres-
sure amounts to two pounds on each
portion of its surface equal to that oj
the small piston, the large piston must
be exposed to an upward pressure
thnty times as much, or of sixty pounds. If now this weight be placed
upon the large piston, both will remain in equihbrium ; but, if the weight is
greater or less, this is no longer the case. If S and .y are the areas of the
large and small piston respectively, and P and p the corresponding loads,

then^ = ^ ; whence P = ^-.
p s s

It is important to observe that in speaking of the transmission of pres-
sures to the sides of the containing vessel, these pressures must always be
supposed to be perpendicular to the sides ; for any oblique pressure may be
decomposed into two others, one at right angles to the side, and the other
acting parallel with the side ; but, as the latter has no action on the side, the
perpendicular pressure is the only one to be considered.

Fig. 69.

PRESSURE PRODUCED IN LIQUIDS BY GRAVITY.

99. Vertical downward, pressure : its laws. — Any given liquid being
in a state of rest in a vessel, if we suppose it to be divided into horizontal
layers of the same density, it is evident that each layer supports the weight
of those above it. Gravity, therefore, produces internal pressures in the
mass of a liquid which vary at different points. These pressures are sub-
mitted to the following general laws: —

I. The pressure in each layer is proportional to the deptJi.

I I . With differetzt liquids and the same depth, the pressure is proportional
to the density of the liquid.

III. The pressure is the same at all points of the same horizontal layer.

90 On Liquids. [99-

The first two laws are self-evident ; the third necessarily follows from the
first and from Pascal's principle.

Meyer has found, by direct experiments, that pressure is transmitted
through liquids contained in tubes, with the same velocity as that with which
sound travels in the same circumstances.

loo. Vertical upward pressure. — The pressure which the upper layers
of a liquid exert on the lower layers causes them to exert an equal reaction
in an upward direction, a necessary consequence of the principle of trans-
mission of pressure in all directions. This upward pressure is termed the
buoyancy of licjuids ; it is very sensible when the hand is plunged into a
liquid, more especially one of great density, like mercury.

The following experiment (fig. 70) serves to exhibit the upward pressure
of licjuids. A large open glass tube A, one end of which is ground, is fitted
with a ground-glass disc O, or still better with a
thin card or piece of mica, the weight of which may
be neglected. To the disc is fitted a string C, by
which it can be held against the bottom of the tube.
The whole is then immersed in water, and now the
disc does not fall, although no longer held by the
string ; it is consequently kept in its position by the
upward pressure of the water. If water be now
slowly poured into the tube, the disc will only sink
when the height of the water inside the tube is
equal to the height outside. It follows thence that
the upward pressure on the disc is equal to the
pressure of a column of water, the base of which is
'"■ ''" the internal section of the tube A, and the height

the distance from the disc to the upper surface of the liquid. Hence the
tipivard pressure of liquids at any point is governed by the same laws as the
downward pressure.

loi. Pressure is independent of the shape of the vessel. — The
pressure exerted by a liquid, in virtue of its weight, on any portion of the
liquid, or on the sides of the vessel in which it is contained, depends on the
depth and density of the liquid, but is independent of the shape of the vessel
and of the quaiitity of the liquid.

This principle, which follows from the law of the equality of pressure,
may be experimentally demonstrated by many forms of apparatus. The
following is the one most frequently used, and is due to Haldat. It consists
of a bent tube, ABC (fig. 71), at one end of which. A, is fitted a stop-cock, in
which can be screwed two vessels, M and P, of the same height, but different
in shape and capacity, the first being conical, and the other nearly cylindri-
cal. Mercury is poured into the tube ABC, until its level nearly reaches A.
The vessel M is then screwed on and filled with water. The pressure of
the water acting on the mercury causes it to rise in the tube C, and its
height may be marked by means of a little collar, a., which slides up and
down the tube. The level of the water in M is also marked by means of the
movable rod o. When this is done, M is emptied by means of the stop-cock,
unscrewed, and replaced by P. When water is now poured in this, the
mercury, which had resumed its original level in the tube ABC, again rises

-101] Pressure is Independent of the Shape of the Vessel. 91

in C ; and when the water in P has the same height as it had in M, which
is indicated by the rod o, the mercury will have risen to the height it had

Fig. 71.

before, which is marked by the collar a. Hence the pressure on the mercury
in both cases is the same. This pressure is therefore independent of the
shape of the vessels, and, consequently, also of the quantity of liquid. The
base of the vessel is obviously the same in both cases; it is the surface of
the mercury in the interior of the tube A.

Another mode of demonstrating this principle is by means of an apparatus
devised by Masson. In this (fig. 72) the pressure of the water contained in
the vessel M is not exerted upon the column of mercury, as in thatof Haldat,
but on a small disc or stop a, which closes a tubulure <:, on which is screwed
the vessel M. The disc is now fixed to the tubulure, but is sustained by a
thread attached to the end of a scale-beam. At the other end is a pan, in
which weights can be placed until they counterbalance the pressure exerted
by the water on the stop. The vessel M being emptied is unscrewed,
and replaced by the narrow tube P. This being filled to the same height
as the large vessel, which is observed by means of the mark o^ it will be
observed that to keep the disc in its place just the same weight must be
placed in the pan as before, which leads, therefore, to the same conclusion
as does Haldat's experiment. The same result is obtained if, instead of the
vertical tube P, the oblique tube Q be screwed to the tubulure.

From a consideration of these principles it will be readily seen that a
very small quantity of water can produce considerable pressures. Let us
imagine any vessel— a cask, for example — filled with water, and with a long
narrow tube tightly fitted into the side. If water is poured into the tube,
there will be a pressure on. the bottom of the cask equal to the weight of a
column of water whose base is the bottom itself, and whose height is equal

On Liquids.

[101-

to that of the water in the tube. The pressure may be made as great as we
please ; by means of a narrow thread of water forty feet high, Pascal suc-
ceeded in bursting a very solidly constructed cask.

The toy known as the hydrostatic bellows depends on the same principle,
and we shall see a most important application of it in the hydraulic press
(io8).

From the principle just laid down, the pressures produced at the bottom
of the sea may be calculared. It will be presently demonstrated that the
pressure of the atmosphere is equal to that of a column of sea water about

thirty- three teet high. At sea the lead has frecjuently descended to a depth
of thirteen thousand feet ; at the bottom of some seas, therefore, there must
be a pressure of four hundred atmospheres.

I02. Pressure on the sides of vessels. — Since the pressure caused by
gravity in the mass of a liquid is transmitted in every direction, according to
the general law of the transmission of fluid pressure, it follows that at every
point of the side of any vessel a pressure is exerted, at right angles to the
side, which we will suppose to be plane. The resultant of all these pressures
is the total pressure on the sides. But since these pressures increase in
proportion to the depth, and also in proportion to the horizontal extent of
their side, their resultant can only be obtained by calculation, which shows
that the total pressure on any given portion of the side is equal to the
weight of a column of liquid which has this portion of the side for its base.,
and whose height is the vertical distance from the centre of gravity of the
portion to the surface of the liquid. If the side of a vessel is a curved surface,
the same rule gives the pressure on the surface, but the total pressure is
no longer the resultant of the fluid pressures.

The point in the side supposed plane, at which the resultant of all the
pressure is applied, is called the centre of pressure., and is always below the

-104] Equilibrium of a Liquid in a Single Vessel. 93

centre of gravity of the side. For if the pressures exerted at different parts
of the plane side were equal, the point of application of their resultant, the
centre of pressure, would obviously coincide with the centre of gravity of the
side. But since the jjressure increases with the depth, the centre of pressure
is necessarily below the centre of gravity. This point is determined by cal-
culation, which leads to the following results : —

i. With a rectangular side whose upper edge is level with the water, the
centre of pressure is at two-thirds of the line which joins the middle of the
horizontal sides measured from the top.

ii. With a triangular side whose base is horizontal, and coincident with
the level of the water, the centre of pressure is at the middle of the line which
joins the vertex of the triangle with the middle of the base.

iii. With a triangular side whose vertex is level with the water, the centre
of pressure is in the line joining the vertex and the middle of the base, and
at three-fourths of the distance of the latter from the vertex.

103. Hydrostatic paradox. — We have already seen that the pressure on
the bottom of a vessel depends neither on the form of the vessel nor on the
quantity of the liquid, but simply on the height of the liquid above the
bottom. But the pressure thus exerted must not be confounded with the
pressure which the vessel itself exerts on the body which supports it. The
latter is always equal to the combined weight of the liquid and the vessel in
which it is contained, while the former may be either smaller or greater than
this weight, according to the form of the vessel.
This fact is often termed the hydrostatic paradox,
because at first sight it appears paradoxical.

CD (fig. T^) is a vessel composed of two cylin-
drical parts of unequal diameters, and filled with
water to a. From what has been said before, the
bottom of the vessel CD supports the same pressure
as if its diameter were everywhere the same as that
of its lower part ; and it would at first sight seem
that the scale MN of the balance, in which the
vessel CD is placed, ought to show the same
weight as if there had been placed in it a cyhn-
drical vessel having the same height of water, and
having the diameter of the part D. But the
pressure exerted on the bottom of the vessel is not
all transmitted to the scale MN ; for the upward -prtssuxe upon the surface 7to
of the vessel is precisely equal to the weight of the extra quantity of water
which a cylindrical vessel would contain, and balances an equal portion of
the downward pressure on in. Consequently the pressure on the plate MN is
simply equal to the weight of the vessel CD and of the water which it contains.

Fig. 73-

[04.

CONDITIONS OF THE EQUILIBRIUM OF LIQUIDS.
Equilibrium of a liquid in a slngrle vessel. — In order that a liquid

may remain at rest in a vessel of any given form, it must satisfy the two
following conditions : —

I. Its surface must be everywhere perpendicular to the resultant of the
forces which act on the molecules of the liquid.

On Liquids.

[104-

II. Every niolecttle of the mass of tlie liquid Jiiust be subject in every direc-
tion to equal and contrary pressures.

The second condition is self-evident ; for if, in two opposite directions,
the pressures exerted on any given molecule were not equal and contrary,
the molecule would be moved in the direction of the greater pressure, and
there would be no equilibrium. Thus the second condition follows from the
principle of the equality of pressures, and from the reaction which all pres-
sure causes on the mass of liquids.

To prove the first condition, let us suppose that inp is the resultant of all
the forces acting upon any molecule vi on the
surface (fig. 74), and that this surface is inclined
in reference to the force mp. The latter can
consequently be decomposed into two forces,
niq and nif; the one perpendicular to the sur-
face of the liquid, and the other to the direction
nip. Now the first force mq would be destroyed
by the resistance of the liquid, while the second
n the direction nif which shows that the equili-

Fig. 74-

would move the molecule
brium is impossible.

If gravity be the force acting on the liquid, the direction nip is vertical ;
hence, if the liquid is contained in a basin or vessel of small extent, the sur-
face ought to be plane and horizontal (67), because then the direction of
gravity is the same in every point. But the case is different with liquid sur-
faces of greater extent, like the ocean. The surface will be perpendicular

to the direction of gravity ; but as
this changes from one point to another,
and always tends towards a point near
the centre of the earth, it follows that
the direction of the surface of the ocean
will change also, and assume a nearly
spherical form.

105. Equilibrium of the same
liquid in several communicating'
vessels. — When several vessels of
any given form communicate with
each other, there will be equili-
brium when the liquid in each vessel
satisfies the two preceding conditions
(104), and further, when the surfaces of
the liquids in all the vessels are in the
same horizontal plane.
In the vessels ABCD (fig 75), which communicate with each other, let
us consider any transverse section of the tube mn ; the liquid can only
remain in equilibrium as long as the pressures which this section supports
from m in the direction of ;;, and from n in the direction of ;//, are equal and
opposite. Now it has been already proved that these pressures are respec-
tively equal to the weight of a column of water, whose base is the supposed
section, and whose height is the distance from the centre of gravity of this
section to the surface of the liquid. If we conceive, then, a horizontal plane,

Fig. 75-

-107]

Eqiiilibriiwt of Tzvo Different Liquids.

m/i, drawn through the centre of gravity of this section, it will be seen that
there will only be equilibrium as long as the height of the liquid above this
plane is the same in each vessel, which demonstrates the principle enunciated.

lo6. Equilibrium of superposed liquids. — In order that there should
be equilibrium when several heterogeneous liquids are superposed in the
same vessel, each of them must satisfy the conditions necessary for a single
liquid (104) ; and further, there will be stable equilibriuin only when the
liquids are arranged in the order of their decreasing densities from the
bottom upwards.

The last condition is expermientally demonstrated by means oi ihQ phial
of four ele/nents. This consists of a long narrow bottle containing mercury,
water saturated with carbonate of potass, alcohol coloured red, and petroleum.
When the phial is shaken the liquids mix, but when it is allowed to rest they
separate ; the mercury sinks to the bottom, then comes the water, then the
alcohol, and then the petroleum. This is the order of the decreasing densi-
ties of the bodies. The water is saturated with carbonate of potass to prevent
its mixing with the alcohol.

This separation of the liquids is due to the same cause as that which
enables solid bodies to float on the surface of a liquid of greater density than
their own. It is also on this account that fresh water, at the mouths of
rivers, floats for a long time on the denser salt water of the sea ; and it is
for the same reason that cream, which is lighter than milk, rises to the surface.

107. Equilibrium of two different
liquids in communicating' vessels. —
When two liquids of different densities,
which do not mix, are contained in two
communicating vessels, they will be in
equilibrium when, in addition to the pre-
ceding principles, they are subject to the
following : that the heights above the hot i-
zontal surface of contact of two columns of
liquid in equilibtium are in the inverse ratio
of their densities.

To show this experimentally, mercury is
poured into a bent glass tube, w;?, fixed
against an upright wooden support (fig. 76),
and then water is poured into one of the
legs, AB. The column of water, AB, press-
ing on the mercury at B, lowers its level in
the leg AB, and raises it in the other by a

quantity CD ; so that if, when equilibrium is established, we imagine
a horizontal plane, BC, to pass through B, the column of water in AB will
balance the column of mercury CD. If the heights of these two columns are
then measured by means of the scales, it will be found that the height of the
column of water is about 13^ times that of the height of the column of mercury.
We shall presently see that the density of mercury is about 13^ times that of
water, from which it follows that the heights are inversely as the densities.

It may be added that the equilibrium cannot exist unless there is a sufficient
quantity of the heavier liquid for part of it to remain in both legs of the tube.

On Liquids.

[107-

The preceding principle may be deduced by a veiy simple calculation.
Let d and d' be the densities of water and mercury, and h and h' their re-
spective heights, and let g be the force of gravity. The pressure on B will
be proportional to the density of the liciuid, to its height, and to the force of
gravity ; on the whole, therefore, to the product dhg. Similarly the pres-
sure at C will be proportional to d'h'g. But in order to produce equilibrium,
dlig must be equal to d'h'g, or dh = d'h'. This is nothing more than an
algebraical expression of the above principle ; for since the two products
must always be equal, d' must be as many times greater than d as h' is less
than //.

In this manner the density of a liquid may be determined. Suppose one
of the branches contained water and the other oil, and their heights were,
respectively, 15 inches for the oil and 14 inches for the water. The density
of water being taken as unity, and that of oil being called x, we shall have

15 X .t-= 14 X I ; whence x =

0-933-

APPLICATIONS OF THE PRECEDING HYDROSTATIC PRINCIPLES.

108. Hydraulic press. — The law of the equality of pressure has received
a most important application in the hydraulic press, a machine by which

Fig. 77.

enormous pressures may be produced. Its principle is due to Pascal, but it
was first constructed by Bramah in 1796.

-108]

Hydraulic Press.

It consists of a cylinder B, with very strong thick sides (fig. 77), in
which there is a cast-iron ram P working water-tight in the collar of the
cylinder. On the ram P there is a cast-iron plate on which the substance
to be pressed is placed. Four strong columns serve to support and fix a
second plate Q.

By means of a leaden pipe K, the cylinder B, which is filled with water,
communicates with a small force-pump A, which works by means of a lever
M. When the piston of this pump/ ascends, a vacuum is produced, and the
water rises in the tube a, at the end of which there is a rose, to prevent the
entrance of foreign matters. When the piston p descends, it drives the water
into the cylinder by the tube K.

Fig. 78 represents a section, on a larger scale, of the system of valves
necessary in working the apparatus. The valve <?, below the piston/, opens
when the piston rises,
and closes when it
descends. The valve
o, during this descent,
is opened by the
pressure of the water
which passes by the
pipe K. The valve z
is a safety-valve, held
by a weight which
acts on it by means of
a lever. By weight-
ing the latter to a
greater or less extent
the pressure can be
regulated, for as soon as there is an upward pressure greater than that ot the
weight upon it, it opens and water escapes. A screw r serves to relieve the
pressure, for when it is opened it affords a passage for the efflux of the water
in the cylinder B.

A most important part is the leather collar, ft, the invention of which by
Bramah removed the difficulties which had been experienced in making the
large ram work water-tight when submitted to
great pressures. It consists of a circular piece of
stout leather (fig. 79), saturated with oil so as to
be impervious to water, in the centre of which a
circular hole is cut. This piece is bent so that
a section of it i-epresents a reversed U, and is
fitted into a groove tt made in the neck of the Fig. 79.

cylinder. This collar being concave downwards,

in proportion as the pressure increases, it fits the more tightly against the
ram P on one side and the neck of the cylinder on the other, and quite pre-
vents any escape of water.

The pressure which can be obtained by this press depends on the relation
of the piston P to that of the piston/. If the former has a transverse section
fifty or a hundred times as large as the latter, the upward pressure on the
large piston will be fifty or a hundred times that exerted upon the small one.

Fig. 78.

98 Oti Liquids. [108-

By means of the lever M an additional advantage is obtained. If the
distance from the fulcrum to the point where the power is applied is five times
the distance from the fulcrum to the piston^, the pressure on/ will be five
times the power. Thus, if a man acts on M with a force of sixty pounds, the
force transmitted by the piston p will be 300 pounds, and the force which
tends to raise the piston P will be 30,000 pounds, supposing the section of P
is a hundred times that oi p.

The hydraulic press is used in all cases in which great pressures are re-
quired. It is used in pressing cloth and paper, in extracting the juice of beet-
root, in compressing hay and cotton, in expressing oil from seeds, and in
bending iron plates ; it also sei'ves to test the strength of cannon, of steam
boilers, and of chain cables. The parts composing the tubular bridge which
spans the Menai Straits were raised by means of an hydraulic press. The
cylinder of this machine, the largest which has ever been constructed, was
nine feet long and twenty-two inches in internal diameter ; it was capable of
raising a weight of two thousand tons.

The principle of the hydraulic press is advantageously employed in cases
in which great power is only required at intervals, such as in opening dock
gates, working cranes, in lifts in hotels, warehouses, and the like. It has
even been used in working stage machinery. In these cases an hydraulic accii-
jiiiilator is used. The piston P is loaded with very great weights, and water
is continually forced into the cylinder B by powerful pumps. From the bottom
of this cylinder a tube conducts water to any place where the power is to be
applied, and the flow of even small quantities of water which is under high
pressure can perform a great amount of work.

Suppose, for instance, that the area of the piston P is four square feet, and
that it has a load of 100 tons ; this represents a pressure of over 370 pounds
on the square inch or more than 25 atmospheres. When the large piston
sinks through the y^th of an inch about a pint of watei will flow out, and this
represents a work of about 1,100 foot-pounds. In London hydraulic power is
supplied by water delivered under a pressure of 750 pounds per square inch.

109. The water-level. — The water-level is an application of the con-
ditions of ecjuilibrium in communicating vessels. It consists of a metal tube

Fig. So.

bent at both ends, in which are fitted glass tubes D and E (fig. 80). It is
placed on a tripod, and water poured in until it rises in both legs. When the

Artesian Wells.

-111]

liquid is at rest, the level of the water in both tubes is the same ; that is,
they are both in the same horizontal plane.

This instrument is used in levelling, or ascertaining how much one point
is higher than another. If, for example, it is desired to find the difference
between the heights of B and A, a levelling-staff'x's, fixed on the latter place.
This staff consists of a rule formed of two sliding pieces of wood, and sup-
porting a piece of tin plate M, in the centre of which there is a mark. This
staff being held vertically at A, an observer looks at it through the level
along the surfaces D and E, and directs the holder to raise or lower the slide
until the mark is in the prolongation of the line DE. The height AM is
then measured, and subtracting it from the height of the level the height of
the point A above B is obtained.

I lo. The Spirit-level. — The spirit-level is both more delicate and more
accurate than the water-level. It consists of a glass tube AB (fig. 8i), very
slightly curved ; that is,
the tube, instead of being
a true cylinder as it seems
to be, is in fact slightly
curved in such a manner
that its axis is an arc of
a circle of very large
radius. It is filled with
spirit with the exception
of a bubble of air, which
tends to occupy the high-
est part. The tube is
placed in a brass case

CD (fig. 82), which is so arranged that when it is in a perfectly horizontal
position the bubble of air is exactly between the two points marked in the
case.

To take levels with this apparatus, it is fixed on a telescope, which can
be placed in a horizontal position.

III. Artesian wells. — All natural collections of water exemplify the
tendency of water to find its level. Thus a group of lakes, such as the
great lakes of North America, may be regarded as a number of vessels in
communication, and consequently the waters tend to maintain the same
level in all. This, too, is the case with the source of a river and the sea,
and, as the latter is on the lower level, the river continually flows down to the
sea along its bed, which is, in fact, the means of communication between
the two.

Perhaps the most striking instance of this class of natural phenomena is
that of artesian wells. These wells derive their name from the province
of Artois, where it has long been customary to dig them, and whence their
use in other parts of France and Europe was derived. It seems, however,
that at a very remote period wells of the same kind were dug in China and
Egypt.

To understand the theory of these wells it must be premised that the
strata composing the earth's crust are of two kinds : the one permeable to
water, such as sand, gravel, &c. ; the other iupermeable, such as clay. Let

H 2

On Liquids.

[Ill-

us suppose, then, a geographical basin of greater or less extent, in which the
two impermeable layers AB, CD (fig. 83), enclose between them a permeable
layer KK. The rain-water falling on that part of this layer which comes to the
surface, and which is called the outcrop, will filter through it, and following
the natural fall of the ground will collect in the hollow of the basin, whence
it cannot escape owing to the impermeable strata above and below it. If,
now, a vertical hole, I, be sunk down to the water-bearing stratum, the water
striving to regain its level will spout out to a height which depends on the
difference between the levels of the outcrop and of the point at which the
perforation is made.

The waters which feed artesian wells often come fiom a distance of
sixty or seventy miles. The depth varies in different places. The well at

Crenelle is 1,800 feet deep ; it gives 656 gallons of water in a minute, and
is one of the deepest and most abundant which have been made. The
temperature of the water is 27° C. It follows from the law of the in-
crease of temperature with the increasing depth below the surface of the
ground, that, if this well were 210 feet deeper, the water would have all
the year round a temperature of 32° C. ; that is, the ordinary temperature of
baths.

BODIES IMMERSED IN LIQUIDS.

112. Pressure supported by a body Immersed in a liquid. — When a
solid is immersed in a liquid, every portion of its surface is submitted to a
perpendicular pressure which increases with the depth. If we imagine all
these pressures decomposed into horizontal and vertical pressures, the first
set are in equilibrium. The vertical pressures are obviously unequal, and
will tend to move the body upwards.

Let us imagine a cube immersed in a mass of water (fig. 84), and that
four of its edges are vertical. The pressures upon the four vertical faces being
clearly in equilibrium, we need only consider the pressures exerted on the
horizontal faces A and B. The first is pressed downwards by a column of
water whose base is the face A, and whose height is AD ; the lower face B
is pressed upwards by the weight of a column of water whose base is the

-113]

Principle of Archimedes.

Fig. 84.

face itself, and whose height is BD (100). The cube, therefore, is urged
upwards by a force equal to the difference between these two pressures,
which latter is manifestly equal to the weight of a column of water having
the same base and the same height as this cube. Consequently, this upward
pressure is equal to the weight of the volitme of water displaced by the im-
mersed body.

We shall readily see from the following reasoning that every body
immersed in a liquid is pressed upwards by a force equal to the weight of
the displaced liquid. In a liquid at rest let us sup-
pose a portion of it of any given shape, regular
or irregular, to become solidified, without either
increase or decrease of volume. The liquid thus
solidified will remain at rest, and therefore must
be acted upon by a force equal to its weight, and
acting vertically upwards through its centre of
gravity ; for otherwise motion would ensue. If in
the place of the solidified water we imagine a solid
of another substance of exactly the same volume
and shape, it will necessarily receive the same
pressures from the surrounding liquid as the solidi-
fied portion did ; hence, like the latter, it will sustain
the pressure of a force acting vertically upwards
through the centre of gravity of the displaced liquid,
and equal to the weight of the displaced liquid. If, as almost invariably
happens, the liquid is of uniform density, the centre of gravity of the displaced
liquid means the centre of gravity of the immersed part of the body supposed to
be of uniform density. This distinction is sometimes of importance : for ex-
ample, if a sphere is composed of a hemisphere of iron and another of wood,
its centre of gravity would not coincide with its geometrical centre, but, if it
were placed under water, the centre of gravity of the displaced water would
be at the geometrical centre — that is, would have the same position as the
centre of gravity of the sphere if of uniform density.

1 1 3. Principle of Archimedes. — The preceding principles prove that
every body immersed in a liquid is submitted to the action of two forces :
gravity which tends to lower it, and the buoyancy of the liquid which tends
to raise it with a force equal to the weight of the liquid displaced. The
weight of the body is either totally or partially overcome by its buoyancy,
from which it is concluded that a body immersed ift a liquid loses apart of
its weight equal to the weight of the displaced liquid.

This principle, which is the basis of the theory of immersed and floating
bodies, is called the principle of Archimedes, after the discoverer. It may
be shown experimentally by means of the hydrostatic balance (fig. 85). This
is an ordinary balance, each pan of which is provided with a hook ; the
beam can be raised by means of a toothed rack, which is worked by a little
pinion C. A catch, D, holds the rack when it has been raised. The beam
being raised, a hollow brass cylinder. A, is suspended from one of the pans,
and below this a solid cylinder, B, whose volume is exactly equal to the
capacity of the first cylinder ; lastly, an equipoise is placed in the other pan.
If now the hollow cylinder A be filled with water, the equilibrium is disturbed ;

On Liquids.

[113-

I02

but if at the same time the beam is lowered so that the sohd cylinder B be-
comes immersed in a vessel of water placed beneath it, the equilibrium will
be restored. By being immersed in water the cylinder B loses a portion of
its weight equal to that of the water in the cylinder A. Now, as the capacity
of the cylinder A is exactly equal to the volume of the cylinder B, the prin-
ciple which has been before laid down is proved.

es^pa

Fig. 85.

114. Determination of the volume of a body. — The principle of
Archimedes furnishes a method for obtaining the volume of a body of any
shape, provided it is not soluble in water. The body is suspended by a fine
thread to the hydrostatic balance, and is weighed first in the air, and then in
distilled water at 4° C. The loss of weight is,^'the weight of the displaced
water, from which the volume of the displaced water is readily calculated.
But this volume is manifestly that of the body itself. Suppose, for example,
155 grammes is the loss of weight. This is consequently the weight of the
displaced water. Now it is known that a gramme is the w-eight of a cubic
centimetre of water at 4°; consequently, the volume of the Ijody immersed
is 155 cubic centimetres.

115. Equilibrium of floating- bodies. — A body when floating is acted
on by two forces, namely, its weight, which acts vertically downwards
through its centre of gravity, and the resultant of the fluid pressures, which

-115] Equilibrium of Floating Bodies. 103

(112) acts vertically upwards through the centre of gravity of the fluid
displaced ; but if the body is at rest these two forces must be equal and
act in opposite directions ; whence follow the conditions of equilibrium',
namely, —

i. The jioating body must displace a volume of liquid ivJiose weight equals
that of the body.

ii. The centre of gravity of the floating body must be i?t the same vertical
line with that of the fluid displaced.

Thus in fig. 86, if C is the centre of gravity of the body, and G that of
the displaced fluid, the line GC must be vertical, since when it is so the
weight of the body and the fluid pressure will act in opposite directions
along the same line, and will be in equilibrium if equal. It is convenient,
with reference to the subject of the present article, to speak of the line CG
produced as the axis of the body.

Next let it be inquired whether the equilibrium be stable or unstable.
Suppose the body to be turned through a small angle (fig. 87), so that the
axis takes a position
inclined to the vertical.
The centre of gravity
of the displaced fluid
will no longer be G,
but some other point,
G'. And since the fluid
pressure acts vertically
upwards through G',
its direction will cut
the axis in some point
M', which will gene-
rally have different positions according as the inclination of the axis to the
vertical is greater or smaller. If the angle is indefinitely small, M'will have
a definite position M, which always admits of determination, and is called
the metacentre.

If we suppose M to be above C, an inspection of fig. 88 will show that
when the body has received an indefinitely small displacement, the weight of
the body W, and the resultant of the fluid pressures R, tend to bring the
body back to its original position ; that is, in this case, the equilibrium is
stable (70). If, on the contrary, M is below C, the forces tend to cause the
axis to deviate farther from the vertical, and the equilibrium is unstable.
Hence the rule — ■

iii. The equilibrium oj a floating body is stable or unstable according as
the metacentre is above or below the centre of gravity.

The determination of the metacentre can rarely be effected except by
means of a somewhat difficult mathematical process. When, however, the
form of the immersed part of a body is spherical, it can be readily determined ;
for since the fluid pressure at each point converges to the centre, and con-
tinues to do so when the body is slightly displaced, their resultant must in
all cases pass through the centre, which is therefore the metacentre. • To
illustrate this : let a spherical body float on the surface of a liquid (fig. 89) ;
then, its centre of gravity and the metacentre both coinciding with the

Fig. 89.

104 On Liquids. [115-

geometrical centre C, its equilibrium is neutral (70). Now suppose a small
heavy body to be fastened at P, the summit of the vertical diameter. The
centre of gravity will now be at some point G above C. Consequently, the
equilibrium is unstable, and the sphere, left to itself, will instantly turn over
and will rest when P is the lower end of a vertical diameter.

On investigating the position of the metacentre
of a cylinder, it is found that, when the ratio of
the radius to the height is greater than a certain
quantity, the position of stable equilibrium is that
in which the axis is vertical ; but if it be less than
that quantity, the equilibrium is stable when the
axis is horizontal. For this reason the stump of a
tree floats lengthwise, but a thin disc of wood floats
flat on the water. Hence, also, if it is required to
make a cylinder of moderate length float with
its axis vertical, it is necessary to load it at the
lower end. By so doing its centre of gravity is brought below the meta-
centre.

The determination of the metacentre and of the centre of gravity is of
great importance in the stowage of vessels, for on their relative positions
the stability depends.

1 16. Cartesian diver — The different effects of suspension, immersion,

and floating are reproduced by means of a well-
known hydrostatic toy, the Cartesian diver (fig. 90).
It consists of a glass cylinder nearly full of water,
on the top of which a brass cap, provided with a
piston, is hermetically fitted. In the liquid there is
a little porcelain figure attached to a hollow glass
ball a, which contains air and water, and floats on
the surface. In the lower part of this ball there is
a little hole by which water can enter or escape,
according as the air in the interior is more or less
compressed. The quantity of water in the globe
is such that very little more is required to make it
sink. If the piston is slightly lowered the air is
compressed, and this pressure is transmitted to the
water of the vessel and the air in the bulb. The
consequence is that a small quantity of water pene-
trates into the bulb, which therefore becomes
heavier and sinks. If the pressure is relieved, the
air in the bulb expands, expels the excess of water
which had entered it, and the apparatus, being
now lighter, rises to the surface. The experiment
may also be simplified by replacing the brass cap
and piston by a cover of sheet india-rubber, which
Fig, go. is tightly tied over the mouth ; when this is pressed

by the hand the same effects are produced.

117. Swimmingr-bladder of fishes — Most fishes have an air-bladder
below the spine, which is called the sivimming-bladder. The fish can com-

-120] Specific Gravity of Solids. 105

press or dilate this at pleasure by means of a muscular effort, and produce
the same effects as those just described — that is, it can either rise or sink in
water.

1 1 8. Swimming:. — The human body is lighter, on the whole, than an
equal volume of water : it consequently floats on the surface, and still better
in sea-water, which is heavier than fresh water. The difficulty in swimming
consists not so much in floating, as in keeping the head above water, so as
to breathe freely. In man the head is heavier than the lower parts, and
consecjuently tends to sink, and hence swimming is an art which requires to
be learned. With quadrupeds, on the contrary, the head, being less heavy
than the posterior parts of the body, remains above water without any effort,
and these animals therefore swim naturally.

SPECIFIC GRAVITY — HYDROMETERS.

119. Determination of specific gravities. — It has been already ex-
plained (24) that the specific gravity of a body, whether solid or liquid, is the
number which expresses the relation of the weight of a given volume of this
body to the weight of the same volume of distilled water at a temperature
of 4°. In order, therefore, to calculate the specific gravity of a body, it is
sufficient to determine its weight and that of an equal volume of water, and
then to divide the first weight by the second : the quotient is the specific
gravity of the body.

Three methods are commonly used in determining the specific gravities
of solids and liquids. These are — ist, the method of the hydrostatic balance ;
2nd, that of the hydrometer ; and 3rd, the specific gravity flask. All three,
however, depend on the same principle — that of first ascertaining the weight
of a body, and then that of an equal volume of water. We shall first apply
these methods to determining the specific gravity of solids, and then to the
specific gravity of liquids.

120. Specific gravity of solids. — i. Hydrostatic balance. — To obtain the
specific gravity of a solid by the hydrostatic balance (fig. 85), it is first
weighed in the air, and is then suspended to the hook of the balance and
weighed in water (fig. 91). The loss of weight which it experiences is,
according to Archimedes' principle, the weight of a volume of water equal
to its own volume ; consequently, dividing the weight in air by the loss of
weight in water, the quotient is the specific gravity required. If P is the
weight of the body in air, P' its weight in water, and D its specific gravity,

p
P - P' being the weight of the displaced water, we have D = .

It may be observed that though the weighing is performed in air, yet,
strictly speaking, the quantity required is the weight of the body in vacuo ;
and, when great accuracy is required, it is necessary to apply to the observed
weights a con-ection for the weights of the unequal volumes of air displaced
by the substance, and the weights in the other scale-pan. The water in
which bodies are weighed is supposed to be distilled water at the standard
temperature.

ii. Nicholsoii' s hydrometer. — The apparatus consists of a hollow metal

io6

On Liquids.

[120-

cylinder B (fig. 92), to which is fixed a cone C, loaded with lead. The
object of the latter is to bring the centre of gravity below the metacentre,
so that the cylinder may float with its axis vertical. At the top is a stem
terminated by a pan, in which is placed the substance whose specific gravity
is to be determined. On the stem a standard point, 0, is marked.

The apparatus stands partly out of the water, and the first step is to

ascertain the weight which
must be placed in the pan in
order to make the hydrometer
sink to the standard point 0.
Let this weight be 125 grains,
and let sulphur be the sub-
stance whose specific gravity
is to be determined. The
weights are then removed
from the pan, and replaced
by a piece of sulphur which
weighs less than 125 grains,
and weights added till the hy-
drometer is again depressed
to the standard o. If, for
instance, it has been neces-
sary to add 55 grains, the
weight of the sulphur is evi-
dently the difference between
125 and 55 grains ; that is, 70
grains. Having thus deter-
mined the weight of the sulphur in air, it is now only necessary to
ascertain the weight of an equal volume of water. To do this, the piece of
sulphur is placed in the lower pan C at ;;z, as represented in the figure. The
whole weight is not changed, nevertheless the hydrometer no longer sinks to
the standard ; the sulphur, by immersion, has lost a part of its weight equal
to that of the water displaced. Weights are added to the upper pan until
the hydrometer sinks again to the standard. This weight, 34-4 grains, for
example, represents the weight of the volume of water displaced ; that is, of
the volume of water equal to the volume of the sulphur. It is only necessary,
therefore, to divide 70 grains, the weight in air, by 34-4 grains, and the
quotient, 2-03, is the specific gravity.

If the body in question is lighter than water, it tends to rise to the surface,
and will not remain on the lower pan C. To obviate this, a small movable
cage of fine wire is adjusted so as to prevent the ascent of the body. The
experiment is in other respects the same.

121. Specific gravity bottle. Pyknometer When the specific gravity

of a substance in a state of powder is required, it can be found most conve-
niently by means of \\\q. pyknometer, or specific gravity bottle. This instru-
ment is a bottle, in the neck of which is fitted a thermometer A, an enlarge-
ment on the stem being carefully ground for this purpose (fig. 93). In the
side is a narrow capillary stem widened at the top and provided with a
stopper, as shown in the figure. On this tube is a mark w, and the thermo-

Fig. 91.

Fig. 92.

122]

Bodies Soluble

Water.

to;

meter stopper having been inserted, the bottle is filled with water exactly to
this mark at each weighing. The bottle may conveniently have dimensions
such that when the thermometer stopper is inserted and the liquid filled to
the mark m, it represents a definite volume. This is done by filling the
bottle when wholly under water, and putting in the stopper while it is im-
mersed. The bottle and the tube are then completely filled, and the quantity
of water in excess is removed by blotting-paper. To find the specific gravity
proceed as follows : Having weighed the powder, place it in one of the
scale-pans, and with it the bottle filled exactly
to in, and carefully dried. Then balance it by
placing small shot, or sand, in the other pan.
Next, remove the bottle and pour the powder
into it, and, as before, fill it up with water to
the mark a. On replacing the bottle in the
scale-pan it will no longer balance the shot,
since the powder has displaced a volume of
water equal to its own volume. Place weights
in the scale-pan along with the bottle until
they balance the shot. These weights give
the weight of the water displaced. Then the
weight of the powder and the weight of an
equal bulk of water being known, its specific
gravity is determined as before. The thermo-
meter gives the temperature at which the
determination is made, and thus renders it easy
to make a correction (124).

It is important in this determination to I'e-
move the layer of air which adheres to the
powder, and unduly increases the quantity of
water expelled. This is effected by placing the
bottle under the receiver of an air-pump and
exhausting. The same result is obtained by
boiling the water in which the powder is
placed.

1 22. Bodies soluble in water. — If the body,
whose specific gravity is to be determined by
any of these methods, is soluble in water, the
determination is made in some liquid in which

it is not soluble, such as oil of turpentine or naphtha, the specific gravity of
which is known. The specific gravity is obtained by multiplying the number
obtained in the experiment by the specific gravity of the liquid used for the
determination.

Suppose, for example, a determination of the specific gravity of potassium
has been made in naphtha. For equal volumes, P represents the weight of
the potassium, P' that of the naphtha, and P" that of water ; consequently,
p
—will be the specific gravity of the substance in reference to naphtha, and

Fig- 93-

-the specific gravity of the naphtha in reference to water. The product

io8

On Liquids.

[122-

of these two fractions — is the specific gravity of the substance compared

with water.

In determining the specific gravity of porous substances, they are varnished
before being immersed in water, which renders them impervious to moisture
without altering their volume.

Specific gravity of solids at zero as compared with di stilted water at 4° C.

Platinum, rolled . . 22*069 Aluminium . . . 2-680

„ cast . . 20-337 Rock crystal . . . 2-653

Gold, stamped . . 19-362 St. Gobin glass . . 2-488

„ cast . . . 19-258 China porcelain . . 2-380

Lead, cast . . . 11-352 Sevres porcelain . . 2.140

Silver, cast . . . 10-474 Native sulphur . . 2-043

Bismuth, cast . . 9-822 Ivory .... 1-917

Copper, drawn wire . 8-878 Anthracite . . . 1-800

„ cast . . . 8-788 Magnesia , . . 1-740

Bronze coinage . . 8-66 Boxwood . . . 1-330

German silver . . 8-432 Compact coal . . 1-329

Brass .... 8-383 Amber .... 1-078

Steel, not hammered . 7-816 Sodium. . . . 0-970

Iron, bar . . . 7-788 Melting ice . . . 0-930

„ cast . . ■ . 7-207 Paraffin .... 0-874

Tin, cast . . .7-291 Potassium . . . 0-865

Zinc, cast . . . 6-861 Beech .... 0-852

Antimony, cast . . 6-712 Oak .... 0-845

Iodine .... 4"95o Elm .... 0-800

Heavy spar . . . 4.430 Yellow pine . . . 0-657

Faraday's glass . . 4-36 Lithium . . . 0-585

Diamond . 3'53i to 3-501 Common poplar . . 0-389

Flint glass . . . 3-329 Cork .... 0-240

Statuary marble . . 2-837

In this table the different woods are supposed to be in the ordinary air-
dried condition.

123. Specific gravity of liquids. — i. Method of the hydrostatic balance.
From the pan of the hydrostatic balance a body is suspended, on which
the liquid whose specific gravity is to be determined exerts no chemical
action ; for example, a ball of platinum. This is then successively weighed
in air, in distilled water, and in the liquid. The loss of weight of the body
in these two liquids is noted. They represent respectively the weights of
equal volumes of water and of the given liquid, and consequently it is only
necessary to divide the second of them by the first to obtain the required
specific gravity.

Let P be the weight of the platinum ball in air, P' its weight in water, P"
its weight in the given liquid, and let D be the specific gravity sought. The
weight of the water displaced by the platinum is P — P', and that of the

P — P''

P", from which we get D = — -.

second liquid is P

-124] Temperature in ascertaining Specific Gravities. 109

ii. Fahrenheit's hydrometer. — This instrument (fig. 94) resembles Nichol-
son's hydrometer, but it is made of glass, so as to be used in all liquids. At
its lower extremity, instead of a pan, it is loaded with a small bulb containing
mercury. There is a standard mark on the stem.

The weight of the instrument is first accurately determined in air ; it
is then placed in water, and weights added to the scale-pan until the mark
on the stem is level with the water. It follows, from the first principle of
the equilibrium of floating bodies, that the weight of the hydrometer, together
with the weight in the scale-pan, is equal to the weight of the volume of the
displaced water. In the same manner the weight of an equal volume of
the given liquid is determined, and the specific
gravity is found by dividing the latter weight by
the former.

Neither Fahrenheit's nor Nicholson's hydro-
meter gives such accurate results as the hydro-
static balance or the specific gravity bottle.

iii. Specific g7'avity bottle. — This has been
already described (121). In determining the
specific gravity of a liquid, a bottle of special
construction is used ; it consists of a cylindrical
reservoir b (fig. 95), to which is fused a capillary
tube c, and to this again a wider tube a, closed
with a stopper. The bottle is first weighed
empty, and then successively full of water to
the mark c on the capillary stem, and of the
given liquid. If the weight of the bottle be
subtracted from the two weights thus obtained,
the result represents the weights of equal

volumes of the liquid and of water, from which the specific gravity is obtained
by division.

iv. Specific gravity bulbs. — The specific gravity of a liquid is often de-
termined for technical and even scientific purposes by means of specific
gravity bulbs ; these are small hollow glass bulbs, which are prepared in
series, loaded and adjusted so that they exactly float in a liquid of a definite
specific gravity. When carefully prepared they are susceptible of considerable
accuracy.

Solutions of certain metallic salts of high specific gravity have been used
for the mechanical separation of individual minerals of certain rocks. Such
minerals will float or sink according as their specific gravities are lower or
higher than that of a given solution. A saturated solution of the double
iodide of barium and mercury, the specific gravity of which is 3-58, has been
used for this purpose.

124. On the observation of temperature in ascertainine: specific
grravities. — As the volume of a body increases with the temperature, and
as this increase varies with different substances, the specific gravity of any
given body is not exactly the same at different temperatures ; and, con-
,sequently, a certain fixed temperature is chosen for these determinations.
That of water, for example, has been made at 4° C, for at this point it has
the greatest density. The specific gravities of other bodies are assumed to

Fig. 94.

F!g. 95.

no On Liquids. [124-

be taken at zero ; but, as this is not always possible, certain corrections must
be made, which we shall consider in the Book on Heat.

Specific gravities of liquids at zero, compared %uith that of luater at 4° C.
as tinlty.

Mercury

• 13-598

Sea water

1-026

Bromine

. 2-960

Urine

I -020

Ethylic iodide

■ 1-946

Distilled water at 4°

C. .

I -000

Sulphuric acid

. 1-841

„ „ at 0°

C. .

0-999

Chloroform .

■ 1-525

Claret .

0-994

Nitric acid .

. I -420

Olive oil

0-915

Bisulphide of carbon ,

. 1-293

Oil of turpentine .

0-870

Glycerine

I -260

Oil of lemon .

0-852

Hydrochloric acid

I -240

Petroleum

0-836

Blood . . . .

I -060

Absolute alcohol .

0-793

Milk . . . .

1-029

Ether .

0-713

125. Use of tables of specific gravity. — Tables of specific gravity
admit of numerous applications. In mineralogy the specific gravity of a
mineral is often a highly distinctive character. By means of tables of
specific gravities the weight of a body may be calculated when its volume is
known, and conversely the volume when its weight is known.

With a view to explaining the last-mentioned use of these tables, it will be
well to premise a statement of the connection existing between the British
units of length, capacity, and weight. It will be sufficient for this purpose
to define that which exists between the yard, gallon, and pound avoirdupois,
since other measures stand to these in well-known relations. The yard,
consisting of 36 inches, may be regarded as the primary unit. Though it is
essentially an arbitrary standard, it is determined by this, that the simple
pendulum which makes one oscillation in a mean second, at London on the
sea-level, is 39'i3983 inches long. The gallon contains 2j'j-2jj^ cubic inches.
A gallon of distilled water at the standard temperature weighs ten pounds
avoirdupois or 70,000 grains troy ; or, which comes to the same thing, one
cubic inch of water weighs 252-5 grains.

On the French system the metre is a primary unit, and is so chosen
that 10,000,000 metres are the length of a quadrant of the meridian from
either pole to the equator. The metre contains 10 deci/iietres, or 100 centi-
metres, or 1,000 millimetres ; its length equals 1-0936 yards. The unit
of the measure of capacity is the litre or cubic decimetre. The unit of
weight is the gramme, which is the weight of a cubic centimetre of distilled
water at 4° C. The kilogramme contains 1,000 grammes, or is the weight
of a decimetre of distilled water at 4° C. T^x^ gramme equals 15-443 grains.

If V is the number of cubic centimetres (or decimetres) in a certain
quantity of distilled water at 4° C, and P its weight in grammes (or kilo-
grammes), it is plain that P = V. Now consider a substance whose specific
gravity is D ; every cubic centimetre of this substance will weigh as much
as D cubic centimetres of water, and therefore V centimetres of this sub-
stance will weigh as much as DV centimetres of water. Hence, if P is
the weight of the substance in grammes, we have P = DV, If, however, V

-427J

Beaume's Hydrometer.

the volume in cubic inches, and P the weight in grains, we shall have
P = 252-5 DV.

As an example, we may calculate the internal diameter of a glass tube.
Mercury is introduced, and the length ahd weight of the column at 4° C.
are accurately determined. As the column is cylindrical, we have V = Trr'-/,
where r is the radius, and / the length of the column in centimetres. Hence,
if D is the specific gravity of mercury, and P the weight of the column in
grammes, we have P = 7rrVD, and therefore

If rand /are in inches and P in grains, we shall have P = 252-57rr-/D
and therefore

\/^.

52-57rD/

In a similar manner, by weighing a given length, the diameter of very fine
metal wires can be determined with great accuracy.

126. Hydrometers of variable immersion. — The hydrometers of
Nicholson and Fahrenheit are called hydrometers of constant i/ninersion
but variable weight, because they are always immersed to the same extent,
but carry different weights. There are also hydrometers of variable immer-
sion but of constant weight.

12J. Beaume's hydrometer. — This, which was the first of these instru-
ments, may serve as a type of them. It consists of a glass tube (fig. 96)
loaded at the bottom with mercury, and with a bulb blown in the middle.
The stem, the external diameter of which is as regular as possible, is hollow,
and the scale is marked upon it.

The graduation of the instrument differs according as the lic|uid, for
which it is to be used, is heavier or lighter than water. In
the first case, it is so constructed that it sinks in water
nearly to the top of the stem, to a point A, which is marked
zero. A solution of fifteen parts of salt in eighty-five parts of
water is made, and the instrument immersed in it. It sinks
to a certain point on the stem, B, which is marked 15 ; the
distance between A and B is divided into 1 5 equal parts, and
the graduation continued to the bottom of the stem. Some-
times the graduation is on a piece of paper inside the
stem.

The hydrometer thus graduated only serves for liquids
of a greater specific gravity than water, such as acids and
saline solutions. For liquids lighter than water a different
plan must be adopted. Beaume took for zero the point to
which the apparatus sank in a solution of 10 parts of salt in
90 of water, and for 10° he took the level in distilled water.
This distance he divided into 10°, and continued the division
to the top of the scale.

TweddeWs hydrometer is in common use in England
for testing liquids denser than water. It is graduated in such a manner

Fig. 96.

112 On Liquids. [127-

that the reading or number of degrees multiplied by five and added to i,ooo
gives the specific gravity with reference to water at i,ooo. Thus io°
Tweddell represents the specific gravity 1050, and 90° represents 1450.

The graduation of these hydrometers is entirely conventional, and they
give neither the densities of the liquids nor the quantities dissolved. But
they are very useful in making mixtures or solutions in given proportions,
and in evaporating acids, alkaline liquids, solutions of salts, worts, syrups,
and the like to a proper degree of concentration, the results they give being
sufficiently near in the majority of cases.

128. Gay-lussac's alcoholometer. — This instrument is used to deter-
mine the strength of spirituous liquors ; that is the proportion of pure
alcohol which they contain. It differs from Beaume's hydrometer in the
graduation.

The alcoholometer is so constructed that, when placed in pure distilled
water, the bottom of its stem is level with the water, and this point is zero.
It is next placed in absolute alcohol, which marks 100°, and then successively
in mixtures of alcohol and water containing 10, 20, 30, &c., per cent. The
divisions thus obtained are not exactly equal, but their difference is not great,
and they are subdivided into 10 divisions, each of which marks one per cent,
of absolute alcohol in a liquid. Thus a brandy in which the alcoholometer
stood at 48° would contain 48 per cent, of absolute alcohol, and the rest
would be water.

All these determinations are made at 15° C, and for that temperature
only are the indications correct. For, other things being the same, if the
temperature rises the liquid expands, and the alcoholometer will sink, and
the contrary if the temperature fall. To obviate this error, Gay-Lussac con-
structed a table which for each percentage of alcohol gives the reading of
the instrument for each degree of temperature from 0° up to 30°. When the
exact analysis of an alcoholic mixture is to be made, the temperature of the
liquid is first determined, and then the point to which the alcoholometer sinks
in It. The number in the table corresponding to these data indicates the
percentage of alcohol. From its giving the percentage of alcohol, this is
often called the cenfesifnal alcoholometer.

129. Salimeters. — Salivietcrs^ or instruments for indicating the per-
centage of a salt contained in a solution, are made on the principle of the
centesimal alcoholometer. They are graduated by immersing them in pure
water, which gives the zero, and then in solutions containing different percent-
ages of the salt, and marking on the scale the corresponding points. These
instruments are open to the objection that eveiy salt requires a special
instrument. Thus one graduated for common salt would give false indications
in a solution of nitre.

Lactometers are similar instruments, and are based on the fact that
the average density of a good natural quality of milk is ro29. Hence if
water is added to milk, it will indicate a lower specific gravity. But a
common plan of adulteration is to remove cream from the milk, by which
its specific gravity is increased, and then add water so as to reproduce the
original density ; the lactometer will not reveal a fraud of this kind. Urino-
victers are frequently used in medicine to test the variations in the density
of urine, which accompany and characterise certain forms of disease.

-130] Densimeter. 113

130. Densimeter. — Rousseaii's densimeter (fig. 97) is of great use in many
scientific investigations, in determining the specific gravity of a small
quantity of a liquid. It has the same form as Beaume's
hydrometer, but there is a small tube AC at' the top
of the stem in which is placed the substance to be de-
termined. A mark A on the side of the tube indicates
a measure of a cubic centimetre.

The instrument is so constructed that when AC is
empty it sinks in distilled water to a point B, just at
the bottom of the stem. It is then filled with distilled
water to the height measured on the tube AC, which
indicates a cubic centimetre, and the point to which it
now sinks is 20°. The interval between o and 20 is
divided into 20 equal parts, and this graduation is
continued to the top of the scale. As this is of uniform
bore, each division corresponds to -\7 gramme or 0-05.

To obtain the density of any liquid, bile for ex-
ample, the tube is filled with it up to the mark A ; if
the densimeter sinks to 20 divisions, its weight is
0-05 X 20-5 = 1-025 ; that is to say, with equal volumes, the weight of water
being i, that of bile is 1-025. The specific gravity of bile is therefore 1-025.

Fig. 97-

114

On Liquids.

[131-

CHAPTER II,

CAPILLARITY, ENDOSMOSE, EFFUSION, AND ABSORPTION.

131. Capillary phenomena. — When solid bodies are placed in contact
with liquids, phenomena are produced which are classed under the general head
oi capillary phe7ioi)iefta, because they are best seen in tubes whose diameters
are so small as to be coxnparable with that of a hair. These phenomena are
treated of in physics under the head of capilhwity or capillary attraction ; the
latter expression is also applied to the force which produces the phenomena.

The phenomena of capillarity are very various, but may all be referred
to the relation of the attraction of the liquid molecules for each other, to the
attraction between these molecules and solid bodies. The following are
some of these phenomena : —

When a body is placed in a liquid which wets it — for example, a glass
rod in water— the liquid, as if not subject to the laws of gravitation, is raised
upwards against the sides of the solid, and its surface, instead of being hori-
zontal, becomes sHghtly concave (fig. 98). If on the contrary, the solid is

L.^.__

Fig. 98.

Fig. 99.

Fig. 100.

one which is not moistened by the hquid, as glass by mercury, the liquid is
depressed against the sides of the solid, and assumes a convex shape, as
represented in fig. 99. The surface of the liquid exhibits the same concavity
or convexity against the sides of a vessel in which it is contained, accord-
ing as the sides are or are not moistened by the liquid.

These phenomena are much more marked when a tube of small
diameter is placed in a liquid. And according as the tubes are or are not
moistened by the liquid, an ascent or a depression of the liquid is produced,
which is greater in proportion as the diameter is less (figs. 100 and loi).

When the tubes are moistened by the liquid, its surface assumes the
form of a concave hemispherical segment, called the concave moiiscus
(fig. 100) ; when the tubes are not moistened, there is a convex meniscus
(fig. lOl).

-132] Ascent aitd Depression in Capilhny Tubes. 1 1 5

132. ILaws of the ascent and depression in capillary tubes. — The

most important law in reference to capillarity is known as Jiiriiis law. It
is : For the same liquid, atid the same temperature, the mean height of the
ascent in a capillary tube is inversely as the diameter of the tube. Thus, if
water rises to a height of 30 mm. in a tube i mm. in diameter, it will only
rise to a height of 15 mm. in a tube 2 mm. in diameter, but to a height of
300 mm. in a tube OT mm. in diameter. This law has been verified with
tubes whose diameters ranged from 5 mm. to 0-07 mm. It presupposes that
the liquid has previously moistened the tube.

The mean height is the height of a cylinder with a circular base which
has exactly the same volume as the liquid column raised. If h is this
height and 2r the diameter of the tube, Jurin's law may be expressed by the
equation

2rh = const.

If r, the radius, is taken at i mm., then the height in millimetres to
which any liquid rises is a measure of the capillary constant.

For various liquids, and the same temperature, the mean heights raised in
capillary tubes of the same diameter vary with the nature of the liquid. Of
all liquids water rises the highest ; thus in a glass tube i -29 mm. in diameter,
the heights of water, alcohol, and turpentine are respectively 23-16, 9-18, and
9-85 mm.

For the same liquid, and the same temperature, the 7nean heights are
independent of the form of the capillary tube. That is to say, the shape of
the tube above or below the
meniscus has no effect on the j

phenomenon. The columns ^r*" »ihI r-Ju L

raised would be of very un-
equal weights, but of equal
heights h, in the tubes repre- ^
sented in fig 102, all of which ^
have the same diameter when
the liquid stops. The co-
efficient r is the diameter
which corresponds to the region of the meniscus.

Provided the liquid moistens the tube, neither its thickness nor its nature
has any influence on the height to which the Hquid rises. Thus water rises
to the same height in tubes of different kinds of glass, and of rock crystal,
provided the diameters are the same.

The height to which a given liquid rises in a capillary tube diminishes
as the temperature increases. Thus in a capillary tube in which water stood
at a height of 307 mm at 0°, it stood at 28-6 mm. at 35°, and at 26 mm. at 80°.
This diminution of height is considerably greater than is accounted for by the
diminished density of the water ; for, while this is about 0-00045 ^or each
degree between 0° and 100°, the mean diminution of the height is 0-00182,
or about four times as much.

At the same time that the heights become less the menisci 2a& flattened,
so that from a certain temperature, which varies with different liquids, the
capillary surface becomes flat and horizontal, and its level is that of the

ii6

On Liquids.

[132-

external liquid. Working in closed vessels Wolff found this temperature to
be 191° for ether, and 500° for water.

In regard to the depression of liquids in tubes which they do not
moisten, Jurin's law has not been found to hold with the same accuracy.
The reason for this is probably to be found in the following circumstances : —
When a liquid moistens a capillary tube, a very thin layer of liquid is formed
against the sides, and remains adherent even when the liquid sinks in the
tube. The ascent of the column of liquid takes place then, as it were, inside
a central tube, with which it is physically and chemically identical. The
ascent of the liquid is thus an act of cohesion. It is therefore easy to
understand why the nature of the sides of the capillary tube should be
without inlluence on the height of the ascent, which only depends on the
diameter.

With licjuids, on the contrary, which do not moisten the sides of the tube,
the capillary action takes place between the sides and the liquid. The
nature and structure of the sides are never quite homogeneous, and there is
always, moreover, a layer of air on the inside, which is not dissolved by the
liquid. These two causes undoubtedly exert a disturbing influence on the
law of Jurin.

133. Ascent and depression between parallel or inclined surfaces.^
When two bodies of any given shape are clipped in water, analogous phe-
nomena are produced, provided the bodies are sufficiently near. If, for
example, two parallel glass plates are immersed in water at a very small
distance from each other, water will rise between the two plates in the
inverse ratio of the distance which separates them. The height of the
ascent for any given distance is half what it would be in a tube whose dia-
meter is equal to the distance between the plates.

If the parallel plates are immersed in mercury, a corresponding depression
is produced, subject to the same laws.

If two glass plates AB and AC, with their planes vertical and inclined to
one another at a small angle, as represented in fig. 103, have their ends

Fig. 103.

Fig. 105.

dipped into a liquid which wets them- the liquid will rise between them.
The elevation will be greatest at the line of contact of the plates, and
from hence gradually less, the surface taking the form of an equilateral
hyperbola.

If a drop of water be placed within a conical glass tube whose angle is
small, and axis horizontal, it will have a concave meniscus at each end

-134] Tension of the Free Surface of Liquids. 117

(fig. 104), and will tend to move towards the vertex. But if the drop be of
mercury it will have a convex meniscus at each end (fig. 105), and will tend
to move from the vertex.

1 34. Tension of the free surface of liquids. — The great mobility which is
characteristic of the liquid state undergoes an alteration in the neighbour-
hood of theyr^^ surface of a liquid, or that which is bounded by a gas or by
a vacuum. This surface has greater cohesion than any other. For, consider
any particle a at the surface (fig. 106), and let the sphere represent the
range through which the molecular attraction is exerted, or what is called
the radius of iiwlecular activity. The attractive forces of the adjacent
particles, which are exerted in all directions, may be resolved into horizontal
and vertical components ; the attractions of the former will compensate each
other. But the attractions represented by the molecules within the hemi-
sphere beneath the surface ^ ^ j^
are not so compensated, and
consequently the latter will
exercise a considerable pull
towards the interior.

Consider, again, a par-
ticle b., so much below the
surface that the greater part
of the sphere comes into
operation. If a plane de be
laid as much below b as the

surface is above it, the attractive forces from the molecules within ghed will
neutralise each other. But the segment def remains uncompensated, and
exerts a pull similar to, though weaker than, that which acts on the molecule a.

The molecule c finally is surrounded uniformly by its adjacent ones, and
their resultant action is zero.

The effect of these actions is to lessen the mobility of particles at or
veiy near the surface, while those in the interior are c^uite mobile ; the sur-
face, as it were, is stretched by an elastic skin, the result being the same as
if the surface layer exerted a pressure on the interior. This surface tension,
as it is called, is greater, the greater the cohesion of the liquid.

When the surface of a liquid increases, more particles enter into the
condition of the surface layer, to effect which a certain amount of work is
required. On the other hand, when the surface is diminished, the molecules
pass into the state of the internal layer, and they perform work. The work
clone when a sc|uare mm. of surface passes into the interior is called the
coefficient of surface tension.

The existence of this surface tension may be illustrated by several inter-
esting experiments. In that of Dupre (fig. 107), a quadrangular flat vessel
ABCD is used, of which one side
CD is movable about a hinge.
By means of a string this side
is pressed against a wedge, and

the vessel is filled with water. Fig. 107.

On burning the wire the side CD'
reverts to its original position CD. Now, as the hydrostatic pressure would

ii8

On Liquids.

[134-

have kept it pressed against the wedge, there must be a tangential force at
work restoring it to the vertical, which is an effect of the surface tension.

Another experiment by Mensbrugghe is made by means of a wire frame
(fig. io8 a\ which is immersed in a solution of soap, such as is used for blow-
ing soap bubbles. On removing this a thin
film is formed. A loop of fine silk thread
moistened with the liquid in question is care-
fully placed on the film and assumes any
shape (fig. 1 08 a). By means of a spill of blot-
ting paper, the liquid is carefully removed
from inside the loop, and the contour is then
seen to stretch and assume a circular form
(fig. 108 b), which is owing to the lateral pull
exerted uniformly on the edge of the loop.

The surface tension depends on the form
of the surface. Its value has been determined
in the case of spheroidal bodies. If the pres-
sure which is exerted on a plane surface be called P, the pressure /, on a

spherical surface of radius p, is / = P -h ^ for convex, and / = P — "-liox

20
P

concave surfaces.

Hence for a spheroidal shell, the internal radius OA (fig. 109) of which is

/J, and its thickness AB = (r/, the pressure of the outer layer is/-P-t- ~^,,

p + a

^-, and the resultant is
P

a pressure exerted inwards.

and of the inner layer /i = P

2(/. 20

their differences

p + a p

since/ >/j. This is well illustrated by blowing a soap
bubble on a glass tube. So long as the other end of
the tube is closed, the bubble remains, the elastic force
of the enclosed air counterbalancing the tension of
the surface ; but when the tube is opened, the tension
of the surface being unchecked, the bubble gradually contracts and finally
disappears.

Insects can often move on the surface of water without sinking. This
phenomenon is caused by the fact that, as their feet are not wetted by the
water, a depression is produced, and the elastic reaction of the surface layer
keeps them up in spite of their weight. Similarly a sewing-needle, gently
placed on water, does not sink, because its surface, being covered with an
oily layer, does not become wetted. The pressure of the needle brings
about a concavity, the surface tension of which acts in opposition to the
weight of the needle. But if washed in alcohol or in potash, the metal is
wetted and at once sinks to the bottom. -

Among the phenomena due to surface tension may be mentioned the well-
known one of the ' tears of wine.' The^ surface tension of water in contact
with air is greater than that of any othei" liquid except mercury. It is more
than three times as great as that of alcohol. When a wine-glass is half filled
with a strong wine, the wine rises up against the sides like any other liquid ;

-136] lufinence of Cnrvatuvc on Capillary Phetioinena. 1 1 9

but the alcohol evaporates rapidly from the surface, the consequence of which
IS that the liquid layer becomes more watery. Near the surface of the
liquid the strength of the liquid layer is kept up by diffusion, but higher up,
owing to the increased surface tension of the more aqueous wine, it creeps up
the sides and draws with it some of the stronger alcoholic liquid below, the
increasing weight of which ultimately causes it to break and run down in
drops.

If a thin layer of water be spread on a plate, and a drop of ether be
placed upon it, the water retreats from the drop. Here, instead of the surface
tension between water and air, we have that between water and ether, which
is smaller ; the effect is much the same as if there were a tightly stretched
india-rubber skin, and a portion of it were softened or made thinner.

135. Cause of the curvature of liquid surfaces in contact with solids.
The form of the surface of a liquid in contact with a solid depends on the
relation between the attraction of the solid for the liquid, and of the mutual
attraction between the molecules of the liquid.

Let 111 be a liquid molecule (fig. no) in contact with a solid. This
molecule is acted upon by three forces : by gravity, which attracts it in the
direction of the vertical mV ; by the attraction of the hquid F, which acts in

the direction wF ; and by the attraction of the plate », which is exerted in
the direction m)i. According to the relative intensities of these forces, their
resultant can take three positions : —

i. The resultant is in the direction of the vertical ;;zR (fig. no). In this
case the surface m is plane and horizontal ; for, from the condition of the
equihbrium of liquids, the surface must be perpendicular to the force which
acts upon the molecules.

ii. If the force n increases or F diminishes, the resultant R is within the
angle mii? (fig. 1 1 1) ; in this case the surface takes a direction perpendicular
to 7«R, and becomes concave.

iii. If the force F increases or 11 diminishes, the resultant R takes the
direction ;«R (fig. 112) within the angle PwF, and the surface, becoming
perpendicular to this direction, is convex.

136. Influence of curvature on capillary phenomena. — The elevation
or depression of a liquid in a capillaiy tube depends on the concavity or
convexity of the meniscus. In a concave meniscus, abed (fig. 113), the liquid
molecules are sustained in equilibrium by the forces acting on them, and they
exert no downward pressure on the inferior layers. On the contrary, in virtue
of molecular attraction, they act on the nearest inferior layers, from which it
follows that the pressure on any layer mn, in the interior of the tube, is less

I20

On Liqiiids.

[136-

than if there were no meniscus. The consequence is that the Hquid rises
in the tube until the internal pressure on the layer ;//;/ is equal to the pressure
op^ which acts externally on a point p of the same layer.

Where the meniscus is convex (fig. 114), equilibrium exists in virtue of
the molecular forces acting on the liquid : but as the molecules which

would occupy the same space ghik^ if there were no molecular action, do
not exist, they exert no attraction on the lower layers. Consequently, the
pressure on any layer w;?, in the interior of the tube, is greater than if the
space gJiik were filled, for the molecular forces are more powerful than
gravity. The liquid ought, therefore, to sink in the tube until the internal
pressure on a layer, inn, is equal to the external pressure on any point, p, of
this layer.

137. Various capillary phenomena. — The attractions and repulsions
observed between bodies floating on the surface of liquids find their expla-
nation in the concave or convex curvature which the liquid assumes in con-
tact with the solid. The following are some of them.

When two floating balls both moistened by the liquid — for example, cork
upon water — are so near that the liquid surface between them is not level,
an attraction takes place. The same effect is produced when neither of the
balls is moistened, as is the case with balls of wax on water.

Lastly, if one of the balls is moistened and the other not, as a ball of cork
and a ball of wax in water, they repel each other if the curved surfaces of the
liquid in their respective neighbourhoods intersect.

A drop of mercury on a table has a spherical shape, which, like that of
the heavenly bodies, is due to attraction. The globule of mercury behaves
as if its molecules had no weight, since it remains spherical. That is, the
molecular attraction is far greater than the weight, which only alters the
shape of the globule if the quantity of mercury is much greater ; it then
flattens, but always retains at its edge the convex form which molecular
attraction imparts to it. A liquid immersed in another, with which it does
not mix, of exactly the same specific gravity, such as olive oil in a mixture
of alcohol and water, assumes the spherical form (fig. 60).

To this cause also is due the spherical form acquired by small masses of
liquid which fall through great heights, such as raindrops, and molten lead in
casting small shot.

When a capillary tube is immersed in a liquid which moistens it, and
IS then carefully removed, the column of liquid in the tube is seen to be twice
as long as while the tube was immersed in the liquid. This arises from
the fact that a drop adheres to the lower extremity of the tube and forms a

-138] Determination of the Constant of Capillarity. 12 1

convex meniscus, which concurs with that of the upper meniscus to form a
longer column (131).

For the same reason a liquid does not overflow in a capillary tube,
although the latter may be shorter than the liquid column which would
otherwise be formed in it. For when the liquid reaches the top of the tube,
its upper surface, though previously concave, becomes convex, and, as the
downward pressure becomes greater than if the surface were plane the
ascending motion ceases.

It is from capillarity that oil ascends in the wicks of lamps, that water
rises in woods, sponge, bibulous paper, sugar, sand, and in all bodies which
possess pores of a perceptible size. In the cells of plants the sap rises with
great force, for here we have to do with vessels whose diameter is less than
o-oi mm. Efflorescence of salts is also due to capillarity ; a solution rising
against the side of a vessel, the water evaporates, and the salt forms on the

Fig. IIS.

side a means of furthering still more the ascent of a liquid. Capillarity is,
moreover, the cause of the following phenomenon : — When a porous sub-
stance, such as gypsum, or chalk, or even earth, is placed in a porous vessel
of unbaked porcelain, and the whole is dipped in water, the water penetrates
into the pores, and the air is driven inwards, with such force, so that it is
under four or five times its usual pressure and density. Jamin has proved
this by cementing a manometer into blocks of chalk, gypsum, &c., and he
has made it probable that a pressure of this kind, exerted upon the roots,
promotes the ascent of sap in plants.

138. Determination of the constant of capillarity .^ — This determina-
tion may be effected in various ways, of which the simplest and perhaps the
most accurate is that of the measuring the ascent of a liquid in capillary
tubes. For this purpose capillary tubes of glass are used, the diameter of

122

On Liquids.

[138-

which is determined by introducing a thread of mercury into the tube and

ascertaining the weight of a given length (125).

The height to which the Hquid rises in the capillary tube may be read

oft" by a cathetometer (fig. 115). The capillary tube is fixed to a cross-piece

of wood, which is placed on the edges of a glass tube ee half filled with the
liquid. In order that the liquid may properly moisten the
tube it is sucked up by means of a caoutchouc tube beyond
the height at which it finally stands. The cathetometer is
then raised to the level 1 1 n oi the lowest point of the
meniscus. The pointed screw b is then screwed until its point
just grazes the liquid, and the position of the point is read
off". The difference of these two readings gives the desired
height.

A simpler arrangement is the following (fig. 116). The
capillary tube is fixed to a strip of opaque glass, graduated in
millimetres. The lower end of the tube, which is fixed in
a suitable support, is first dipped in a small vessel of the
liquid, and then the movable steel point p, being placed
opposite the zero of the graduation, liquid is added drop
by drop until its level just grazes the point. This height
may be read off" by a lens.

In the case of a liquid which wets the tube, the force
which holds up the liquid in the tube is the surface tension,
a acting along the cross-section of the tube ; that is 27rra,
where r is the diameter of the tube. This force is equal
to the weight of the column of liquid, which is tvr-hs, where
h is the height of the column of liquid, and j' its specific
hrs,

gravity.

J- is unity

From this we get
/ir.

and for water, where

Fig.

This, which is known as the capillary

constant, gives the weight supported by the unit of length,
which is usually taken at a millimetre. The following are
some of the values expressed in milligrammes : —
Water .... 7"24 ' Turpentine .... 277
Hydrochloric acid . 7-15 Petroleum .... 2-57

Olive oil . . . 3'27 Alcohol .... 2-27

Quincke determined the capillary constant of such metals as gold and
silver by fusing the ends of their wires and weighing the drops which detached
themselves. The constant, as can be shown, is equal to the quotient of the
weight of the drop by the cross-section of the wire.

139. Endosmose and exosmose. — When two different liquids are sepa-
rated by a thin porous partition, either inorganic or organic, a current sets
in from each liquid to the other ; to these currents the names endosmose
and exosmose are respectively given. These terms, which signify impulse
from within and impulse from without, were originally introduced by
Dutrochet, who first drew attention to these phenomena. The general
phenomenon may be termed diosmose. They may be well illustrated by

-139J

Eudosmosc and Exosniosc.

123

means of the endosmo>neter. This consists of a long tube, at the end of
which a membranous bag is firmly bound (fig. 117). The bag is then filled
with a strong syrup, or some other solution denser than water, such as milk
or albumen, and is immersed in water. The liquid is found gradually to
rise in the tube to a height which may attain
several inches ; at the same time the level
of the liquid in which the endosmometer is
immersed becomes lower. It follows, there-
fore, that some of the external liquid has
passed through the membrane and has
mixed with the internal liquid. The ex-
ternal liquid, moreover, is found to contain
some of the internal liquid. Hence two
currents have been produced in opposite
directions. The flow of the liquid towards
that which increases in volume is endosiiiose^
and the current in the opposite direction is
exosmose. If water is placed in the bag,
and immersed in the syrup, endosmose is
produced from the water towards the syrup,
and the liquid in the interior diminishes in
volume while the level of the exterior is
raised.

The phenomena ot endosmose are ex-
plained as follows : — The diaphragm is made
up of numerous capillary apertures, and
according to the difference in the molecular
attraction of its material for different liquids
it absorbs different quantities of them. Thus
Liebig found that in 24 hours 100 grammes of dry ox-bladder absorbed 268
^Tammes of water, or 133 grammes of solution of chloride of sodium. If,
therefore, such a bladder separates water, and solution of salt, it v/ill absorb
both, but water in larger quantities. These liquids will now be withdrawn
from the bladder by the different liquids on the two sides, but in unequal
quantities, for the quantities present in the bladder are different. Hence
more water will pass in one direction than in the other.

The height of the ascent in the endosmometer varies with different
liquids. Of all vegetable substances, sugar is that which, for the same
density, has the greatest power of endosmose, while albumen has the
highest power of all animal substances. In general it may be said that
endosmose takes place towards the denser liquid. Alcohol and ether form
an exception to this ; they behave like liquids which are denser than water.
With acids, according as they are more or less dilute, the endosmose is from
the water towards the acid, or from the acid towards the water.

It is necessary for the production of endosmose — (i.) that the liquids be
different but capable of mixing, as alcohol and water — there is no dios-
mose, for instance, with water and oil; (ii.) that the liquids be of different
densities ; and (iii.) that the membrane must be permeable to at least one of
the substances.

Fig. 117.

124 ^^^ Liquids. [139-

The current through thin inorganic plates is feeble, but continuous, while
organic membranes are rapidly decomposed, and diosmose then ceases.

If a tube filled with water be closed at both ends by bladder (fig. ii8),
and one end is placed in a vessel of water, the other being in contact with
the air, the water gradually evaporates through the bladder.
This water, however, is as rapidly replaced, so that, in con-
sequence of evaporation, water moves towards the place
where this takes place. Hence endosmose plays a part in
the motion of the fluids in animals and vegetables. The
evaporation from the skin of animals brings about a motion
of liquids from the interior towards the evaporating sur-
face. In like manner the passage of water to the rootlets of
plants, as well as the ascent of sap to the highest points
of the trees, is favoured by evaporation from branchlets.
leaves, flowers, and fruit.

The well-known fact that dilute alcohol kept in a porous
vessel becomes concentrated depends on endosmose. If a
mixture of alcohol and water be kept for some time in a bladder, the volume
diminishes, but the alcohol becomes much more concentrated. The reason
doubtless is that the bladder absorbs water more readily than alcohol, and
accordingly water evaporates on the surface, and thus brings about a con-
centration of the residue.

Dutrochefs method is not adapted for quantitative measurements, for it
does not take into account the hydrostatic pressure produced by the column.
Jolly has examined the endosmose of various liquids by determining the
weights of the bodies diffused. He calls the cndosmotic equivalent of a sub-
stance the number which expresses how many parts by weight of water pass
through the bladder in^exchange for one part by weight of the substance. The
following are some of the endosmotic equivalents which he determined : —

Sulphate of copper . . 9-5

„ magnesium . 117

Caustic potass . . 216-0

He also found that the endosmotic equivalent increases with the temperature,
and that the quantities of substances which pass in equal times through the
bladder are proportional to the strengths of the solutions.

140. diffusion of liquids. — If oil be poured on water, no tendency to
intermix is observed, and even if the two liquids be violently agitated to-
gether, on allowing them to stand, two separate layers are formed. With
alcohol and water the case is different ; if alcohol, which is specifically
lighter, be poured upon water, the liquids gradually intermix, in spite of the
difference of the specific gravities : they diffuse into one another.

This point may be illustrated by the experiment represented in fig. 119.
A tall jar contains w^ater coloured by solution of blue litmus ; by means of
a funnel some dilute sulphuric acid is carefully poured in, so as to form a
layer at the bottom ; the colour of the solution is changed into red, pro-
gressing upwards, and after forty-eight hours the change is complete — a

Sulphuric acid

0-4

Alcohol .

4-2

Chloride of sodium

4-3

Sugar .

7-1

-140] Diffusion of Liquids. 125

result of the action of the acid, and a proof, therefore, that it has diffused
throughout the entire mass.

The laws of this diffusion, in which no porous diaphragm is used, were
completely investigated by Graham. The method by which his latest
experiments were made was the following : — A small wide-necked bottle A
(fig. 120) filled with the liquid whose rate of diffusion was to be examined
was closed by a thin glass disc and placed in a larger vessel B, in which
water was poured to a height of about an inch above the top of the bottle.
The disc was carefully removed, and then after a given time successive
layers were carefully drawn off by means of a siphon or pipette, and their
contents examined.

The general results of these investigations may be thus stated : —

i. When solutions of the same substance, but of different strengths, are
taken, the quantities diffused in equal times are proportional to the strengths
of the solutions.

ii. In the case of solutions containing equal weights of different substances
the quantities diffused vary with the nature of the substances. Saline

Fig. 119.

substances may be divided into a number of cqiddiffiisive groups, the rates
of diffusion of each group being connected with the others by a simple
numerical relation.

iii. The quantity diffused varies with the temperature. Thus, taking the
rate of diffusion of hydrochloric acid at 15° C. as unity, at 49° C. it is 2-18.

iv. If two substances which do not combine be mixed in solution, they
may be partially separated by diffusion, the more diffusive one passing out
most rapidly. In some cases chemical decomposition even may be effected
by diffusion. Thus, bisulphate of potassium is decomposed into free sulphuric
acid and neutral sulphate of potassium.

v. If liquids be dilute, a substance will diffuse into water containing
another substance dissolved, as into pure water ; but the rate is materially
reduced if a portion of the same diffusing substance be already present.

The following table gives the approximate times of equal diffusion : —

126

On Liquids.

[140-

Hydrochloric acid . . ro Sulphate of magnesium . 7-0
Chloride of sodium . • 2-3 Albumen. . . . 49-0
Sugar 7'o Caramel . . . .98-0

It will be seen from the above table that the difference between the rates
of diffusion is very great. Thus sulphate of magnesium, one of the least
diffusible saline substances, diffuses 7 times as rapidly as albumen and 14
times as rapidly as caramel. These last substances, like hydrated silicic
acid, starch, dextrine, gum, &c., constitute a class of substances which are
characterised by their incapacity for taking the crystalline form, and by the
mucilaginous character of their hydrates. Considering gelatine as the type
of this class, Graham has proposed to call them colloids (ko'AXt/, glue), in con-
tradistinction to the far more easily diffusible cryslalloid substances. Colloids
are for the most part bodies of high molecular weight, and it is probably the
larger size of their molecules which hinders their passing through minute
apertures.

Graham devised a method of separating bodies based on their un-
ecjual dififusibility, which he called dialysis. His dialyser (fig. 121) consists of
a ring of gutta-percha, over which is stretched while wet a sheet of parch-
ment paper, forming thus a vessel about two inches high and ten inches in

Fig. 121

Fig.

diameter, the bottom ot which is 01 parchment paper. After pouring in the
mixed solution to be dialysed, the whole is floated on a vessel containing a
very large quantity of water (fig. 122). In the course of one or two days a
more or less complete separation will have been effected. Thus a solution
of arsenious acid mixed with various kinds of food readily diffuses out. The
process has received important applications to laboi-atory and pharmaceutical
purposes.

Eimilsions such as are of frequent use in medicine are prepared by mix-
ing intimately oil with a solution of gum, albumen, or some other colloid, and
water. As stated above, the reason of difficulty with which a colloid diffuses
through the membrane of another colloid is probably that its molecules are
too large and too near each other— in other words that the pores are too
small. With an ordinary emulsion, the minute droplets of oil are dispersed
among the large and difficult mobile particles of the colloid, which thus
hinder their motion, and thereby prevent them from uniting and forming a
coherent layer.

Diosmose plays a most important part in organic life ; the cell-walls are
diaphragms, through which the liquids in the cells set up diosmotic com-
munications.

-143] Velocity of Effiux. TorricellV s Theorem. 127

CHAPTER III.

HYDRODYNAMICS.

141. Hydrodynamics. — The science which treats of the motion of Hquids
is called hydrodyftamics ; and the application of the principles of this science
to conducting and raising water in pipes and to the use of water as a motive
power is known by the name of Jiydraiilics.

142. Velocity of efflux. Torricelli's theorem. — Let us imagine an
aperture made in the bottom of any vessel, and consider the case of a par-
ticle of liquid on the surface, without reference to those which are beneath.
If this particle fell freely, it would have a velocity on reaching the orifice
equal to that of any other body falling through the distance between the
level of the liquid and the orifice. This, from the laws of falling bodies, is
\/2gk, in which g is the accelerating force of gravity, and h the height. If
the liquid be maintained at the same level, for instance by a stream of water
running into the vessel sufficient to replace what has escaped, the particles
will follow one another with the same velocity, and will issue in the form of
a stream. Since pressure is transmitted equally in all directions, a liquid
would issue from an orifice in the side with the same velocity, provided the
depth were the same.

The law of the velocity of efflux was discovered by Torricelli. It may be
enunciated as follows : — The velocity of efflux is the velocity which a freely
falling body would have on reaching the orifice after having started fro)n
a state of rest at the surface. It is algebraically expressed by the formula
v=^2gh.

It follows directly from this law that the velocity of efflux depends on the
depth of the orifice below the surface, and not on the nature of the liquid.
Through orifices of equal size and of the same depth, water and mercury
would issue with the same velocity, for although the density of the latter
liquid is greater, the weight of the column, and consequently the pressure, are
greater too. It follows further that the velocities of efflux are directly pro-
portional to the square roots of the depth of the orifices. Water would issue
from an orifice 100 inches below the surface with ten times the velocity with
which it would issue from one an inch below the surface.

The quantities of water which issue from orifices of different areas are
very nearly proportional to the size of the orifice, provided the level remains
constant.

143. Direction of the jet from lateral orifices. — From the principle of
the equal transmission of pressui^e, water issues from an orifice in the side of
a vessel with the same velocity as from an aperture in the bottom of a vessel
at the same depth. Each particle of a jet issuing from the side of a vessel

128 On Liquids. [143-

begins to move horizontally with the velocity above mentioned, but it is at
once drawn downward by the force of gravity in the same manner as a bullet

fired from a gun, with its axis hori-
zontal. It is well known that the
bullet describes a parabola (51)
with a vertical axis, the vertex
being the muzzle of the gun. Now,
since each particle of the jet moves
in the same curve, the jet itself
takes the parabolic form (123).

In every parabola there is a
certain point called the focus, and
the distance from the vertex to the
Fig. 123. focus fixes the magnitude of a

parabola in much the same manner
as the distance from the centre to the circumference fixes the magnitude
of a circle. Now it can easily be proved that the focus is as much below
as the surface of the water is above the orifice. Accordingly, if water issues
through orifices which are small in comparison with the contents of the vessel,
the jets from orifices at different depths below the surface take diiTerent
forms as shown in fig. 123. If these are traced on paper held behind the jet,
then, knowing the horizontal distance and the vertical height, it is easy to
demonstrate that the jet forms a parabola.

144. Height of the jet. — If a jet issuing from an orifice in a vertical
direction has the same velocity as a body would have which fell from the
surface of the liquid to that orifice, the jet ought to rise to the level of the
liquid. It does not, however, reach this ; for the particles which fall hinder
it, But by inclining the jet at a small angle with the vertical, it reaches
about j^^ of the theoretical height, the difference being due to friction and
to the resistance of the air. By experiments of this nature the truth of
Torricelli's law has been demonstrated.

145. Quantity of efflux. Vena contracta.- — If we suppose the sides of
a vessel containing water to be thin, and the orifice to be a small circle whose

area is A, we might think that the quantity of water E dis-
charged in a second would be given by the expression
A.\/2gh, since each particle has, on the average, a velocity
equal to \/2gh, and particles issue from each point of the
orifice. But this is by no means the case. This may be
explained by reference to fig. 124, in which AB represents an
orifice in the bottom of a vessel — what is true in this case
being equally true of an orifice in the side of the vessel.
Every particle above AB endeavours to pass out of the
vessel, and in so doing exerts a pressure on those near it.
Those that issue near A and B exert pressures in the
directions MM and NN ; those near the centre of the orifice in the direction
RQ, those in the intermediate parts in the directions PQ, PQ. In. conse-
quence, the water within the space PQP is unable to escape, and that which
does escape, instead of assuming a cylindrical form, at first contracts, and
takes the form of a truncated cone. It is found that the escaping jet

Fig. 124.

-146] Influence of Tubes on the Quantity of Efflux. i 29

continues to contract, until at a distance from the orifice about equal to the
diameter of the orifice. This part of the jet is called the vena contracta. \x
is found that the area of its smallest section is about § or 0-625 of that of the
orifice. Accordingly, the true value of the efiflu.x per second is given approxi-
mately by the formula ^ ^ o-62A^2-/.,

or the actual value of E is about 0-62 of its theoretical amount.

146. Influence of tubes on the quantity of efflux. — The ixsult given
in the last article has reference to an aperture in a thin wall. If a cylindrical
or conical efflux tube, or ajutage, is fitted to the aperture, the amount of the
efflux is considerably increased, and in some cases falls but a little short of
its theoretical amount.

A short cylindrical ajutage, whose length is from two to three times its dia-
meter, has been found to increase the efflux per second to about 0-82 A ^/2_^/^.
In this case the water on entering the ajutage forms a contracted vein (fig.
126), just as it would do on issuing freely into the air ; but afterwards it ex-
pands, and, in consequence of the adhesion of the water to the interior surface
of the tube, has, on leaving the ajutage, a section greater than that of the
contracted vein. The contraction of the jet within the ajutage causes a par-
tial vacuum. If an aperture is made in the ajutage, near the point of greatest
contraction, and is fitted with a vertical tube, the
other end of which dips into water (fig. 126), it is
found that water rises in the vertical tube, thereby
proving the formation of a partial vacuum.

If the ajutage has the form of a conic frustum
whose larger end is at the aperture, the efflux in
a second maybe raised to o-<^2p^^ igh, provided
the dimensions are properly chosen. If the
smaller end of a frustum of a cone of suitable
dimensions be fitted to the orifice, the efflux
may be still further increased, and fall very little
short of the theoretical amount.

When the ajutage has more than a certain
length, a considerable diminution takes place in
the amount of the efflux : for example, if its length
is 48 times its diameter, the efflux is reduced to o-6'},K\/2gh. This arises from
the fact that, when water passes along cylindrical tubes, the resistance in-
creases with the length of the tube ; for a thin layer of liquid is attracted to
the walls by adhesion, and the internal flowing liquid rubs against this.
The resistance which gives rise to this result is called hydraidic friction : it
is independent of the material of the tube, provided it be not roughened ;
but depends in a considerable degree on the viscosity of the liquid ; for
instance, ice-cold water experiences a greater resistance than lukewarm water.

According to Prony, the mean velocity v of water in a cast-iron pipe of
the length /, and the diameter d., under the pressure^, is in metres

This is on the assumption that the tubes are straight. An)- angle or
curvature of the tube diminishes it, seeing that part of the motion is used up

I30

On Liquids.

[146-

in pressure against the sides. Thus Venturi found the time requisite to fill
a small vessel by means of a tube 38 inches in length by 3-3 in diameter, was
45, 50, or 70 seconds, according as the tube was straight, curved, or bent at
a right angle.

By means of hydraulic pressure Tresca submitted solids such as silver,
lead, iron and steel, powders like sand, soft plastic substances such as clay,
and brittle bodies like ice, to such enormous pressures as 100,000 kilo-
grammes, and has found that they then behave like fluid bodies. His ex-
periments show also that these bodies transmit pressure equally in all
directions when the pressure is considerable enough.

147. Efflux throug-h capillary tubes. — This was in\estigated by
Poisseuille by means of the apparatus represented in fig. 127, in which the
capillary tube AB is sealed to a glass tube on which a bulb is blown. The
volume of the space between the marks M and N is accurately determined,
and the apparatus, having been filled with the liquid under examination
by suction, is connected at the end M with a reservoir of compressed
air, in which the pressure is measured by means of a mercury mano-
meter (183). The time is then noted which is required for the level of the
liquid to sink from M to N, the pressure remaining constant. It is thus found
that V, the volume which flows out in a given time, is represented by the

foi'mula ,,x

_TTpr_

^' ~ 8 el

where / is the length, and r the diameter of the tube, p the pressure, and e the
coefficient of internal frictioti (48) ; which may be defined as the resistance to

motion offered by two layers
of the liquid of unit surface,
at unit distance, and moving
away from each other with
unit velocity. Knowing the
dimensions, a determination
of the volume which flows
out in a given time is a ready
means of obtaining this coeffi-
cient. If the experiment be
made with water, which is
taken as standard, then, using
the same apparatus, other
liquids may be compared with
it, which has thus the advan-
tage of dispensing with a sepa-
rate determination of the diameter of the tube. This is a matter of importance,
as its fourth power occurs in the formula, and any error in its determination
greatly affects the result. Bodies with a high coefficient of internal friction are
said to be viscous (96). The liquids ether, water, sulphuric acid, linseed oil,
Venice turpentine represent, for instance, a series with increasing viscosity.
The coefficient of internal friction is greater in the case of solution of salts
than with water, and increases with the strength of the solution. It greatly
diminishes with the temperature, and at 60° is one-third what it is at zero.

-149j

Hydra u lie Touni iqiic t.

148. Porm of the jet.— After the contracted vein, the jet has the form
of a sohd I'od for a short distance, but then begins to separate into drops,
which present a pecuHar appearance. They seem to form a series of ventral
and nodal segments (fig. 128). The ventral segments consist of drops extended
in a horizontal direction, and the nodal segments in a longitudinal dii^ection.
And as the ventral and nodal segments have respectively a fixed position,
each drop must alternately become elongated and flattened while it is
falling (fig. 129). Between any two drops there are smaller ones, so that the
whole jet has a tube-like appearance.

These alterations in form have been explained as being due to vibrations
in the mouth of the vessel itself Their position is modified by extraneous
influences such as musical and other sounds, but only when these influences
afi'ect the edges themselves.

If the jet is momentarily illuminated by the electric spark, its structure is
well seen ; the drops appear then to be stationary, and separate from each
other. If the aperture is not circular, the form of the jet undergoes curious
changes.

149. HydratElic tourniquet. — If water be contained in a vessel, and an
aperture be made in one of the sides, the pressure at this point is removed.

'■0,

Fig. 128. Fig. 129.

for it is expended in sending out the water ; but it remains on the other side ;
and if the vessel were movable in a horizontal direction, it would move in a
direction opposite to that of the issuing jet. This is illustrated by the appa-
ratus known as the hydraulic tourniquet or Barker's mill (fig. 130). It con-
sists of a glass vessel, M, containing water, and capable of moving about its
^•ertical axis. At the lower part there is a tube, C, bent horizontally in oppo-
site directions at the two ends. If the vessel were full of water and the tubes

K 2

132 On Liquids. [149-

closed, the pressure on the sides of C would balance each other, being equal
and acting in contrary directions ; but, being open, the water runs out, and the
pressure is not exerted on the open part, but only on the opposite side, as
shown in the figure A. And this pressure, not being neutralised by an
opposite pressure, imparts a rotatory motion in the direction of the arrow,
the velocity of which increases with the height of the liquid and the size of
the aperture.

The same principle may be illustrated by the following experiment. A
tall cylinder containing water, and provided with a lateral stop-cock near the
bottom, is placed on a light shallow dish on water, so that it easily floats.
On opening the stop-cock so as to allow water to flow out, the vessel is
observed to move in a direction diametrically opposite to that in which the
water is issuing. Similarly, if a vessel containing water be suspended by a
string, on opening an aperture in one of the sides, the water will jet out, and
the vessel be deflected away from the vertical in the opposite direction.

Segner's water-wheel and the reaction machine depend on this principle.
So also do rotating fireworks ; that is, an unbalanced reaction from the
heated gases which issue from openings in them gives them motion in the
opposite direction.

1 50. "Water- wheels. Turbines. — When water is continuously flowing
from a higher to a lower level, it may be made use of as a motive power.
The motive power of water is generally utilised either by means of water-
wheels, turbines, rams, or hydraulic engines.

Water-wheels are wheels provided with buckets or float-boards at the
circumference, and on which the water acts either by pressure or by impact.
They are made to turn in a vertical plane round a horizontal axis, and are
of two principal kinds, undershot and overshot. In imdershot wheels the
float-boards are placed radially, that is, at right angles to the circumference
of the wheel. The lowest float-boards are immersed in the water, which
flows with a velocity depending on the height of the fall. Such wheels are
applicable where the quantity of water is great, but the fall inconsiderable.
Overshot wheels are used with a small quantity of water which has a high
fall, as with small mountain streams. On the circumference of the wheel
there are buckets of a peculiar shape. The water falls into the buckets on
the upper part of the wheel, which is thus moved by the weight of the water,
and as each bucket arrives at the lowest point of revolution it discharges all
the water, and ascends empty.

An overshot wheel driven by an extraneous force may be used for raising
water, as in dredging machines ; and an undershot one for moving a vessel
to which its axis is fixed, as in the paddles of steam-vessels.

The turbine is a horizontal water-wheel, and is similar in principle to the
hydraulic tourniquet or reaction wheel (149). It consists of a pair of discs,
one above the other, connected together by a number of specially shaped thin
arms or blades, which divide the space between the discs into an equal
number of curved radial chambers. The wheel works generally upon a
vertical axis, and one of the discs is cut away at the centre. In an outward
flow turbine, the water enters through the opening so made into the space
between the discs, and passes outwards radially through the chambers above
mentioned, causing the wheel to rotate by its reaction upon their curved

150a]

The Hydraulic Ram.

133

walls. In order to prevent waste of energy in giving useless rotation to the
water, the peripheral openings of the wheel are surrounded by a series of
corresponding fixed chambers, whose sides (guide-blades) are so curved that
the water when it leaves them has lost all its rotational motion, and simplj'
flows away at right angles to the axis. In an inward flow turbine the water
enters the peripheral opening of the wheel through the guide-blades, and
leaves the wheel at the centre.

The total theoretical effect of a fall of water is never realised ; for the
water, after acting on the wheel, still retains some velocity, and therefore
does not impart the whole of its velocity to the wheel. In many cases water
flows past without acting at all ; if the water acts by impact, vibrations are
produced which are transmitted to the earth and lost ; the same effect is
produced by the friction of water over an edge of the sluice, in the channel
which conveys it, or against the wheel itself, as well as by the friction of
this latter against the axle. A wheel working freely in a stream, as with the
corn-mills on the Rhine near Mainz, does not utilise more than 20 per cent,
of the theoretical effect. One of the more perfect forms of turbines will
\\ork up to over (So per cent. Turbines also, when properly designed, may
be made to have a very high efficiency either with high or low falls ; while, on
account of the great speed at which they run, they are very much smaller
than water-wheels in proportion to their power. They are thus more ' effi-
cient ' motors than steam-engines, which, even if perfect, can only transform
into work from 25 to 30 per cent, of the energy represented by the coal they
burn, and seldom in practice utilise more than half of this percentage.

150c?. The Hydraulic Ram. — If a quantity of water flow through a pipe
open at one end, and if this aperture be cjuickly closed, a sudden impact will be
exerted on the closure as well as on the sides of the pipe. Some of the
energy of the falling water is thereby converted into heat, and some exerts a
dangerous pressure on the pipe. The existence of this pressure may be readily
observed in any town with a high-pressure water supply, by the sharp click
heard if the tap, through which water is flowing, is suddenly closed.

The hydraulic ram invented by Montgolfier is an arrangement by which
the energy of falling
water is applied so I
as to raise a portion ||
of it to a greate
height than the re- j
servoir from which it
is fed. I

The principle of j
such an arrangement (
is represented in fig. !
1 3 1 , in which E is the L
reservoir, A the pipe
in which the water
falls, B the channel, which should be long and straight, a and b the valves,
C the windchest, and D the rising main. Water first flows out in quantity
through the valve a, and as soon as it has acquired a certain velocity it raises
that valve, and the aperture is shut. The impact thus produced acting on

134 On Liquids. [150a-

the sides of the pipe and on the valve b raises this valve, and a quantity of water
passes into the windchest shutting off air, and compressing" it in the space
above the mouth d of the rising main D. This air by its elastic force closes
the valve b, and the water which has entered is raised in the main pipe D.

As soon as the impulsive action is over, and the water in the channel is
at rest, the valve a falls again by its own weight, the flow begins afresh,
and when it has acquired sufficient velocity the valve b is again closed,
and the whole process is repeated.

In this way water can be raised to a height several times as great as the
difference in level from E to the valve b. If no energy were lost in
friction, and in raising the valves, the height of ascent would be to the fall
as the quantity of water which flows out at a is to that which is raised.
Thus \ of the water flowing out of the channel could be raised to 5 times the
height of the available fall.

151. Hydraulic Eng-ine. — Historically, falling water was one of the
earliest sources of power ; but it is only in recent times that attention has been
called (first by Lord Armstrong) to the advantage of using hydraulic power in

. / ... ",:j

towns and other places where there is no natural fall of water for driving-
certain classes of machines, in those cases more especially where the use of
the machinery is only intermittent.

For this purpose the most important docks and large warehouses are
now generally furnished with means of obtaining a water-supply at a very
high pressure, generally about 700 pounds to the square inch. Steam-
jDumping engines are employed to pump water more or less continuously
into what are practically large cylinders with immensely heavy pistons loaded
to the required pressure. These vessels are called accumulators, and pipes
from them are led away to the various places (lock gates, sluice valves,
cranes, capstans, &c.) where power maybe wanted. At each of these places
there is some kind of hydraulic motor suitable to the particular work to be

-151] Hydraulic Engine. 135

done, and this motor can be instantaneously set to work by opening the
communication between it and the high-pressure water in the accumulator.
The motor used is not uncommonly a small engine similar in principle to a
steam-engine, and one of the best of these engines is that illustrated in
fig. 132, which is the invention of Schmidt of Ziirich. It consists of a
cylinder fitted with a piston c whose rod is connected diirectly to a crank
upon a horizontal shaft. The cylinder has two ports or passages, a and b,
one at each end, both terminating below in openings upon a convex curved
face, which is kept continually pressed against a similar concave face upon
the framing of the engine. In this fixed face are also an inlet port or passage

A, and outlet passages B. "When the cylinder is in the position shown
in the figure, the high-pressure water is passing through A and b, forcing
the piston along, and driving out the already used water through a and

B. As the piston moves and turns the crank, the cylinder oscillates on
its bearings, and by the time the piston has got to the end of its stroke,
the cylinder then being horizontal, the process is just being reversed, water
passing in through A and a, and out through b and B. W is an air-vessel
for preventing shocks.

The chief drawback about the use of water power, except where there is
a large natural supply under pressure, is its expense. For each revolution
of the crank shaft, two complete cylinders full of water must be passed
through such an engine, as, whether the power be wanted or not, the water
cannot be expanded like steam.

With any given pressure it is easy to find out how much water will be
required for a given power. At a pressure of 30 pounds per square inch,
for instance, one horse-power will require, supposing the efficiency of the

machine to be 70 per cent. (472), — 33ooo x o ^ about 855 cubic feet or 4,000

"30X 144x07
gallons per hour, a quantity the cost of which would in most cases put the use
of this power out of the question. The pressure in town mains generally
lies between 20 and 40 pounds per square inch, and it is therefore only in
cases where a special high-pressure supply is available that the power can be
economically used.

In London, water is supplied to consumers by the Hydraulic Power Company
under a pressure of 700 pounds ; and the quantity required for one horse-
power would be about 175 gallons. The cost of power supplied in this way
is about fourpence per horse-power per hour, which, although expensive for
continuous working, is not so when it is intermittently used, and when
only the quantity consumed is paid for.

Water-power is usually represented by the weight of the water multiplied
mto the height of the available fall ; or it may also be represented by half
the product of the mass into the square of the velocity. Both measurements
give the same result (60). The water-power of the Niagara Falls is calcu-
lated to be equal to four and a half millions of horse-power.

136 On Gases. [152-

BOOK IV.

ON GASES.

CHAPTER I.

PROPERTIES OF GASES. ATMOSPHERE. BAROMETERS.

152. Physical properties of gases. — Gases are bodies which, unHke
solids, have no independent shape, and, unhke hquids, have no independent
volume. Their molecules possess almost perfect mobility ; they are con-
ceived as darting about in all directions, and are continually tending to
occupy a greater space. This property of gases is known by the names
expansibility, tension, or clastic force, from which they arc often cdW&d. elastic
fluids.

Gases and liquids have several properties in common, and some in which
they seem to differ are in reality only different degrees of the same property.
Thus, in both, the particles are capable of moving ; in gases with almost
perfect freedom ; in liquids not quite so freely, owing to a greater degree of
viscosity. Both are compressible, though in very different degrees. If a
lit|uid and a gas both exist under the pressure of one atmosphere, and then
the pressure be doubled, the water is compressed by about the j-,^-^ part,
while the gas is compressed by one-half In density there is a great differ-
ence : water, which is the type of liquids, is 770 times as heavy as air, the
type of gaseous bodies, while under the pressure of one atmosphere. A
spiral spring only shows elasticity when it is compressed ; it loses its tension
wl^en it has returned to its primitive condition. A gas has no original volume ;
it is always clastic, or in other words it is always striving to attain a greater
volume ; this tendency to indefinite expansion is the chief property by which
gases are distinguished from liquids.

Matter assumes the solid, liquid, or gaseous form according to the rela-
tive strength of the cohesive and repulsive forces exerted between their
molecules. In liquids these forces balance ; in gases repulsion preponderates.

By the aid of pressure and of low temperatures, the force of cohesion
may loe so far increased in many gases that they are readily converted into
liquids, and we know now that with sufficient pressure and cold they may all
be liquefied. On the other hand, heat, which increases the vis viva of the
molecules, converts liquids, such as water, alcohol, and ether, into the aeriform

155]

Weight of Gases.

^37

state in which they obey all the laws of gases. The aeriform state of liquids
is known by the name oi vapour ; while gases are bodies which, under ordi-
nary temperature and pressure, remain in the aeriform state.

In describing exclusively the properties of gases we shall, for obvious
reasons, refer to atmospheric air as their type.

153. acxpansibility of gases. — This property of gases, their tendency to
assume continually a greater volume, is exhibited by means of the following
experiment : — A bladder, closed by a stop-cock and about half full of air, is
placed under the receiver of the air-pump (fig. 133), and a vacuum is produced,
on which the bladder immediately distends.
This arises from the fact that the molecules
of air flying about in all directions (293)
press against the sides of the bladder. Under
ordinary conditions, this internal pressure is
counterbalanced by the air in the receiver,
which exeits an equal and contrary pressure.
But when this pressure is removed, by ex-
hausting the receiver, the internal pressure
becomes evident. When air is admitted into
the receiver, the bladder resumes its original
form.

154. Compressibility of g-ases. — The
compressibility of gases is readily shown by
the pneumatic syringe (fig. 134). This con-
sists of a stout glass tube closed at one end,
and provided with a tight-fittmg sohd piston.
When the rod of the piston is pressed it Fi-. 133.
moves down in the tube, and the air becomes

compressed into a smaller volume ; but as soon as the force is removed the
air regains its original volume, and the piston rises to its former position.

i:;:!'

155. "Weig-ht of gases. — From their extreme fluidity and expansibility,
gases seem to be uninfluenced by the force of gravity : they nevertheless
possess weight like solids and liquids. To show this, a glass globe of 3 or 4
ciuarts capacity is taken (fig. 135), the neck of which is provided with a stop-
cock, which hermetically closes it, and by which it can be screwed to the
plate of the air-pump. The globe is then exhausted, and its weight deter-
mined by means of a delicate balance. Air is now allowed to enter, and the
globe again weighed. The weight in the second case will be found to be

138

On Gases.

[155-

greater than before, and if the capacity of the vessel is known, the increase
will obviously be the weight of that volume of air.

By a modification of this method, and with the adoption of certain pre-
cautions, the weight of air and of other gases has been determined. Perhaps
the most accurate are those of Regnault, who found that a litre of dry air at
o" C, and under a pressure of 760 millimetres, weighs i •293 187 grammes.
Since a litre of water (or 1,000 cubic centimetres) at 0° weighs o*999877
gramme, thedensity of air is o'ooi29334 that of water under the same circum-
stances ; that is, water is ']']'}> tinies as heavy as air. Expressed in English
measures, 100 cubic inches of dry air under the ordinary at-
^ mospheric pressure of 30 in. and at the temperature of 16° C.

weigh 31 grains ; the same volume of carbonic acid gas under
the same circumstances weighs 47-25 grains ; 100 cubic
inches of hydrogen, the lightest of all gases, weigh 2* 14
grains ; and 100 cubic inches of hydriodic acid gas weigh
146 grains.

156. Pressure exerted toy g-ases. — Gases exert on their
own molecules, and on the sides of vessels which contain
them, pressures which may be regarded from two points
of view. First, we may neglect the weight of the gas ;
secondly, we may take account of its weight. If we neglect
the weight of any gaseous mass at rest, and only consider its
expansive force, it will be seen that the pressures due to this
force act with the same strength on all points, both of the
mass itself and of the vessel in which it is contained. For
it is a necessary consequence of the elasticity and fluidity
of gases, that the repulsive force between the molecules is
the same at all points, and acts equally in all directions.
This principle of the equality of the pressure of gases in
all directions may be shown experimentally by means of an apparatus re-
sembling that by which the same principle is demonstrated for liquids (fig. 68).
If we consider the weight of any gas, we shall see that it gives rise to
pressures which obey the same laws as those produced by the weight of
liquids. Let us imagine a cylinder, with its axis vertical, several miles high,
closed at both ends and full of air. Let us consider any small portion of
the air enclosed between two horizontal planes. This portion must sustain
the weight of all the air above it, and transmit that weight to the air beneath
it, and likewise to the curved surface of the cylinder which contains it, and
at each point in a direction at right angles to the surface. Thus the pressure
increases from the top of the column to the base ; at any given layer it
acts equally on equal surfaces, and at right angles to them, whether they
are horizontal, vertical, or inclined. ■ The pressure acts on the sides of
the vessel, and on any small surface it is equal to the weight of a column
of gas whose base is this surface, and whose height its distance from the
summit of the column. The pressure is also independent of the shape and
dimensions of the supposed cylinder, provided the height remain the same.
For a small quantity of gas the pressures due to its weight are quite in-
significant, and may be neglected ; but for large quantities, like the atmo-
sphere, the pressures are considerable, and must be allowed for.

Fig. 135.

-158] AtuiospJieric Pressure. 139

157. The atmosphere : its composition. — ^The atmosphere is the layer
of air which surrounds our globe in every part. It partakes of the rotatory
motion of the globe, and would remain fixed relatively to terrestrial objects
but for local circumstances, which produce winds, and are constantly dis-
turbing its equilibrium.

It is essentially a mixture of oxygen and nitrogen gases ; its average com-
position by volume being as follows : —

Nitrogen . . . 78"49

Oxygen 20-63

Aqueous vapour 0-84

Carbonic acid 0-04

I GO-GO

The carbonic acid arises from the respiration of animals from the pro-
cesses of combustion, and from the decomposition of organic substances.
Boussingault estimated that in Paris the following quantities of carbonic
acid are produced every 24 hours : —

By the population and by animals. . 1 1,895,000 cubic feet
By processes of combustion , . . 92,101,000 ,,

103,996,000 „

Notwithstanding this enormous continual production of carbonic acid
the composition of the atmosphere does not vary ; for plants in the process
of vegetation decompose the carbonic acid, assimilating the carbon, and
restoring to the atmosphere the oxygen, which is being continually consumed
in the processes of respiration and combustion.

158. Atmospheric pressure. — If we neglect the perturbations to which
the atmosphere is subject, as being inconsiderable, we may consider it
as a fluid sea of a certain depth, surrounding the earth on all sides, and
exercising the same pressure as if it were a liquid of very small density.
Consequently, the pressure on the unit of area is constant at a given level,
being equal to the weight of the column of atmosphere above that level
whose horizontal section is the unit of area (99). It will act at right angles
to the surface, whatever be its position. It will diminish as we ascend, and
increase as we descend from that level. Consequently, at the same height,
the atmospheric pressures on unequal plane surfaces will be proportional to
the areas of those surfaces, provided they be small 'in proportion to the
height of the atmosphere.

In virtue of the expansive force of the air, it might be supposed that the
molecules would expand indefinitely into the planetaiy spaces. But, in pro-
portion as the air expands, its expansive force decreases, and is further
weakened by the low temperature of the upper regions of the atmosphere, so
that, at a certain height, equilibrium is established between the expansive
force which separates the molecules, and the action of gravity which draws
them towards the centre of the earth. It is therefore concluded that the
atmosphere is limited.

From the weight of the atmosphere, and its increase in density, and from
the observation of certain phenomena of twilight, its height has been esti-
mated at from 30 to 40 miles. Above that height the air is extremely rarefied.

140 On Gases. [168-

and at a height of 60 miles it is assumed that there is a perfect vacuum. On
the other hand, meteorites have been seen at a height of 200 miles, and, as
their luminosity is undoubtedly due to friction against air, there must be air
at such a height. This higher estimate is supported by observations made
at Rio Janeiro on the twilight arc, by M. Liais, who estimated the height
of the atmosphere at between 198 and 212 miles. The question as to the
exact height of the atmosphere must therefore be considered as still awaiting
settlement.

As it has been previously stated that 100 cubic inches of air weigh 31
grains, it will readily be conceived that the whole atmosphere exercises a
considerable pressure on the surface of the earth. The existence of this
pressure is shown by the following experiments.

1 59. Crusliingr force of the atmosphere. — On one end of a stout glass
cylinder, about 5 inches high, and open at both ends, a piece of bladder is
tied quite airtight. The other end, the edge of which is ground and well
greased, is pressed on the plate of the air-pump (fig. 136). As soon as the
air in the vessel is rarefied by working the air-pump, the bladder is depressed
by the weight of the atmosphere above it, and finally bursts with a loud
report caused by the sudden entrance of the air.

lir

160. IWag'deburg' hemispheres. — The preceding experiment only serves
to illustrate the downward pressure of the atmosphere. By means of the
Magdeburg hemispheres (figs. 137 and 138), the invention of Avhich is due to
Otto von Guericke, burgomaster of Magdeburg, it can be shown that the
pressure acts in all directions. This apparatus consists of two hollow brass
hemispheres of 4 to 4^^ inches diameter, the edges of which ai-e made to fit
tightly, and are well greased. One of the hemispheres is provided with a
stop-cock, by which it can be screwed on to the air-pump, and on the other there
is a handle. As long as the hemispheres contain air they can be separated

-162]

Pascal's Experiments.

141

without any difficulty, for the external pressure of the atmosphere is counter-
balanced by the elastic force of the air in the interior. But when the air in
the interior is pumped out by means of the air-pump, the hemispheres
cannot be separated without a powerful effort ; and as this is the case in
whatever position they are held, it follows that the atmospheric pressure is
transmitted in all directions.

DETERMINATION OF THE ATMOSPHERIC PRESSURE. BAROMETERS.

161. Torricelli's experiment. — The above experiments demonstrate the
existence of the atmospheric pressure, but they give no precise indication
as to its amount. The following experiment, which was first made, in 1643,
by Torricelli, a pupil of Galileo, gives an
exact measure of the weight of the atmo-
sphere.

A glass tube is taken, about a yard
long and a quarter of an inch internal
diameter (fig. 139). It is sealed at one
end, and is quite filled with mercury.
The aperture C being closed by the
thumb, the tube is inverted, the open end
placed in a small mercury trough, and
the thumb removed. The tube being in
a vertical position, the column of mercury
sinks, and, after oscillating some time, it
finally comes to rest at a height A, which
at the level of the sea is about 30 inches
above the mercury in the trough. The
mercury is raised in the tube by the
pressure of the atmosphere on the mer
cury in the trough. There is no contrary
pressure on the mercury in the tube,
because it is closed ; but, if the end of
the tube be opened, the atmosphere will
press equally inside and outside the tube,
and the mercury will sink to the level of
that in the trough. It has been shown in
hydrostatics (107) that the heights of
two columns of liquid in communication
with each other are inversely as their Fig. 1^9.

densities, and hence it follows that the

pressure of the atmosphere is equal to that of a column of mercury, the
height of which is 30 inches. If, however, the weight of the atmosphere
diminishes, the height of the column which it can sustain must also diminish.
162. Pascal's experiments. — Pascal, who wished to ascertain whether
the force which sustained the mercury in the tube was really the pressure of
the atmosphere, made the following experiments, (i.) If it were the case,
then the column of mercury ought to be lower in proportion as we ascend in
the atmosphere. He accordingly requested one of his relatives to repeat

142 On Gases. [162-

Torricelli's experiment on the summit of Puy de Dome in Auvergne.
This was done, and it was found that the mercurial cokimn was about 3
inches lower, thus proving that it is really the weight of the atmosphere
which supports the mercury, since, when this weight diminishes, the height
of the column also diminishes, (ii.) Pascal repeated Torricelli's experiment
at Rouen, in 1646, with other liquids. He took a tube closed at one end
nearly 50 feet long, and, having filled it with water, placed it vertically in a
vessel of water, and found that the water stood in the tube at a height of
34 feet ; that is, 13-6 times as high as mercury. But, since the mercury is 13-6
times as heavy as water, the height of the column of water was exactly
equal to that of a column of mercury in Torricelli's experiment, and it was
consequently the same force, the pressui'e of the atmosphere, which succes-
sively supported the two liquids. Pascal's other experiments with oil and
with wine gave similar results.

163. Amount of the atmospheric pressure. — Let us assume that the
tube in the above experiment is a cylinder, the section of which is equal to a
square inch ; then, since the height of the mercurial column in round num-
bers is 30 inches, the column will contain -^^^ cubic inches ; and as a cubic
inch of mercury weighs 3433'5 grains = 0-49 of a pound, the pressure of such
a column on a square inch of surface is equal to 147 pounds. In round
numbers the pressure of the atmosphere is taken at 15 pounds on the square
inch. A surface of a foot square contains 144 square inches, and therefore
the pressure upon it is equal to 2,160 pounds, or nearly a ton. Expressed
in the metrical system, the standard atmospheric pressure at 0° and the sea-
level is 760 millimetres, which is equal to 29-9217 inches ; and a calculation
similar to the above shows that the pressure on a square centimetre is
= I -032896 kilogrammes.

A gas or liquid which acts in such a manner that a square inch of surface
is exposed to a pressure of 1 5 pounds, is called a pressure of one atniospha-c.
If, for instance, the elastic force of the steam of a boiler is so great that each
square inch of the internal surface is exposed to a pressure of 90 pounds
( = 6 X 15), we say it is under a pressure of six atmospheres.

The surface of the body of a man of middle size is about 16 square feet ;
the pressure, therefore, which a man supports on the surface of his body is
35,560 pounds, or nearly 16 tons. Such an enormous pressure might seem
impossible to be borne ; but it must be remembered that, in all directions,
there are equal and contrary pressures which counterbalance one another.
It might also be supposed that the effect of this force, acting in all directions,
would be to press the body together and crush it. But the solid parts of the
skeleton could resist a far greater pressure ; and as to the air and licjuids
contained in the organs and vessels, the air has the same density as the
external air, and cannot be further compressed by the atmospheric pressure ;
and from what has been said about liquids (97), it is clear that they are vir-
tually incompressible. When the external pressure is removed from any part
of the body, either by means of a cupping vessel or by the air-pump, the
pressure from within is seen by the distension of the surface.

164, Different kinds of barometers. — The instruments used for measur-
ing the atmospheric pressure are called barometers. In ordinary barometers
the pressure is measured by the height of a column of mercury, as in Torri-

-164]

Cistern Barovieter.

143

celli's experiment : the barometers which we are about to describe are of this
kind. But there are barometers without any hquid, one of which, the aneroid
(187), is remarkable for its simplicity and portability.

165. Cistern barometer. — The dslern barometer consists of a straight
glass tube closed at one end, about -^l, inches long, filled with mercuiy, and
dipping into a cistern containing the same metal. In order to render the
barometer more portable, and the variations of the level in the cistern [,less
perceptible when the mercury rises or falls in the tube, several different

liliiiliiliiliilliiillliiii ^

Fig. 14

forms have been constructed. Fig. 140 represents one form of the cistern
barometer. The apparatus is fixed to a m.ahogany stand, on the upper part
of which there is a scale graduated in millimetres or inches from the level
of the mercury in the cistern : a movable index, z", shows on the scale the
level of the mercury. A thermometer on one side of the tube indicates the
temperature.

There is one fault to which this barometer is liable, in common with all

144 On Gases. [165-

others of the same kind. The zero of the scale does not always correspond
to the level of the mercury in the cistern. For, as the atmospheric pressure
is not always the same, the height of the mercurial column varies ; some-
times mercury is forced from the cistern into the tube, and sometimes from
the tube into the cistern, so that in the majority of cases the graduation of
the barometer does not indicate the true height. If the diameter of the
cistern is large, relatively to that of the tube, the error from this source, which
is known as the error of capacity, is lessened.

The height of the barometer is the distance between the levels of the
mercury in the tube and in the cistern. Hence the barometer should
always be perfectly vertical, for if not, the tube being inclined, the column of
mercuiy is elongated (fig. 141), and the number read off on the scale is too
great. As the pressure which the mercury exerts by its weight at the base
of the tube is independent of the form of the tube and of its diameter (loi),
provided it is not capillary, the height of the barometer is independent of
the diameter of the tube and of its shape, but is inversely as the density of
the liquid. With mercury the mean height at the level of the sea is 29"92,
or in round numbers 30, inches ; in a water barometer it would be about 34
feet, or 10-33 metres.

In marine barometers the error of capacity is got rid of by graduating the
scale not in the true measurements, but by an empirical correction depending
on the relative diameters of the tube and cistern. Thus if a rise of 10 mm.
in the tube produced a fall of i mm. in the cistern, the true change would not
be 10 mm. but 11 mm. This is obviously allowed for by dividing the space
of 10 mm. on the scale into 1 1 mm. The correctness of such an instrument
depends on the accuracy with which the scale is laid off.

166. rortin's toarometer. — Fortin^s barometer differs in the shape of
the cistern from that just described. The base of the cistern is made of
leather, and can be raised or lowered by means of a screw ; this has the
advantage that a constant level can be obtained, and also that the instru-
ment is made more portable. For, in travelling, it is only necessary to
raise the leather until the mercury, which rises with it, quite fills the cistern ;
the barometer may then be inclined, and even inverted, without any fear
that a bubble of air may enter, or that the shock of the mercury may crack
the tube.

Fig. 142 represents the arrangement of the barometer, the tube of which
is placed in a brass case. At the top of this case there are two longitudinal
slits on opposite sides, so that the level of the mercury, B, is seen. The
scale on the case is graduated in millimetres. An index A, moved by the
hand, gives, by means of a vernier, the height of the mercury to j-th of a milli-
metre. At the bottom of a case there is a cistern b, containing mercury 0.

Fig. 143 shows the details of the cistern on a larger scale It consists of
a glass cylinder b, through which the mercury can be seen ; this is closed at
the top by a boxwood disc fitted on the under surface of the brass cover M.
Through this passes the barometer tube E, which is drawn out at the end,
and dips in the mercury ; the cistern and the tube are connected by a piece
of buckskin, ce, which is firmly tied at ^ to a contraction in the tube, and at e
to a brass tubulure in the cover of the cistern. This mode of closing
prevents the mercury from escaping when the barometer is inverted, while

167]

Gay-Liissacs Syphon Barometer.

145

the pores of the leather transmit the atmospheric pressure. The bottom of

the cyhnder b is cemented on a boxwood cyHnder sz, on a contraction in

which, ii, is firmly tied the buckskin, vtjt, which forms the base of the cistern.

On this skin is fastened a wooden button x, which rests against the end of

a screw C. According as this is turned in one direction or the other, the

skin mtt is raised or lowered, and with it the mercury. In using this baro-
meter, the mercury is first made exactly level with the point a, which is

effected by turning the screw C either in one direction or the other. The

graduation of the scale is

counted from this point «,

and thus the distance of

the top B of the column of

mercury from a gives the

height of the barometer.

The bottom of the cistern

is surrounded by a brass

case, which is fastened to

the cover M by screws, k,

k, k. We have already

seen (165) the importance

of having the barometer

quite vertical, which is

effected by the following

plan, known as Cardajis

suspoision.

The metal case contain-
ing the barometer is fixed

in a copper sheath X by

two screws a and b (fig.

144). This is provided

with two axles (only one of

which, o, is seen in the

figure), which turn freely in

two holes in a ring Y. In

a direction at right angles

to that of the axles, 00^ the
ring has also two similar

axles, in and «, resting on

a support Z. By means of this double suspension the barometer can
oscillate freely about the axes, imi and 00., in two directions at right angles to
each other. But as care is taken that the point at which these axes cross
corresponds to the tube itself, the centre of gravity of the system, which
must always be lower than the axis of suspension, is below the point of inter-
section, and the barometer is thus perfectly vertical.

167. Cay.Iiussac's syphon barometer. — -The syphon barometer is a
bent glass tube, one of the branches of which is much longer than the other.
The longer branch, which is closed at the top, is filled \\\\\\ mercury as in the
cistern baro.meter, while the shorter branch, which is open, serves as a
cistern. The difference between the two levels is the height of the barometer.

146

On Gases.

[167-

Fig. 145 represents the syphon barometer as modified by Gay-Lussac.
In order to render it more available for travelling, by preventing the entrance
of air, he joined the two branches by a capillary tube (fig. 146); when the
instrument is inverted (fig. 147) the tube always remains full in virtue of its
capillarity, and air cannot penetrate into the longer branch. A sudden
shock, however, might separate the mercury and admit some air. To avoid
this, Bunten introduced an ingenious modification into the apparatus. The

Fig. 147.

longer branch is drawn out to a fine point, and is joined to a tube B of the
form represented in fig. 148. This arrangement forms an air-trap ; for if air
passes through the capillary tube it cannot penetrate the drawn-out extremity
of the longer branch, but lodges in the upper part of the enlargement B.
In this position it does not affect the observations, since the vacuum is
always at the upper part of the tube ; it is, moreover, easily removed.

In the syphon barometer the shorter branch is closed, but there is a

-169J Correction for Capillarity. 147

capillary aperture in the side /, through which the atmospheric pressure is
transmitted.

The barometric height is determined by means of two scales, which have
a common zero at O, towards the middle of the longer branch, and are gra-
duated in contrary directions, the one from O to E, and the other from O to
B, either on the tube itself, or on brass rules fixed parallel to the tube. Two
sliding verniers, in and «, indicate tenths of a millimetre. The total height of
the barometer, AB, is the sum of the distances from O to A and from O to B.

Fig. 149 represents a very convenient mode of arranging the open end of
a syphon barometer for transport. The quantity of mercury is so arranged
that when the Torricellian space is quite filled with mercury, by inclining the
tube the enlargement is just filled to d. This is closed by a carefully fitted
cork fixed on the end of a glass tube about a millimetre in the clear, which
allows for the expansion of mercury by heat. When the barometer is to be
used, the cork and tube are raised.

168. Precautions in reference to barometers. — In constructing baro-
meters mercuiy is chosen in preference to any other liquid, for, being the
densest of all liquids, it stands at the least height. When the mercurial
barometer stands at 30 inches, the water barometer would stand at about
34 feet (165). It also deserves preference because it does not moisten the
glass. It is necessary that the mercury be pure and free from oxide, other-
wise it adheres to the glass and tarnishes it. Moreover, if it is impure, its
density is changed, and the height of the barometer is too great or too small.
Mercury is purified, before being used for barometers, by treatment with
dilute nitric acid, and by distillation.

The space at the top of the tube (figs. 140 and 145), which is called the
Torricellian vacuum., must be quite free from air and from aqueous vapour,
for otherwise either would depress the mercurial column by its elastic force.
To obtain this result, a small quantity of pure mercury is placed in the tube
and boiled for some time. It is then allowed to cool, and a further quantity,
previously warmed, added, which is boiled, and so on, until the tube is quite
full ; in this manner the moisture and the air which adhere to the sides of the
tube (193) pass off with the mercurial vapour. A barometer tube should not
be too narrow, for otherwise the mercury is moved with difiiculty ; and before
reading off, the barometer should be tapped so as to get rid of the adhesion
to the glass.

A barometer is free from air and moisture if, when it is inclined, the
mercury strikes with a sharp metallic sound against the top
of the tube. If there is air or moisture in it, the sound is ||||| i ' j||
deadened. |ll'i ' j ,''

169. Correction for capillarity. — In cistern barometers
there is always a certain depression of the mercurial column
due to capillarity, unless the internal diameter of the tube
exceeds o-8 inch. To make the correction due to this
depression, it is not enough to know the diameter of the
tube ; we must also know the height of the meniscus od (fig.
150), which varies according as the meniscus has been
formed during an ascending or descending motion of the mercury in the
tube. Consequently, the height of the meniscus must be determined by

L 2

148

On Gases.

[169-

bringing the pointer to the level ab, and then to the level d, when the differ-
ence of the readings will give the height od required. These two terms —
namely, the internal diameter of the tube and the height of the meniscus —
being known, the resulting correction can be taken out of the following-
table :

Internal
diameter
in-inches

Height of sag

itta of meniscus in inches

O'OIO

0-015

0-020
0-0555

0-025

0030
0-0780

0-035

0-040

0-I57

0-0293

0-0431

0-0677

0-0870

0-0948

0-236

0-0119

0-0176

0-0231

0-0294

0-0342

0-0398

0-0432

0-315

0-0060

0-0088

O-OI18

0-0144

0-0175

0-0196

0-0221

0-394

0-0039

0-0048

0-0063

0-0078

0-0095

o-oiio

00125

0-472

0-0020

0-0029

0-0036

0-0045

0-0053

0-0063

0-00T2,

.0-550

0-00 10

0-0017

0-0024

0-0029

0-0034

0-0039

0-0044

In the syphon barometer the two tubes are of the same diameter, so
that the error caused by the depression in the one tube very nearly corrects
that caused by the depression in the other. As, however, the meniscus in
the one tube is formed by a column of mercury with an ascending motion,
while that in the other is formed by a column with a descending motion,
their heights will not be the same, and the reciprocal correction will not be
quite exact.

170. Correction for temperature. — In all observations with barometers,
whatever be their construction, a correction must be made for temperature.
Mercury contracts and expands with different temperatures, hence its
density changes, and consequently the barometric height, for this height is
inversely as the density of the mercury, so that for different atmospheric
pressures the mercurial column might have the same height. Accordingly,
in each observation the height observed must be reduced to a determinate
temperature. The choice of this is quite arbitrary, but that of melting ice is
always adopted in practice. It will be seen, in the Book on Heat, how this
correction is made.

171. Variations in tlie height of the barometer. — When the barometer
is observed for several days, its height is found to vary in the same place,
not only from one day to another, but also during the same day.

The extent of these variations — that is, the difference between the greatest
and the least height — is different in different places. It increases from the
equator towards the poles. Except under extraordinary circumstances, the
greatest variations do not exceed six millimetres under the equator, 30 under
the tropic of Cancer, 40 in France, and 60 at 25 degrees from the pole. The
greatest variations are observed in winter.

The 7nccm daily height is the height obtained by dividing the sum of 24
successive hourly observations by 24. In our latitudes the barometric height
at noon corresponds to the mean daily height.

The 77iean monthly height is obtained by adding together the mean daily
heights for a month, and dividing by 30. The mean yearly height \^ simi-
larly obtained.

Under the equator, the mean annual height at the level of the sea is

-173] Relation of Barometric Variations to WeatJier. 149

o'"758, or 29-84 inches. It increases from the equator, and between the
latitudes 30° and 40° it attains a maximum of o™763, or 30-04 inches. In
lower latitudes it decreases, and in Paris it does not exceed o'^-7568.

The general mean at the level of the sea is o™-76i, or 29-96 inches.

The mean monthly height is greater in winter than in summer, in conse-
quence of the cooler atmosphere.

Two kinds of variations are observed in the barometer : — ist, the acci-
dental 7Jariatio?is, which present no regularity ; they depend on the seasons,
the direction of the winds, and the geographical position, and are common
in our climates ; 2nd, the daily variations, which are produced periodically
at certain hours of the day.

At the equator, and between the tropics, no accidental variations are
observed ; but the daily variations take place with such regularity that a
barometer may serve to a certain extent as a clock. The barometer sinks
from midday till towards four o'clock ; it then rises, and reaches its maximum
at about four o'clock in the evening. It then again sinks, and reaches a
second minimum towards four o'clock in the morning, and a second maxi-
mum at ten o'clock. In the temperate zones there are also daily variations,
but they are detected with difficulty, since they occur in conjunction with
accidental variations.

The hours of the maxima and minima appear to be the same in all
climates, whatever be the latitude ; they merely vary a little with the seasons.

172. Causes of barometric variations. — It is observed that the course
of the barometer is generally in the opposite direction to that of the thermo-
meter ; that is, that when the temperature rises, the barometer falls, and vice
versa ; which indicates that the barometric variations at any given place are
produced by the expansion or contraction of the air, and therefore by its
change in density. If the temperature were the same throughout the whole
extent of the atmosphere, no currents would be produced, and at the same
height, atmospheric pressure would be everywhere the same. But when
any portion of the atmosphere becomes warmer than the neighbouring parts,
its specific gravity is diminished, and it rises and passes away through
the upper regions of the atmosphere, whence it follows that the pressure
is diminished, and the barometer falls. If any portion of the atmosphere
retains its temperature, while the neighbouring parts become cooler, the same
effect is produced ; for in this case, too, the density of the first-mentioned
portion is less than that of the others. Hence, also, it usually happens that
an extraordinary fall of the barometer at one place is counterbalanced by an
extraordinary rise at another place. The daily variations appear to result
from the expansions and contractions which are periodically produced in
the atmosphere by the heat of the sun during the rotation of the earth.

173. Relation of barometric variations to the state of the weather. —
It has been observed that, in our climate, the barometer in fine weather is
generally above 30 inches, and is below this point when there is rain, snow,
wind, or storm ; and also, that for any given number of days at which the
barometer stands at 30 inches, there are as many fine as rainy days. From
this coincidence between the height of the barometer and the state of the
weather, the following indications have been marked on the barometer
counting by thirds of an inch above and below 30 inches ; —

I50

On Gases.

[173-

Height

31 inches
3o| „
30^ „
30 „
29I »
29i „

29 »

In using the ba

State of the weather

. Very dry.

. Settled weather.

. Fine weather.

. Variable.

. Rain or wind.

Much rain.
. Tempest.
rometer as an indicator of the state of the weather, we
must not forget that it really only serves to measure the weight of the atmo-
sphere, and that it only rises or falls as the weight increases or diminishes ;
and although a change of weather frequently coincides with a change in the
pressure, they are not necessarily connected. This coincidence arises from
meteorological conditions peculiar to our climate, and does not occur every-
where. That a fall in the barometer usually precedes rain in our latitudes is
caused by the position of Europe. The prevailing winds here are the south-
west and north-east. The former, coming to us from the equatorial regions,
are warmer and lighter. They often, therefore, blow for hours or even days
in the higher regions of the atmosphere before manifesting themselves on the
surface of the earth. The air is therefore lighter, and the pressure lower.
Hence a fall of the barometer is a probable indication of the south-west
winds, which gradually extend downwards, and reaching us, after having
traversed large tracts of water, are charged with moisture, and bring us rain.
The north-east blows simultaneously above and below, but the hindrances
to the motion of the current on the earth, by hills, forests, and houses, cause
the upper current to be somewhat in advance of the
lower ones, though not so much so as the south-west
wind. The air is therefore somewhat heavier even
before we perceive the north-east, and a rise of the
barometer affords a forecast of the occurrence of this
wind, which, as it reaches us after having passed over
the immense tracts of dry land in Central and Northern
Europe, is mostly dry and fine.

When the barometer rises or sinks slowly, that is,
for two or three days, towards fine weather or towards
rain, it has been found from a great number of observa-
tions that the indications are then extremely probable.
Sudden variations in either direction indicate bad
weather or wind.

174. "Wheel barometer. — The ivlieel barometer,
which was invented by Hooke, is a syphon barometer,
and is especially intended to indicate good and bad
weather (fig. 151). In the shorter leg of the syphon
there is a float which rises and falls with the mercury.
A string attached to this float passes round a pulley,
and at the other end there is a weight somewhat lighter
than the float. A needle fixed to the pulley moves
round a graduated circle, on which is marked stormy, rain, set fair, &c.
When the pressure varies the float sinks or rises, and moves the needle round
to the correspondmg points on the scale.

Fig. 151-

-176] Glycerine Barometer. 151

The barometers ordinarily met with in houses, and which are called
^cueatker-glasses, are of this kind. They are, however, of little use, for two
reasons. The first is, that they are neither very delicate nor very accurate
in their indications. The second, which applies equally to all barometers, is
that those commonly in use in this country are made in London, and the
indications, if they are of any value, are only so for a place of the same level
and of the same climatic conditions as London. Thus a barometer standing
at a certain height in London would indicate a certain state of weather, but
if removed to Shootei-'s Hill it would stand half an inch lower, and would
indicate a different state of weather. As the pressure differs with the level
and with geographical conditions, it is necessary to take these into account
if exact data are wanted.

175. Fixed barometer. — For accurate observa-
tions Regnault uses a barometer the height of which
he measures by means of a cathetometer (88). The
cistern (fig. 152) is of cast iron ; against the frame on
which it is supported a screw is fitted, which is pointed
at both ends, and the length of which has been deter-
mined, once for all, by the cathetometer. To mea-
sure the barometric height, the screw is turned until
its point grazes the surface of the mercury in the
bath, which is the case when the point and its image
are in contact. The distance then from the top of
the point to the level of the mercury in the tube b is
measured by the cathetometer, and this, together with
the length of the screw, gives the barometric height
with great accuracy. This barometer has, moreover,
the advantage that, as a tube an inch in diameter
may be used, the influence of capillarity becomes
inappreciable. Its construction, moreover, is very
simple, and the position of the scale leads to no kind
of error, since this is transferred to the cathetometer.
Unfortunately, the latter instrument requires great
accuracy in its construction, and is expensive.

176. Glycerine barometer. — Jordan constructed
a barometer in which the liquid used is pure glycerine.
This has the specific gravity 1*26, and therefore the
length of the column of liquid is rather more than
ten times that of mercury ; hence small alterations
in the atmospheric pressure produce considerable
oscillations in the height of the liquid. The tube
consists of ordinary composition gas-tubing about
I of an inch in diameter and 28 feet or so in length ;
the lower end is open and dips in the cistern, which
may be placed in a cellar ; the top is sealed to a Fig- 152.
closed glass tube an inch in diameter, in which the

fluctuations of the column are observed. This may be arranged in an upper
storey, and the tubing, being easily bent, lends itself to any adjustment
which the locality requires.

15:

On Gases.

[176-

The vapour of glycerine has very low tension at ordinary temperatures,
and is therefore not so exposed to such back pressures, varying with the
temperature, as is water. On the other hand, it readily attracts moisture
from the air, whereby the density and therewith the height of the liquid
column vary. This is prevented by covering the liquid in the cistern with a
layer of paraffine oil.

The ' Philosophical Magazine,' vol. xxx. Fourth series, page 349, contains
a detailed account of a method of constructing a water barometer.

177. Huygrhens' barometer. — The desire to amplify the small variations
which take place in the barometer has led to a number of contrivances, one
of the best known of which was invented by Huyghens (fig. 153).

The barometer tube a is wider at the closed end b, and also at c, where a
liquid of smaller specific gravity than mercury, such .as coloured water, is
poured on the mercury ; it fills the rest of the tube c and a portion of d.

Suppose b and c to have the same diameter, which is n times that of d.
When the column of mercury in b sinks through x millimetres, the level of
the mercury in c rises just as much, while the coloured liquid rises 7ix- milli-
metres, and therefore its level is {n — i)x millimetres higher. A column of
this hquid {n — i)x in height has the same pressure as a column of mercury

{n.

in height, where .y is the number expressing the ratio of the specific

gravities of mercury and the liquid.

Accordingly, when the mercury in b sinks x milli
metres.

y = 2x+ ■ X

is the height of the column of mercury, which corre-
sponds to the decrease of atmospheric pressure. From
this we have

2S + }l-\

Thus, if the section of the tubes b and c is 20 times
that of d, and if the coloured liquid be water, we
have

\y6y _i3"6y.

46-

= 0-2947.

27-2-1-20-

Accordingly, when an ordinary barometer sinks
through J/ millimetres, the mercury in b sinks 0-294;!/ mil-
limetres, while the coloured liquid in Arises 20 x o-294jk
= 5-88jK. Whenever, that is, an ordinary barometer
sinks or rises i millimetre, the coloured liquid rises or
sinks 5-98 millimetres, or nearly six times as much.

Such barometers are useful in cases where the
\'ariations in the height of the barometer, rather than
its actual height, are to be observed. The scale
should be placed behind the tube d, and two points, fixed, near the top and
bottom, by comparison with standard barometers ; the inter\al between the
two is then suitably divided.

-178] Dctcfiiiination of Heights by the Barometer. 1 5 3

178. Determination of beigrhts by tbe barometer. — Since the atmo-
spheric pressure decreases as we ascend, it is obvious that the barometer
will keep on falling as it is taken to a greater and greater height.
On this depends a method of determining the difference between
the heights of two stations, such as the base and summit of a
mountain. The method may be explained as follows.

According to Boyle's law (180), if the temperature of an enclosed
portion of air continues constant, its volume will vary inversely as
the pressure ; that is to say, if we double the pressure we shall halve -"-Q
the volume. But if we halve the volume we manifestly double the tP
quantity of air in each cubic inch — that is to say, we double the
density of the air ; and so on in any proportion. Consequently, the
law is equivalent to this : — That for a constant temperature the
density of air is proportional to the pressure which it sustaifts.

Now suppose A and B (fig. 1 54) to represent two stations, and
that it is required to determine the vertical height of B above A, it . _^j
being borne in mind that A and B are not necessarily in the same Fig. 154.
vertical line. Take P, any point in AB, and Q, a point at a small
distance above P. Suppose a pressure on a square inch of the atmosphere
at P to be denoted by^, and at Q let it be diminished by a quantity denoted
by dp. It is clear that this diminution equals the weight of the column of
air between P and Q, whose section is one square inch. But, since the
density of the air is directly proportional to p, the weight of a cubic inch of
air will equal kgp, where k denotes a certain quantity to be determined
presently, and g the accelerating force of gravity (79). Hence, if we denote
PQ in inches by <r/.i-, the pressure will be diminished by kpg . dx\ and we
may represent this algebraically by the equation

kpg . dx = dp.

By a certain algebraical process this leads to the conclusion that

4-X = log|-,

where X denotes the height of AB, and P and V-^ the atmospheric pressures
at A and B respectively, the logarithms being what are called ' Napierian '
logarithms.' Now, if H and H^ are the heights of the barometer at A and
B respectively, the temperature of the mercury being the same at both
stations, their ratio equals that of P to P,, and therefore

It remains to determine k and^.

(i) Since the force of gravity is different for places in different latitudes,
g will depend upon the latitude (82). It is found that if ^ is the accelerating
force of gravity in latitude (^, and/that force in latitude 45°, then

,^ f

•^ I +0-00256 cos 2(^ '

where /has a definite numerical value.

154 On Gases. [178-

(2) If o- is the density of air at a temperature of /° C, under Q, the pres-
sure exerted by 29-92 inches of mercury, we shall have

But it will be afterwards shown (332) that if p^ is the density of air under
the same pressure Q at 0° C, we shall have

I + af
where a represents the coefficient of expansion of gases. Therefore

^Q = _Pp_
i-vaf

Now if a- is the density of mercury, and if the latitude is 45°, we shall
have

Q = 29-92 . (t/;
and therefore

kf= P-SL . !

o- 29-92 (I +<:;/)

But p„-^cr is the ratio which the density of dry air at a temperature 0° C,
in latitude 45°, under a pressure of 29-92 inches of mercury, bears to the
density of mercury at 0° C, and therefore Po-^or is a determinate number.
Substituting, we have

P = 29-92 in. .-^(i +0-00256 cos 2(p) (i ■+ at) log--.
Po ^1

The value of a is 0-003665, which is nearly equal to 3IJ-J. If we substitute
the proper values for a-i-p,,, and change the logarithms into common loga-
rithms, and instead of / use the mean of T and T^, the temperatures at the
upper and lower stations, it will be found that

X (in feet) = 60346 (1+0-00256 cos 2(b) ( 1 +^STjLIiI) log ^-,

\ 1000 / Hi

which is La Place's barometric formula. In using it, we must remember
that T and Tj are temperatures on the Centigrade thermometer, and that H
and Hj are the heights of the barometer reduced to 0° C. Thus if A is the
measvn-ed height of the barometer at the lower station we have

H. ;,(■-/ ).

V 6500/

If the height to be measured is not great, one observer is enough. For
greater heights the ascent takes some time, and in the interval the pressure
may vary. Consequently, in this case there must be two observers, one at
each station, who make simultaneous observations.

Let us take the following example of the above formula : — Suppose that
in latitude 65° N. at the lower of the two stations the height of the barometer
was 30-025 inches, and the temperature of air and mercury i7°-32 C, while
at the upper the height of the barometer was 28-230 inches, and the tempera-
ture of air and mercury was io°-55 C. What is the height of the upper
station above the lower?

-179] Ruhhnanns Observations. 1 5 5

.(I) Find H and H^ : viz.

H ^30-025(1 -^^-3^) = 39-945.

H, = 28-230(1 -;^^;55)= 28-184.

\ 6500/

Hence log =1-4763243-1-4500026 = 0-0263217.

(2) Find I + ^^ "^ 'J viz. 1-05574.

1000

(3) Find I +0-00256 cos 20.

Since 0-00256 cos 130°= —0-00256 cos 50°= —0-001645,

therefore i +0-00256 cos 20= -0-998355.

Hence the required height in feet equals

60346 X 0-998355 X 1-05574 X 0-0063217 = 1674.
If H and H^ do not greatly differ, the Napierian logarithm of
H ^^H-H,
h; "H + Hi'

If, for instance, H = 30 and Hj = 29 inches, the resulting error would not
exceed the i^--^-^ part of the whole. Accordingly for heights not exceeding
2,000 ft. we may, without much error, use the formula

X (in feet) = 52500(1 + ^^'^ ^ ^A\ x ^-^.
V 1000 / H + Hj

179. Ruhlmann's observations. — The results obtained for the difference
in height of places by using the above formula often differ from the true
heights as measured trigonometrically, to an extent which cannot be ascribed
to errors in observation. The numbers thus found for the heights of places
are influenced by the time of day, and also by the season of year, at which
they are made. Ruhlmann has investigated the cause of this discrepancy
by a series of direct barometric and thermometric observations made at two
different stations in Saxony, and also by a comparison of the continuous
series of observations made at Geneva and on the St. Bernard.

Ruhlmann thus ascertained that the cause of the discrepancy is to be
found in the fact that the mean of the temperatures indicated by the ther-
mometer at the two stations is not an accurate measure of the actual mean
temperature of the column of air between the two stations, a condition which
is assumed in the above formula. The variations in the temperature of the
column of air are not of the same extent as those indicated by the thermo-
meter, nor do they follow them so rapidly ; they drag after them as it were.
If the mean monthly temperatures at the two fixed stations are introduced
into the formula, they give in winter heights which are somewhat too low,
and in summer such as are too high. The results obtained by introducing
the mean yearly temperature of the two stations are very near the true ones.

This influence of temperature is most perceptible in individual observa-
tions of low heights. Thus, using the observed temperatures in the barometric

156 On Gases. [179-

formula, the error in height of the Uetliberg above Ziirich (about 1,700 feet)
was found to be ~ of the total, while the height of the St. Bernard above
Geneva was found within ^§3 of the true height.

The reason why the thermometers do not indicate the true temperature
of the air is undoubtedly that they are too much influenced by radiation
from the earth and surrounding bodies. The earth is highly absorbent, and
becomes rapidly heated under the influence of the sun's rays, and becomes
as rapidly cooled at night ; the air, as a very diathermanous body, is but
little heated by the sun's rays, and on the contrary is little cooled by radia-
tion during the night.

-180] Boyle s Laiv. 157

CHAPTER II

MEASUREMENT OF THE ELASTIC FORCE OF GASES.

180. Boyle's law. — The law of the compressibility of gases was dis-
covered by Boyle in 1662, and afterwards independently by Mariotte in 1679.
It is in England commonly called ' Boyle's Law,' and, on the Continent,
' Mariotte's Law.' It is as follows : —

The iouperatiire remaining the same, the volume of a given quantity of
gas is inversely as the pressure which it bears.

This law may be verified by means of an apparatus devised by Boyle
(fig. 155). It consists of a long glass tube fixed to a vertical support ; it is
open at the upper part, and the other end, which is bent into a short vertical
leg, is closed. On the shorter leg there is a scale which indicates equal
capacities ; the scale against the long leg gives the heights. The zero of
both scales is in the same horizontal line.

A small quantity of mercury is poured into the tube, so that its level in
both branches is at zero, which is effected without much difficulty after a few
trials (fig. 155). The air in the short leg is thus under the ordinary atmo-
spheric pressure which is exerted through the open tube. Mercury is then
poured into the longer tube until the volume of the air in the smaller tube is
reduced to one-half ; that is, until it is reduced from 10 to 5, as shown in
fig. 156. If the height of the mercurial column, CA, be measured, it will be
found exactly equal to the height of the barometer at the time of the experi-
ment. The pressure of the column CA is therefore equal to an atmosphere
which, with the atmospheric pressure acting on the surface of the column at
C, makes two atmospheres. Accordingly, by doubling the pressure, the
volume of the gas has been diminished to one-half.

If mercury be poured into the longer branch until the volume of the air
is reduced to one-third, it will be found that the distance betv.een the level
of the two tubes is equal to two barometric columns. The pressure is now
three atmospheres, while the volume is reduced to one-third. Dulong and
Petit have verified the law for air up to 27 atmospheres, by means of an
apparatus analogous to that which has been described.

The law also holds good in the case of pressures of less than one atmo-
sphere. To establish this, mercury is poured into a graduated tube until it
is about two-thirds full, the rest being air. It is then inverted in a deep
trough M containing meixury (fig. 157), and lowered until the levels of the
mercury inside and outside the tube are the same, and the volume AB noted.
The tube is then raised, as represented in the figure, until the volume of air
AC is double that of AB (fig. 158). The height of the mercury in the tube
above the mercury in the trough CD is then found to be exactly half the

158

On Gases.

[180-

height of the barometric column. The air whose volume is now doubled is
now only under the pressure of half an atmosphere ; for it is the elastic force
of this air which, added to the weight of the column CD, is equivalent to the
atmospheric pressure. Accordingly the volume is inversely as the pressure.

llllllliB>

Fig. 155-

Fig. is6.

Fig. 157. Fig. 158.

In general, if V be the original volume of a gas under the pressure P, and
V the volume of the same gas under another pressure P', we have the ratio
V : V = P' : P or VP = V'P'.

This may be expressed by saying that the tcmpcratufe of a gh'en mass of

gas being constant, the product of pressure and volume is constant ; that is,

PV = const.

In the experiment with Boyle's tube, as the mass of air remains the
same, its density must obviously increase as its volume diminishes, and vice
versa. The law may thus be enunciated : — ' For the same temperature the
density of a gas is proportional to its pressure.^ Hence, as watei is T]'^ times
as heavy as air, under a pressure of TJi atmospheres air would be as dense
as water.

-181]

Boyle's Lazv.

159

Boyle's law must not be understood to mean that gases of equal density
have equal elastic force ; different gases of various densities have the same
tension when they are under the same pressure. A given volume of hydrogen
under the ordinary atmospheric pressure has the same elastic force as the
same volume of air, although the latter is 14 times as heavy as the former.
Since, for the same volume, there are the same number of atoms in all gases,
the lighter atoms must possess a greater velocity in order to exert the same
pressure as the same number of atoms of greater mass.

181. Boyle's law is only approximately true. — Until within the last
few years Boyle's law was supposed to be absolutely true for all gases at all
pressures, but Despretz
obtained results incom-
patible with the law. He
took two graduated glass
tubes of the same length,
and filled one- with air
and the other with the
gas to be examined.
These tubes were placed
in the same mercury
trough, and the whole
apparatus immersed in a
strong glass cylinder filled
with water. By means
of a piston moved by a
screw which worked in a
cap at the top of a cylin-
der the liquid could be
subjected to an increasing
pressure, and it could be
seen whether the com-
pression of the two gases
was the same or not. The
apparatus resembled that
used for examining the
compressibility of liquids
(fig. 64). In this manner
Despretz found that car-
bonic acid, sulphuretted
hydrogen, ammonia, and
cyanogen are more com-
pressible than air : hydro-
gen, which has the same
compressibility as air up to 15 atmospheres, is then less compressible. From
these experiments it was concluded that the law of Boyle was not general.

In some experiments on the elastic force of vapours, Dulong and Arago
had occasion to test the accuracy of Boyle's law. The method adopted was
exactly that of Boyle, but the apparatus had gigantic dimensions.

The gas to be compressed was contained in a strong glass tube, GF (fig.

Fig- 159-

i6o On Gases. [181-

1 59), about six feet long and closed at the top, G. The pressure was pro-
duced by a column of mercury, which could be increased to a height of 65
feet, contained in a long vertical tube, KL, formed of a number of tubes
firmly joined by good screws, so as to be perfectly tight.

The tubes KL and GF were hermetically fixed in a hoi'izontal iron pipe,
DE, which fonned part of a mercurial reservoir, A. On the top of this
reservoir there was a force-pump, BC, by which mercury could be forced into
the apparatus.

At the commencement of the experiment the volume of the air in the
manometer (183) was observed, and the initial pressure determined, by
adding to the pressure of the atmosphere the height of the mercury in K
above its level in H. If the level of the mercury in the manometer had
been above the level in KL, it would have been necessary to subtract the
difference.

By means of the pump, water was injected into A. The mercury, being
then pressed by the water, rose in the tube GF, where it compressed the
air, and in the tube KL, where it rose freely. It was only then necessary
to measui^e the volume of the air in GF ; the height of the mercury in KL
above the level in GF, together with the pressure of the atmosphere, was
the total pressure to which the gas was exposed. These were all the elements
necessary for comparing different volumes and the corresponding tempera-
tures. The tube GF.was kept cold during the experiment by a stream of
cold water.

The long tube was attached to a long mast by means of staples. The
individual tubes were supported at the junction by cords, which passed
round pulleys R and R\ and were kept stretched by small buckets, P, con-
taining shot. In this manner each of the thirteen tubes having been sepa-
rately counterpoised, the whole column was perfectly free notwithstanding its
weight.

Dulong and Arago experimented with pressures up to 27 atmospheres,
and observed that the volume of air always diminished a little more than is
required by Boyle's law. But as these differences were very small, they
attributed them to errors of observation, and concluded that the law was
perfectly exact, at any rate up to 27 atmospheres.

Regnault investigated the same subject with an apparatus resembling
that of Dulong and Arago, but in which all the sources of error were taken
into account, and the observations made with remarkable precision. Thus,
starting with a unit volume of gas under a pressure of i metre of mercury, in
order to reduce this volume to one-half, the pressure should be two metres,
whereas the following were the pressures actually required ; air i "9978 metre ;
nitrogen r9985 ; carbonic acid, 1-9829 ; and hydrogen 2-oii. Similar results
were obtained at higher pressures ; thus to reduce air to ^^ of its original
volume, a pressure of 197 199 m. was required instead of 20; and while car-
bonic acid only required 16705, hydrogen required 20-269 metres.

It thus appears that with increasing pressures hydrogen has a greater, and
the other gases a smaller, volume than is required by Boyle's law.

Very much higher pressures have been employed in similar experiments
by Natterer and by Andrews. Cailletet used a special apparatus by
which the pressure could be raised to 600 atmospheres. Amagat made

-182] Van der Waals^ Formula. i6i

a remarkable series of experiments by a method based on Boyle's experiment.
The pressure could be applied directly by means of mercury in a steel tube
about i,ooo feet in length, arranged in the shaft of a deep coal pit, and
suitably connected at the bottom with a carefully calibrated glass tube. In
this way pressures of as much as 400 atmospheres could be applied, and the
temperatures remained constant.

The general result of these experiments is to show that at high pressures
the volume is greater than that required by Boyle's law, agreeing in this respect
with hydrogen at ordinary pressures. This is well illustrated by the deport-
ment of ethylene as given in the following table, where P is the pressure
in oietres of mercury, and PV the product of pressure into volume, which
according to Boyle's law should be constant.

Pressure 24 34-8 45-1 55-4 64 72 84 134 214 303
PV 21-5 i8-4 12-3 9-8 9-4 97 lo? iS'i 22-1 29-3

It will thus be seen that the product PV decreases with increasing
pressure to a minimum, and then increases agam with the pressure.

The pressure at which this 7nimmu7?i of compressibility occurs is different
with different gases, as is also the extent of the deviation from the law.

At a temperature of 20° this minimum occurs at the following pressures
in metres of mercury : nitrogen and carbonic oxide 50, air and ethylene 65,
oxygen 100, and marsh gas 120.

182. Van der "VW^aals' Formula. — Under high pressures gases do not, as
we have seen, follow Boyle's law with strictness. In order to account for these
discrepancies Van der Waals has introduced a modification into the'formula
PV = const. (180) which is based on the following considerations. We shall
afterwards see (293) that Boyle's law may be deduced from the dynamical
theory' of gases, which assumes that they are made up of infinitely small
particles moving with great velocities ; it is also assumed that these particles
have no cohesion or specific attraction for each other, and also that they are
mere mathematical points. Van der Waals takes account of these limitations.
He considers that the cohesion a, which the particles possess, though small, has
a certain value, the effect of which is to add itself to the pressure ; its force
will be proportional to the number of acting and attracting particles, and
will be directly proportional to the square of the density, or inversely propor-
tional to the square of the volume. The other correction is for the volume
of the particles themselves, b., which, though exceedingly small, has a certain
value. The pressure of a given mass of gas being due to the number of
impacts which take place in a given time, it is clear that if the particles have
a certain magnitude they must collide against each other more frequently than
if they are mere mathematical points ; the influence on the formula will be
that the volume V will be diminished by an amount which represents a multiple
of the molecular volume, or the space actually occupied by the particles.

The formula of Boyle's law, as thus modified by Van der Waals, becomes

(P+ ^-^iy-b)^ const.

It will thus be seen that the two influences mentioned affect Boyle's law
in opposite directions. With hydrogen, where the molecules have little or

l62

On Gases.

[182-

no attraction, there is no cohesion, and accordingly the product PV increases
continuously with the pressure, and there is no maximum of compressibility.

With other gases a has a definite value ; at low pressures the product
PV is less than that required by Boyle's law, and the influence of a pre-
ponderates ; but as the pressure continuously increases this diminishes in
comparison with the influence of b., and the product now increases, and at
high pressures the gases behave as does hydrogen at low ones. Between
these a maximum compressibility is seen, which varies with different gases
according to the values of a and b in each case.

^ Van der Waals deduced from the experimental results

obtained by Regnault for the condensation of various gases
and for their expansion by heat, values for a and b for the
respective gases, which when introduced into the formula
satisfactorily represent the numbers obtained.

183. iMtanometers. — Manometers are instruments for
measuring the tension of gases or vapours. In all such in-
struments the unit chosen is the pressure of one atmosphere,
or 30 inches of mercury at the standard temperature, which,
as we have seen, is nearly 15 lbs. to the square inch.

The open-air manometer consists of a bent glass tube BD
(fig. 160), fastened to the bottom of a reservoir AC, of the
same material, containing mercury, which is connected with
the closed recipient containing the gas or vapour the pres-
sure of which is to be measured. The whole is fixed on a
long plank kept in a vertical position.

In graduating this manometer, C is left open, and the
number i marked at the level of the mercury, for this repre-
sents one atmosphere. From this point the numbers 2, 3, 4,
5, 6, are marked at each 30 inches, indicating so many atmo-
spheres, since a column of mercury 30 inches represents a
pressure of one atmosphere. The intervals, from i to 2, and
from 2 to 3, &c., are divided into tenths. C being then
placed in connection with a boiler, for example, the mercury
rises in the tube BD to a height which measures the tension
of the vapour. In the figure the manometer marks 2 atmo-
spheres, which represents a height of 30 inches, plus the
atmospheric pressure exerted at the top of the column
through the aperture D.

This manometer is only used when the pressures do not
exceed 5 to 6 atmospheres. Beyond this, the length of tube
necessary makes it very inconvenient, and the following ap-
paratus is commonly used.

184. Manometer with compressed air. — The mano-
meter with co7npressed air is founded on Boyle's law : one
form is represented in fig. 161, which may be screwed into

a boiler or steam-pipe where pressure is to be measured. The pressure is
transmitted through the opening a into the closed space b. In this is an
iron vessel containing mercury, in which dips the open end of the mano-
meter tube, which is screwed airtight in the tubulure.

— '^ —

Fig. 160.

-185J

Volumonieter.

163

In the graduation of this manometer, the quantity of air contained in the
tube is such that when the aperture A communicates freely with the atmo-
sphere, the level of the mercury is the same in the tube and in the tubulure.
Consequently, at this level, the number i is marked on the
scale to which the tube is affixed. As the pressure acting
through the tubulure A increases, the mercury rises in the
tube, until its weight, added to the tension of the compressed
air, is equal to the external pressure. It would consequently
be incorrect to mark two atmospheres in the middle of the
tube ; for, since the volume of the air is reduced to one-half,
its tension is equal to two atmospheres, and, together with
the weight of the mercury raised in the tube, is therefore
more than two atmospheres. The position of the number is
at such a height that the elastic force of the compressed air,
together with the weight of the column of mercuiy in the
tube, is equal to two atmospheres. The exact position of
the numbers 2, 3, 4, &c., on the manometer scale can only
be determined by calculation. Sometimes this manometer
is made of one glass tube ; the principle is obviously the
same.

185. Volumometer.— An interesting application of Boyle's
law is met with in the volumonieter, which is used in deter-
minations of the specific gravity of solids which cannot be
brought into contact with water or other liquids. A simple
form consists of a glass tube with a cylinder G at the top
(fig. 162), the edges of which are carefully ground, and which
can be closed hermetically by means of a ground-glass plate
D. The top being open, the tube is immersed until the
level of the mercury inside and outside is the same ; this is
represented by the mark Z. The apparatus is then closed
airtight by the plate, and is raised until the mercury stands
at a height /?, above the level Q in the bath. The original
volume of the enclosed air V, which was under the pressure of
the atmosphere, is now increased to V + 2/, since the pressure
has diminished by the height of the column of mercury h.
Calling the pressure of the atmosphere at the time of obser-
vation b, we shall have V : Y + v = b-h : b.

Placing now in the cylinder a body K, whose volume x is
unknown, the same operations are repeated ; the tube is raised
until the mercury again stands at the same mark as before, but
its height above the bath is now different : a second reading
h^ is obtained, and we have (V - or) : {Y - x) w = b-h^: b.

Combining and reducing, we get ;f = (V + 7/)(i — -^). The

^'■\
volume V-i-z/ is constant, and is determined numerically,
once for all, by making the experiment with a substance of
known volume, such as a glass bulb.

This apparatus, which is also known as the steromefer, is of great value
in determining the gravimetrical density of gunpowder ; this averages from

Fig. 161

164

On Gases.

[185-

I -67 to I '84, and is thus materially different from its apparoit density, or
the weight of a given volume compared with that of an equal volume of
water, which is from 0-89 to 0-94.

186. Reg-nault's barometric manometer. — For measuring pressures of
less than one atmosphere, Regnault devised the following arrangement,
which is a modification of his fixed barometer (fig. 152). In the same cistern
dips a second tube a of the same diameter, open at both ends, and provided
at the top with a three-way cock, one of which is connected with an air-pump
and the other with the space to be exhausted. The further the exhaustion
is carried the higher the mercury rises in the tube a. The differences
of level in the tubes b and a give the pressures. Hence, by measuring the
height ab, by means of the cathetometer, the pressure in the space that is
being exhausted is accurately given. This apparatus is also called the
diffcre?itial barometer.

187. Aneroid barometer. — This instrument derives its name from the
circumstance that no liquid is used in its construction (a, without ; vr\pos,
moist). Fig. 163 represents one of the forms of these instruments, constructed

Fig. 163.

Fig. 164.

by Casella ; it consists of a cylindrical metal box, exhausted of air, the top
of which is made of thin corrugated metal, so elastic that it readily yields to
alterations in the pressure of the atmosphere.

When the pressure mcreases, the top is pressed inwards ; when, on the
contrary, it decreases, the elasticity of the lid, aided by a spring, tends to
move it in the opposite direction. These motions are transmitted by delicate
multiplying levers to an index which moves on a scale. The instrument is
graduated empirically by comparing its indications, under different pressures^
with those of an ordinary mercurial barometer.

The aneroid has the advantage of being portable, and can be constructed
of such dehcacy as to indicate the difference in pressure between the height

-188]

Laivs of the Mixture of Gases.

165

of an ordinary table and the ground. It is hence much used in determining
heights in mountain ascents. But it is somewhat Hable to get out of order,
especially when it has been subjected to great variations of pressure ; and
its indications must from time to time be compared with those of a standard
barometer.

The errors arising from the use of the aneroid are mainly due to the trans-
mission of the motion of the lid by the multiplying arrangement. Goldschmid
of Zurich devised a form in which the motion of the lid is directly observed.

Like that of other aneroids, the lid of a box a (fig. 164), in which the
alterations of pressure are determined, is of fine corrugated sheet metal. To
this is fixed a horizontal metal strip b^ on the front end of which is a small
square e, acting as index. This rises and falls with the movement of the lid,
and indicates on a scale ff\ on the sides of the slit dd'., alterations of
pressure in centimetres. To this strip a second and more delicate one, c, is
fixed on the front end of which is also fixed an index e'. Before making an
observation, the horizontal line of this index is made to coincide with that of
e ; this is effected by means of a micrometer screw 7;/, which is raised or
lowered by the movable ring Ji ; on the corresponding scale millimetres and
tenths of a millimetre are read off. To do this the instrument is provided
with a lens, not represented in the figure. There is also a small thermo-
meter / ; from its indications a correction is made for temperature according
to an empirical scale specially constructed for each instrument.

188. Iiaws of the mixture of g-ases. — If a communication is opened
between two closed vessels containing gases, they at once begin to mix,
whatever be their density, and in a longer or
shorter time the mixture is complete, and will
continue so, unless chemical action is set up.
The laws which govern the mixture of gases
may be thus stated : —

I. The mixture takes place rapidly and is
homogetieous ; that is, each portion of the mix-
ture contains the two gases in the sa7ne propor-
tion.

II. If the gases severally and the inixture
have the same temperature, and if the gases
severally and the mixture occupy the same
volume, then the pressure on the unit of area
exerted by the mixture will equal the sum of
pressures on the unit of area exerted by the
gases severally.

From the second law a very convenient
formula can be easily deduced.

Let v^, 7'o, ■z'o . . . . be the volumes of
several gases under pressure of py,p..,p,, ....
respectively. Suppose these gases when mixed
to have a volume V, under a pressure P, the temperatures being the same.
By Boyle's law we know that v^ will occupy a volume V under a pressure//,
provided that

V// = vp^ ; similarly, Wp./ = v.-f^

Fig. 165.

1 66 On Gases. [188-

and so on. But from the above law

P=A'+A'+ • • •

therefore VP = v^p^ + v.^p.^ + v.^p.^ + . . .

It obviously follows that if the pressures are all the same, the volume of the
mixture equals the sum of the separate volumes.

The first law was shown experimentally by BerthoUet, by means of an
apparatus represented in fig. 165. It consists of two glass globes provided
with stopcocks, which can be screwed one on the other. The upper globe
was filled with hydrogen, and the lower one with carbonic acid, which
has 22 times the density of hydrogen. The globes having been fixed to-
gether were placed in the cellars of the Paris Observatory and the stopcocks
then opened, the globe containing hydrogen being uppermost. BerthoUet
found after some time that the pressure had not changed, and that, in
spite of the difference in density, the two gases had become uniformly mixed
in the two globes. Experiments made in the same manner with other
gases gave the same results, and it was found that the diffusion was more
rapid in proportion as the difference between the densities was greater.

The second law may be demonstrated by passing into a graduated tube,
over mercury, known volumes of gas at known pressures. The pressure and
volume of the whole mixture are then measured, and found to be in accord-
ance with the law.

Gaseous mixtures follow Boyle's law, like simple gases, as has been
proved for air (180), which is a mixture of nitrogen and oxygen.

189. Absorption of gases by liquids.— Water and many liquids possess
the property of absorbing gases. Under the same conditions of pressure and
temperature a liquid does not absorb equal volumes of different gases.
At the temperature 0° C. and pressure 760 mm., one volume of water dissolves
the following volumes of gas : —

Nitrogen . . o'02o Sulphuretted hydrogen . 4-37

Oxygen . . 0-041 Sulphurous acid . . . 7979
Carbonic acid . J79 Ammonia .... 1046-63

From the very great condensation, to which the latter correspond, it may be
inferred that the gases in solution are in the liquid state.

Gases are more soluble in alcohol ; thus at 0° C. alcohol dissolves 4-33
volumes of carbonic acid gas.

The whole subject of gas absorption has been investigated by Bunsen.
The general laws are the following : —

I. For the same gas, the same liquid, attd the same temperature, the
weight of gas absorbed is proportional to the pressure. This may also be
expressed by saying that at all pressures the volume dissolved is the same ;
or that the density of the gas absorbed is in a constant relation with that of
the external gas which is not absorbed.

Accordingly, when the pressure diminishes, the quantity of dissolved
gas decreases. If a solution of gas be placed under the air-pump and
a vacuum created, the gas obeys its expansive force, and escapes with
effervescence.

-190]

Diffusion of Gases.

167

II. T/ie quantity of gas absorbed decreases with the temperature; that is
to say, when the elastic force of the gas is greater. Thus at 15° water
absorbs only i-oo of carbonic acid.

III. The quantity of gas ivhich a liquid can dissolve is independent oj
the nature and of the quantity of other gases which it may already hold in
solution.

In every gaseous mixture each gas exercises the same pressure as it
would if its volume occupied the whole space ; and the total pressure is
equal to the suiii of the individual pressures. When a liquid is in contact
with a gaseous mixture, it absorbs a certain part of each gas, but less than
it would if the whole space were occupied by each gas. The quantity of
each gas dissolved is proportional to the pressure which the unabsorbed
gas exercises alone. For instance, oxygen forms only about \ the quantity
of air ; and water, under ordinary conditions, absorbs exactly the same
quantity of oxygen as it would if the atmosphere were entirely formed of this
gas under a pressure equal to \ that of the atmosphere.

190. Diffusion of gases. —Phenomena analogous to those of endosmose
(139) are seen in a high degree in the case of gases. When two different
gases are separated by a porous diaphragm, an interchange takes place
between them, and ultimately the composition of the gas on both sides of the

Fig. 166. Fig 167.

diaphragm is the same ; but the rapidity with which different gases diffuse
into each other under these circumstances varies considerably. There is,
however, an essential difference between the phenomena of endosmose and
those of diffusion ; for while the inequality in the curi"ents in the former case
is due to the different attraction of the material of the diaphragm for the con-
stituents, in the diffusion of gases this nature has no influence ; from the
smallness of the pores the actions are molecular, and not molar, and the
rate of interchange depends only on the size of the molecules, that is, on the
specific gravities of the gases. The laws of the diffusion of gases were in\esti-
gated by Graham. Numerous experiments illustrate it, some of the most
interesting of which are the following : —

A glass cylinder closed at one end is filled with carbonic acid gas, its
open end tied over with a bladder, and the whole placed under a jar of
hydrogen. Diffusion takes place between them through the porous dia-

1 68 On Gases. [190-

phragm, and after the lapse of a certain time hydrogen has passed through
the bladder into the cylindrical vessel in much greater quantity than the
carbonic acid which has passed out, so that the bladder becomes very much
distended outwards (fig. i66). If the cylinder be filled with hydrogen and
the bell-jar with carbonic acid, the reverse phenomenon will be produced
— the bladder will be distended inwards (fig. 167).

A tube about 12 inches long, closed at one end by a plug of dry plaster
of Paris, is filled with dry hydrogen, and its open end then immersed in a
mercury bath. Diffusion of the hydrogen towards the air takes place so
rapidly that a partial vacuum is produced, and mercury rises in the tube to
a height of se\eral inches (fig. 168). If several such tubes are filled with
different gases, and allowed to diffuse into the
air in a similar manner, in the same time,
different quantities of the various gases will
diffuse, and Graham found that the law regu-
lating these diffusions is that the force of diffu-
sion is inversely as the square roots of the
densities of gases. Thus, if two A'essels of equal
capacity, containing oxygen and hydrogen, be
separated by a porous plug, diffusion takes

1 [|r place ; and after the lapse of some time, for

(HJ ' '" '^^^ every one part of oxygen which has passed into

the hydrogen, four parts of hydrogen have
passed into the oxygen. Now, the density of
hydrogen being i, that of oxygen is 16, hence
the force of diffusion is inversely as the square
roots of these numbers. It is four times as
great in the one which has ^ij the density of the
other.

Let the stem of an ordinary tobacco pipe be
cemented, so that its ends project, in an outer
glass tube, which can be connected with an air-
pump and thus exhausted. On allowing then a
slow current of air to enter one end of the pipe,
its nitrogen diffuses more rapidly on its way
through the porous pipe than the heavier o.xy-
gen, so that the gas which emerges at the other
end of the porous pipe, and which can be col-
lected, is richer in oxygen, and by repeating the
operation on the gas which has passed through,
the proportion of oxygen is so much increased
that the gas can relight a semi-extinguished taper. To this process, in
which one gas can be separated from another by diffusion, the term atmolysis
is given.

Fig. 169 is an excellent illustration of the action of diffusion. A porous
pot A, such as is used for voltaic cells, is fixed by means of a cork to the
glass tube, which contains water up to the bulb C, the upper part con-
taining air. When a beaker containing hydrogen, B, is placed over the pot,
the diffusion of the hydrogen into it is so rapid that the water is at once

-191]

Effusion of Gases.

169

driven down and jets out. When the beaker is removed, the gas inside the
pot being richer in hydrogen now diffuses out with great rapidity, and the
water rises in the tube much higher than its original level.

191. Effusion of g-ases. — A gas can only flow from one space to another
space occupied by the same gas, when the pressure in the one is greater
than in the other. Effusion is the term applied to the phenomenon of the
passage of gases into vacuum, through a minute aperture not much more
or less than 0-013 millimetre in diameter, in a thin plate of metal or of
glass ; for in a tube we are dealing with masses of gases, and friction comes
into play, and in a larger aperture the particles would strike against one
another, and form eddies and whirlpools. The velocity of the efflux is mea-
sured by the formula v= '\/2gh, in which h re-
presents the pressure under which the gas
flows, expressed in terms of the height of a
column of the gas which would exert the same
pressure as that of the effluent gas. Thus for
air under the ordinary pressure flowing into a
vacuum the pressure is equivalent to a column
of mercury 76 centimetres high ; and as mer-
cury is approximately 10,500 times as dense
as air, the equivalent column of air will be
76 X 10,500 = 7,980 metres. Hence the velocity
of efflux of air into vacuum is = ^2 x 9'8 x 7980
= 395-5 metres. This velocity into vacuum
only holds, however, for the first moment, for
the space contains a continually increasing quan-
tity of air, so that the velocity becomes con-
tinually smaller, and is null when the pressure
on each side is the same. If the height of the
column of air hh, corresponding to the ex-
ternal pressure, is known, the velocity may be
calculated by the formula v= sjT.g {h-Ji^.

For gases hghter than air a greater height
must be inserted in the formula, and for
heavier gases a lower height ; and this change
must be inversely as the change of density.
Hence the velocities of efflux of various gases
must be inversely as the square roots of their
densities. A simple inversion of this statement
is that the deftsities of two gases are inversely
as the squares of their velocities of cff'usion.

On this law Bunsen has based an interesting method of determining the
densities of gases and vapours, which is of great service where only small
quantities of the substances are available.

The gas in question is contained (fig. 170) in a glass tube A, closed at the
top with a stopper s, in the neck B. In a little enlargement here a platinum
plate V is fixed, in which is a fine capillary aperture. The tube is inserted
in a deep mercury trough, CC, so that the top r of a glass swimmer D is level
with the mercury. The stopper s having been removed, the gas issues

I/O On Gases. [191-

throLigh the capillary aperture, and the time is noted which elapses until a
mark t in the swimmer is level with the mercury. Working in this way with
different gases, it is found that the ratios of the times of effusion are directly
as the squares of the densities, which is another form of the above statement.
By this method it may often be ascertained whether a gas is a mixture
or not. Thus marsh gas (CHJ has the same specific gravity (o"554) as a
mixture in equal volumes of dimethyl ''C.^H^ sp. gr. 1-039) ^"d hydrogen
(sp. gr. 0-069), ai'id would furnish the same results on chemical analysis.
But if the composition of the gas which had been subjected to diffusion
were examined in the two cases, it would be found that the residual marsh
gas would retain the same composition, while that of the mixture would be
different, for a larger volume of the specifically lighter hydrogen would have
diffused out.

192. Transpiration of grases. — If gases issue through long, fine capillary
tulles into a vacuum, the phenomenon is called tj'anspiration ; and the rate
of efflux, or the velocity of transpiration, is independent of the rate of
diffusion.

i. For the same gas, the rate of transpiration increases, other things
being equal, directly as the pressure ; that is, equal volumes of air of different
densities require times inversely proportional to their densities.

ii. With tubes of equal diameters, the volume transpired in equal times
is inversely as the length of the tube.

iii. As the temperature rises the transpiratioii becomes slozuer.

iv. The rate of transpiration is independent of the material of the tube.

193. Absorption of gases by solids. — The surfaces of all solid bodies
exert an attraction on the molecules of gases with which they are in contact,

of such a nature that they become covered with a
more or less thick layer of co?idensed gas. When a
porous body, such as a piece of charcoal, which conse-
quently presents an immensely increased surface in
proportion to its size, is placed in a vessel of ammonia
gas over mercury (fig. 171), the great diminution of
volume which ensues indicates that considerable quan-
tities of gas are absorbed.

Now, although there is no absorption such as arises
from chemical combination between the solid and the
gas (as with phosphorus and oxygen), still the quan-
tity of gas absorbed is not entirely dependent on the
physical conditions of the solid body ; it is influenced
in some measure by the chemical nature both of the
solid and the gas. Boxwood charcoal has very great
absorptive power. The following table gives the
volumes of gas, under standard conditions of tempera-
ture and pressure, absorbed by one volume of boxwood charcoal and of meer-
schaum respectively : —

Charcoal Meerschaum

Ammonia 90 15

Hydrochloric acid ...... 85 —

Sulphurous acid ...... 65 —

Fig. 171.

-194] Occlusion of Gases. 171

Charcoal

Meerschaur

Sulphuretted hydr

ogen .

Carbonic acid

5-3

Carbonic oxide

9-4

1-2

Oxygen

9-2

1-5

Nitrogen

7-5

1-6

Hydrogen

175

0-5

The absorption of gases is in general greatest in the case of those which are
most easily liquefied.

Cocoa-nut charcoal is even more highly absorbent ; it absorbs 171 of
ammonia, 72) of carbonic acid, and 108 of cyanogen at the ordinary pressure ;
the amount of absorption increases with the pressure. The absorptive
power of pine charcoal is about half as much as that of boxwood. The
charcoal made from cork wood, which is very porous, is not absorbent,
neither is graphite. Platinum, in the finely divided form known as platinum
sponge, is said to absorb 250 times its volume of oxygen gas. Many other
porous substances, such as meerschaum, gypsum, silk, &c., are also highly
absorbent.

If a coin be laid on a plate of glass or of metal, after some time, when
the plate is breathed on, an image of the coin appears. If a figure is traced
on a glass plate with the finger, nothing appears until the plate is breathed
on, when the figure is at once seen. Indeed, the traces of an engraving
which has long lain on a glass plate may be produced in this way.

These phenomena are known as Moser^s linages, for he first investigated
them, although he explained them erroneously. The correct explanation
was given by Waidele, who ascribed them to alterations in the layer of gas,
^'apour, and fine dust which is condensed on the surface of all solids. If
this layer is removed by wiping, on afterwards breathing against the surface
more vapour is condensed on the marks in question, which then present a
different appearance from the rest.

■ If a die or a stamp is laid on a freshly polished metal plate, and one
therefore which has been deprived of its atmosphere, the layer of vapour
from the coin will diffuse on to the metal plate, which thereby becomes
altered ; so that when this is breathed on an impression is seen.

Conversely, if a coin be polished and placed on an ordinary glass plate,
it will partially remove the layer of gas from the parts in contact, so that on
breathing on the plate the image is visible.

194. Occlusion of g:ases Graham found that at a high temperature

platinum and iron allow hydrogen to traverse them even more readily than
does caoutchouc in the cold. Thus while a square metre of caoutchouc o"oi4
millimetre in thickness allowed 129 cubic centimetres of hydrogen at 20° to
traverse it in a minute, a platinum tube i-i millimetre in thickness and of the
same surface allowed 489 cubic centimetres to traverse it at a bright red heat.

This is probably connected with the property which some metals, though
destitute of physical pores, possess of absorbing gases either on their surface
or in their mass, and to which Graham has applied the term occlusion. It
is best observed by allowing the heated metal to cool in contact with the
gas. The gas cannot then be extracted by the air-pump, but is disengaged
on heating. In this way Graham found that platinum occluded four times

i;:

On Gases.

[194-

its volume of hydrogen ; iron wire 0*44 its volume of hydrogen, and 4-15
volumes of carbonic oxide ; silver, reduced from the oxide, absorbed about
seven volumes of oxygen, and nearly one volume of hydrogen when heated
to dull redness in these gases. This property is most remarkable in palla-
dium, which absorbs hydrogen, not only in cooling after being heated, but
also in the cold. When, for instance, a palladium electrode is used in the
decomposition of water, one volume of the metal can absoi"b 980 times its
volume of the gas. This gas is again driven out on being heated, in which
respect there is a resemblance to the solution of gases in liquids. By the
occlusion of hydrogen the volume of palladium is increased by 0-09827 of
its original amount, from which it follows that the hydrogen, which under
ordinary circumstances has a density of 0-000089546 that of water, has here a
density nearly 9,868 times as great, or about o-88 that of water. Hence the
hydrogen must be in the liquid or even solid state ; it probably forms thus
an alloy with palladium, like a true metal— a view of this gas which is
strongly supported by independent chemical considerations. The physical
properties too, in so far as they have been examined, support this \-iew of its
being an alloy.

The phenomenon of occlusion may be illustrated by the following experi-
ment (fig. 172). A platinum wire be is stretched between supports on a
glass plate ; one end of a palladium
: wire fg is also fixed, of which the other
end is attached to the short arm of a light
lever movable about o, the long arm of
which is loaded with a weight (not repre-
sented in the figure) to keep the wire tight.
The platinum wire is connected with the
positive pole a, and the palladium with the
negative pole d, of a voltaic battery, and
the apparatus is partially immersed in
acidulated water ; the water is thereby-
decomposed into its constituent gases ;
oxygen is liberated in bubbles from the
platinum wire, but there is no visible dis-
Fig. 172. engagement at the palladium. It becomes

longer, however, as is seen by the lever
moving downwards. If the current is reversed, the wire again contracts, and
the lever resumes its original position.

195]

ArcJiimcdes' Principle applied to Gases.

17;

CHAPTER III.

PRESSURE OF BODIES IN AIR. BALLOONS.

195. Archimedes' principle applied to g^ases. — The pressure exerted
by gases, on bodies immersed in them, is transmitted equally in all directions,
as has been shown by the experiment
with the Magdeburg hemispheres. It
therefore follows that all which has
been said about the equilibrium of
bodies in liquids applies to bodies in
air ; they lose a part of their weight
equal to that of the air which they dis-
place.

The loss of weight in air is demon-
strated by means of the baroscope,
which consists of a scalebeam, at one
of whose extremities a small leaden
weight is supported, and at the other
there is a hollow copper sphere (fig.
163). In the air they exactly balance
each other ; but when they are placed
under the receiver of an air-pump,
and a vacuum is produced, the sphere
sinks, thereby showing that in reality
it is heavier than the smaller leaden
weight. Before the air is exhausted, each body is buoyed up by the weight
of the air which it displaces. But as the sphere is much the larger of the
two, its weight undergoes most apparent diminution, and thus, though in
reality the heavier body, it is balanced by the small leaden weight. It may
be proved by means of the same apparatus that this loss is equal to the
weight of the displaced air. Suppose the volume of the sphere is 10 cubic
inches. The weight of this volume of air is 3-1 grains. If now this weight
be added to the leaden weight, it will overbalance the sphere in air, but will
exactly balance it in vacuo.

The principle of Archimedes is true for bodies in air ; all that has been
said about bodies immersed in liquids applies to them ; that is, that when a
body is heavier than air, it will sink, owing to the excess of its weight over
the buoyancy. If it is as heavy as air, its weight will exactly counterbalance
the buoyancy, and the body will float in the atmosphere. If the body is
lighter than air, the buoyancy of the air will prevail, and the body will rise
in the atmosphere until it reaches a layer of the same density as its own.

Fig. 173-

174 On Gases. [195-

The force of the ascent is equal to the excess of the buoyancy over the weight
of the body. This is the reason why smoke, vapours, clouds, and air-balloons
rise in the air.

AIR-BALLOONS.

196. Air-balloons. — Air-balloons are hollow spheres made of some light
impermeable material, which, when filled with heated air, with hydrogen
gas, or with coal gas, rise in the air by virtue of their relative lightness.

They were invented by the brothers Montgolfier of Annonay, and the
first experiment was made at that place in June 1783. Their balloon was a
sphere of forty yards in circumference, and weighed 500 pounds. At the
lower part there was an aperture, and a sort of boat was suspended, in which
fire was lighted to heat the internal air. The balloon rose to a height of
2,200 yards, and then descended without any accident.

Charles, a professor of physics in Paris, substituted hydrogen for hot air.
He himself ascended in a balloon of this kind in December 1783. The use
of hot-air balloons was entirely given up in consec^uence of the serious
accidents to which they were liable.

Since then the art of ballooning has been greatly extended, and many
ascents have been made. That which Gay-Lussac made in 1804 was the
most remarkable for the facts with which it has enriched science, and for the
height which he attained — 23,000 feet above the sea-level. At this height
the barometer sank to 12-6 inches, and the thermometer, which was 31° C.
on the ground, was 9 degrees below zero.

In these high regions the dryness was such on the day of Gay-Lussac's
ascent, that hygrometric substances, such as paper, parchment, &c., became
dried and crumpled as if they had been placed near the fire. The respira-
tion and circulation of the blood were accelerated in consequence of the
great rarefaction of the air. Gay-Lussac's pulse made 120 pulsations in a
minute instead of 66, the normal number. At this great height the sky had
a very dark blue tint, and an absolute silence prevailed.

One of the most remarkable of ascents was made by Mr. Glaisher and
Mr. Coxwell, in a large balloon belonging to the latter. This was filled with
90,000 cubic feet of coal gas (sp. gr. 0-37 to 0-33) ; the weight of the load
was 600 pounds. The ascent took place at i P.M. on September 5, 1861 ; at
1.28 they had reached a height of 15,750 feet, and in eleven minutes after a
height of 21,000 feet, the temperature being— 10*4°; at 1.50 they were at
26,200 feet, with the thermometer at— 1 5*2°. At 1.52 the height attained
was 29,000 feet, and the temperature — 16° C. At this height the rarefaction
of the air was so great, and the cold so intense, that Mr. Glaisher fainted,
and could no longer observe. According to an approximate estimation the
lowest barometric height they attained was 7 inches, which would correspond
to an elevation of from 36,000 to 37,000 feet.

197. Construction and manag-ement of balloons. — A balloon (fig. 174)
is made of long bands of silk sewed together and covered with caoutchouc
varnish, which renders it airtight. At the top there is a safety-valve closed
by a spring, which the aeronaut can open at pleasure by means of a cord.
A light wickerwork boat is suspended by means of cords to a network which
entirely covers the balloon.

-197] Construction and Management of Balloons. 175

A balloon of the ordinary dimensions, which can carry three persons, is
about 16 yards high, 12 yards in diameter, and its volume, when it is quite
full, is about 680 cubic yards. The bal-
loon itself weighs 200 pounds ; the ac-
cessories, such as the rope and boat, 100
pounds.

The balloon is filled either with hy-
drogen or with coal gas. Although the
latter is heavier than the former, it is
generally preferred, because it is cheaper
and more easily obtained. It is passed
into the balloon from the gas reservoir
by means of a flexible tube. It is im-
portant not to fill the balloon quite
full, for the atmospheric pressure dimi-
nishes as it rises, and the gas inside,
expanding in consequence of its elastic
force, tends to burst it. It is suffi-
cient for the ascent if the weight of
the displaced air exceeds that of the
balloon by 8 or 10 pounds. And this
force remains constant so long as the
balloon is not quite distended by the
dilatation of the air in the interior. If
the atmospheric pressure, for example,
has diminished to one-half, the gas in the
balloon, according to Boyle's law, has
doubled its volume. The volume of the
air displaced is therefore twice as great ;
but since its density has become only
one-half, the weight and consequently
the upward buoyancy are the same.
When once the balloon is completely
dilated, if it continues to rise, the force of
the ascent decreases, for the volume of
the displaced air remains the same, but
its density diminishes, and a time arrives
at which the buoyancy is equal to the

weight of the balloon. The balloon can now only take a horizontal direction,
carried by the currents of air which prevail in the atmosphere. The aero-
naut knows by the barometer whether he is ascending or descending, and
by the same means he determines the height which he has reached. A long
flag fixed to the boat would indicate, by the position it takes either above or
below, whether the balloon is descending or ascending.

When the aeronaut wishes to descend, he opens the valve at the top of
the balloon by means of the cord, which allows gas to escape, and the
balloon sinks. If he wants to descend more slowly, or to rise again, he
empties out bags of sand, of which there is an ample supply in the car. The
descent is facilitated by means of a grappling iron fixed to the boat. When

a»k.

176

On Gases.

[197-

once this is fixed to any obstacle, the balloon is lowered by pulling the
cord.

The only practical applications which air-balloons have hitherto had
have been in military reconnoitring. At the battle of Fleurus, in 1794, a
captive balloon — that is, one held by a rope — was used, in which there was
an observer who reported the movements of the enemy by means of signals.
At the battle of Solferino the movements and dispositions of the Austrian
troops were watched from a captive balloon ; and in the war in America
balloons were frequently used, while their importance during the siege of
Paris will not have been forgotten. The whole subject of military ballooning
was treated in two papers by Col. Grover and by Col. Beaumont, in a
volume of the Professional Papers of the Royal Engineers ; and experiments
are in progress at Woolwich and at Aldershot, with a view of ascertaining
the most practical means of inflating balloons, and the best form and
equipment for service in the field. It has been proposed to use captive
balloons for observations on the changes of temperature in the air, &c. Air-
balloons can only be truly useful when they can be guided, and as yet all
attempts made with this view have completely failed. There is no other
course at present than to rise in the air until there is a current which has

more or less the desired direc-
tion. Unfortunately, the currents
in the higher regions of the
atmosphere are variable and
irregular.

1 98. Paracbute. — The ob-
ject of the parachute is to allow
the aeronaut to leave the bal-
loon, by giving him the means
of lessening the rapidity of his
descent. It consists of a large
circular piece of cloth (fig. 175),
about 16 feet in diameter, and
which by the resistance of the
air spreads out like a gigantic
umbrella. In the centre there
is an aperture, through which
the air compressed by the
rapidity of the descent makes
its escape ; for otherwise os-
cillations might be produced,
which, when communicated to
the boat, would be dangerous.

In fig. 174 there is a para-
chute attached to the network
1,^, ,_^ of the balloon by means of a

cord which passes round a
pulley, and is fixed at the other end to the boat. When the cord is cut
the parachute sinks, at first very rapidly, but more slowly as it becomes dis-
tended, as represented in the figure.

-199J Calculation of the Weight zvhich a Balloon can raise. 177

199. Calculation of the weight which a balloon can raise. — To

calculate the weight which can be raised by a balloon of given dimensions,
let us suppose it perfectly spherical, and premise that the formuh^ which

express the volume and the superficies in terms of the radius are V = ^^

S = 47rR- ; TT being the ratio of the circumference to the diameter. The
radius R being measured in feet, let p be, in pounds, the weight of a
square foot of the material of which the balloon is constructed ; let P
be the weight of the car and the accessories, a the weight in pounds of
a cubic foot of air at zero, and under the pressure 076'", and a' the weight
of the same volume, under the same conditions, of the gas with which
the balloon is inflated (155). Then the total weight of the envelope in

pounds will be ^Tx'K-p ; that of the gas will be ^~ ^; and that of the dis-
placed air ^^ — -• If X be the weight which the balloon can support, we
have

Whence

47rR^_47rR!a'_ j^.^_.p_
: = 4^(« _ a!) - 47rR-/ - P.

But, as we have before seen (197), in order that the balloon may rise, the
weight must be less by 8 or 10 pounds than that given by this equation.

178

On Gases.

[200-

CHAPTER IV.

APPARATUS WHICH DEPEND ON THE PROPERTIES OF AIR.

200. Air-pump. — The air-pump is an instrument by which a vacuum can
be produced in a given space, or rather by which air can be greatly rarefied,
for an absokite vacuum cannot be produced by its means. It was invented

Fig. 176.

by Otto von Guericke in 1650, a few years after the invention of the baro-
meter.

The air-pump, as now usually constructed, may be described as follows.
Fig. 176 represents a general view ; 177 a section, and figs. 178-183
various parts ; the letters in all the figures having eveiywhere the same
meaning.

The base VGL is of stout metal, and is firmly fixed on a table. At one

200]

A ir-pninp.

179

end two glass cylinders or barrels are firmly cemented, and the two leather
pistons P and P', work airtight in them. To these pistons are attached
racks H, K and by
means of a handle
M N, working about
a pinion X, the pis-
tons P and P' are
moved alternately
up and down. On
the plate V is fitted
a thick glass plate
with a very true
surface. In its
centre is a screw
tubulure«, fixed into
a conduit nc in the
base of the pump,
and which connects
the receiver and
the barrels.

Fig. 178 gives a
vertical section of
one of the pistons
on a larger scale.
It consists of two
brass discs, A and
B, the latter ot

which is provided with a tubulure in which is a screw D ; this presses
together a number of leather washers, very slightly larger than the disc.
The leather is thoroughly soaked with oil, and slides airtight in the barrels,
but with slight friction. D is pierced by a channel which connects it with
the outer air. In the centre of the disc B is a hole /, closed by a metal valve
Z, which is shod with cork, and by means of a rod e is kept in position in
the channel.

A valve s opens and closes the orifice of the channel c which is in con-
nection with the receiver. It is fixed to the end ofa rod a which moves,ibut
with friction, through the piston. Then when the piston sinks it carries with
it the rod <;?, and closes the orifice. As the piston rises it lifts the rod, but
only for a small distance, for the rod strikes against the top of the barrel, and
the piston, continuing its upward motion, slides along the rod.

The stopcock T connects the receiver R with the air-pump gauge E (201),
while S connects the receiver with the barrels. When the receiver has been
exhausted, S is turned through a quarter, and the vacuum is thus . preserved.
Air can be admitted by opening a screw r, at the top of a channel in the
stopcock itself.

The piston P^ being at the bottom of the barrel (fig. 179), as the
handle is worked, the piston rises, and with it the rod a and the valve j-,
while Z is closed by its own weight and the pressure of the air. A partial
vacuum is created under the piston, but the valve s having opened up con-

N 2

Fig. 177.

i8o On Gases. [200-

nection with the receiver R, the air in this expands and fills both the receiver
and the barrel. When P' begins to descend, the valve s is closed by the
descent of the rod a, the rarefied air in the barrel can no longer return to
the receiver, it gets more and more condensed, and its elastic force is ulti-
mately so great as to open the valve Z, and the air under the piston escapes
by the channel D into the outer air, and thus the rarefaction produced
in the receiver is permanent. At the second stroke of the piston the
same phenomenon is repeated, until a limit is reached at which, although
there is air in the receiver, its elastic force is insufficient to raise the
valve Z.

It is clear that when the rarefaction has proceeded to a considerable
extent, the atmospheric pressure on the top of P will be very great, but it will

be very nearly balanced by the atmospheric pressure on the top of the other
piston. Consequently, the experimenter will have to overcome only the
difference of the two pressures. This is the reason why two barrels are
employed, a plan first adopted by Hawksbee.

20I. Air-pump g-augre. — When the pump has been worked some. time,
the pressure in the receiver is indicated by the difference of level of the
mercury in the two legs of a glass tube bent like a syphon, one of which is
opened, and the other closed like the barometer. This little apparatus,
which is called the gauge, is fixed to an upright scale, and placed under a
small bell-jar, which communicates with the receiver E by a stopcock A,
inserted in the tube leading from the orifice G to the cylinders — (fig. 177).

Before commencing to exhaust the air in the receiver, its elastic force
exceeds the weight of the column of mercury which is in the closed branch,

-202] Doubk-exhaustion Stopcock. i8i

and which consequently remains full. But as the pump is worked, the
elastic force soon diminishes, and is unable to support the weight of the
mercury, which sinks and tends to stand at the same level in both legs. It
an absolute vacuum could be produced, they would be exactly on the same
level, for there would be no pressure either on the one side or the other. But
with the very best machines the level is always about a thirtieth of an inch
higher in the closed branch, which indicates that the vacuum is not absolute,
for the elastic force of the residue is ec[ual to the pressure of a column of
mercury of that height.

Theoretically an absolute vacuum is impossible ; for, since the volume
of each cylinder is, say, ~ that of the receiver, only ~ of the air in the
receiver is extracted at each stroke of the piston, and consequently it is im-
possible to exhaust all the air which it contains. The theoretical degree of
exhaustion after a given number of strokes is easily calculated as follows : —
Let a denote the volume of the receiver, including in that term the pipe ;
b the volume of the cyhnder between the highest and lowest positions of
the piston ; and assume, for the sake of distinctness, that there is only one
cylinder : then the air which occupied a before the piston is lifted occupies
a + b after it is lifted ; and consequently if ^^ is the density at the end of the
first stroke, and d the original density, we must have

a + b
If ^, is the density at the end of the second stroke, we have

a + b \a + bJ

Now this reasoning will apply to n strokes ;
consequently, d^ = d( -^, )

If there are two equal cylinders, the same formula holds ; but in this
case, in counting ;/, upstrokes and downstrokes ecjually reckon as ojie.

It is obvious that the exhaustion is never complete, since d ca.n be zero
only when « is infinite. However, no very great number of strokes is re-
quired to render the exhaustion virtually complete, even if a is several times
greater than b. Thus if «= lod a hundred strokes will reduce the density
from ^to 0-0004^^; that is, if the initial pressure is 30 inches, the pressure at
the end of 100 strokes is 0-012 of an inch.

Practically, however, a limit is placed on the rarefaction that can be pro-
duced by any given air-pump ; for, as we have seen, the air becomes ulti-
mately so rarefied that, when the pistons are at the bottom of the cylinder,
its elastic force cannot overcome the pressure in the valves on the inside of
the piston ; they therefore do not open, and there is no further action of the
pump.

202. Bouble-exbaustion stopcock. — By means of this device the ex-
haustion of the air can be carried to a very high degree. Fig. 180 gives a
horizontal section of the stopcock Q, which by means of a central channel
and two lateral ones forms a communication with the receiver and the

On Gases.

[202-

barrels. When the working ceases, that is when Z no longer rises, a quarter-
turn is given to Q (fig. 182). The connections are now altered, as is seen from
the horizontal sections in figs. 180 and 182, and the vertical sections in figs.
181 and 183. The new channels correspond now with those of the base, and
the right barrel is alone connected with the receiver by the channel nmc,
while the left is connected by an oblique channel in the stopcock with a
central aperture s in the base of the right barrel.

The right piston as it rises exhausts air from the receiver ; but when it
sinks the exhausted air is drawn into the left barrel by the apertures o and
d, this latter being always open, for the corresponding conical valve is raised.

When the right piston rises, that of the left sinks ; but the air below does
not return to the right barrel, for the orifice is now closed by the conical
valve. As the right cylinder continues to exhaust the air in the receiver,
and to force it into the left cylinder, the air accumulates here and ultimately
acquires sufficient pressure to raise the valve of the piston Q, which was
impossible before the stopcock was turned, for it is only when the valves in
the piston no longer open that a quarter of a turn is given to the stopcock.
In this way a rarefaction of half a millimetre has been attained.

203. Bianchi's air-pump. — Bianchi invented an air-pump which has
several advantages. It is made entirely of iron, and it has only one cylinder,
which oscillates on a horizontal axis fixed at its base, as seen in fig. 184.
A horizontal shaft, with heavy fly-wheel V, works in a frame, and is turned
by a handle, M. A crank, in, which is joined to the top of the piston rod, is

-203]

BiancJii 's A ir-pii uip.

183

fixed to the same shaft, and consequently at every revohition of the wheel
the cyHnder makes two oscillations.

In some cases, as in that shown in the figure, the crank and the fly-wheel
are on parallel axes connected by a pair of cog-wheels. The modification
in the action produced by this arrangement is as follows : — If the cog-
wheel on the former axis has twice as many teeth as that on the latter axis,

f %'^'x^

Fig. 184.

the pressure which raises the piston is doubled ; an advantage which is
counterbalanced by the inconvenience that now the piston will make one
oscillation for one revolution of the fly-wheel.

The machine is double-acting; that is, the piston PP (fig. 185) produces
a vacuum, both in ascending and descending. This is effected by the fol-
lowing arrangements: — In the piston there is a valve, ^, opening upwards

'^i Jr

184 On Gases. [203-

as in the ordinary machine. The piston rod AA is hollow, and in the inside
there is a copper tube, X, by which the air makes its escape through the valve

b. At the top of the cylinder there
is a second valve, a^ opening up-
wards. An iron rod, D, works with
gentle friction in the piston, and
terminates at its ends in two conical
valves s and s\ which fit into the
openings of the tube BB leading to
the receiver.

Let us suppose the piston de-
scends. The valve s' is then closed,
and, the valve s being open, the air
of the receiver passes into the space
above the piston, while the air in
the space below the piston under-
goes compression, and, raising the
valve, escapes by the tube X, which
communicates with the atmosphere.
When the piston ascends, the ex-
haustion takes place through s', and
the valve s being closed, the com-
pressed air escapes by the valve a.
The machine has a stopcock for
double exhaustion, similar to that
already described (202). It is also
oiled in an ingenious manner. A
cup, E, round the rod is filled with
oil, which passes into the annular
space between the rod AA and the
tube X ; it passes then into a tube
00 in the piston, and, forced by the
atmospheric pressure, is uniformly
distributed on the surface of the
piston.

The apparatus, being of iron, may be made of much greater dimensions
than the ordinary air-pump. A vacuum can also be produced with it in far
less time and in apparatus -of greater size than usual.

204. Deleuil's air-pump. — In this air-pump the main peculiarity is its
piston, which is of considerable length, and consists of a series of accurately
constructed metal discs bolted together. This works easily and smoothly in
the barrel, and no packing or lubricator is used ; or rather, the lubricator
is the air in the space between the piston and the barrel. The internal
friction of the air in this narrow space is so great that the rate at which it
leaks into the barrel is far inferior to the rate at which the pump is exhaust-
ing air from the receiver. And Maxwell showed that the internal friction
is not diminished even when its density is greatly reduced. Hence the
pump works very satisfactorily up to a considerable degree of exhaustion — to
a millimetre of mercury, for instance.

Fig. 185

-205]

SprengeVs A ir-punip.

185

205. Sprengrel's air-pump. — Sprengel has devised a form of air-pump
which depends on the principle of converting the space to be exhausted into
a TorriceHian vacuum.

If an aperture be made in the top of a barometer tube, the mercury sinks
and draws in air ; if the experiment be so arranged as to allow air to enter
along with mercury, and if the supply
of air be limited while that of mercury
is unlimited, the air will be carried
away and a vacuum produced. The
following is the simplest form of the
apparatus in which this action is real-
ised. In fig. 186, cd is a glass tube
longer than a barometer, open at both
ends, and connected by means of india-
rubber tubing with a funnel, A, filled
with mercury and supported by a stand.
Mercur}^ is allowed to fall in this tube
at a rate regulated by a clamp at c ;
the lower end of the tube cd fits in the
flask B, which has a spout at the side
a little higher than the lower end of
cd ; the upper part has a branch at x,
to which a receiver R can be tightly
fixed When the clamp at c is opened,
the first portions of mercury which
run out close the tube and prevent air
from enterin_g below. As the mercury
is allowed to run down, the exhaustion
begins, and the whole length of the
tube from ;r to ^ is filled with cylinders
of air and mercury having a downward
motion. Air and mercury escape
through the spout of the flask B which
is above the basin H, where the mer-
cury is collected. It is poured back
from time to time into the funnel A, to
be re-passed through the tube until
the exhaustion is complete. As this
point is approached, the enclosed air between the mercury cyHnders is seen
to diminish, until the lower part of reforms a continuous column of mercury
about 30 inches high. Towards this stage of the process a noise is heard
like that of a water-hammer when shaken ; the operation is completed when
the column of mercury encloses no air, and a drop of mercury falls on the
top of the column without enclosing the slightest air-bubble. The height of
the column then represents the height of the column of mercury in the
barometer ; in other words, it is a barometer whose Torricellian vacuum
is the receiver R. This apparatus has been used with great success in
experiments in which a very complete exhaustion is required, as in the
preparation of Geissler's tubes and in incandescent electrical lamps. It

1 86

On Gases.

[205-

may be advantageously combined with an exhausting syringe, which first

removes the greater part of the air, the exhaustion being then completed as

above.

The most perfect vacua are obtained by absorbing' the residual gas, after

the exhaustion has been pushed as far as possible, either mechanically or

by some substance with which
it combines chemically. Thus
Dewar has produced a vacuum
which he estimates at — ^ of a
millimetre, by heating charcoal
to redness, in a vessel from
which air had been exhausted
by the Sprengel pump, and then
allowing it to cool. Finkener
filled a vessel with oxygen, then
exhausted as far as possible,
and finally heated to redness
some copper contained in the
vessel. This absorbed the
minute quantity of gas left, with
the formation of cupric oxide.
In some of his experiments
Crookes obtained by chemical
means a vacuum of -^-^,060 of a
millimetre. In these highly
rarefied gases the pressure is so
low that it is veiy difficult to
measure minute differences.
For such cases McLeod has
devised a very valuable gauge,
the principle of which is to con-
dense a measured volume ot

the highly rarefied gas to a much smaller volume, and then to measure its

pressure under the new conditions.

206. Bunsen's Sprengel pump. — This is a very convenient arrangement
for producing a vacuum in cases where a good supply of water is available,
as in laboratories. A composition tube a (fig. 187), connected with the ser-
vice-pipe of a water-supply, is joined by means of a caoutchouc tube to a
glass tube, cdf, to which is attached at / a leaden tube about 10 to 12 yards
long. The tube sr is connected with the space to be exhausted. The water
enters by a, and in falling down the tube carries with it air from the space
to be exhausted. The supply of water, and therewith the rate of exhaustion,
can be regulated by the stopcock b ; the bent tube pq, which contains mer-
cury, measures the degree of exhaustion, which may be reduced to a
pressure of 10 to 15 millimetres.

207. Aspirating- action of currents of air. — When a jet of liquid or of
a gas passes through air, it carries the surrounding air along with it, fresh
air rushes in to supply its place, comes also in contact with the jet, and is
in like manner caiTied away. Thus, then, there is a continual rarefaction

-207j Aspii'atiiig Action of Currents of Air. 187

of the air round the jet, in consequence of which it exerts an aspiratory
action.

This phenomenon may be well illustrated by means of an apparatus re-
presented in fig. 188, the analogy of which to the experiment described (146)
will be at once evident. It consists of a
wide glass tube, in the two ends of which are
fitted two small tubes, nd and B ; in the
bottom is a manometer tube containing a
coloured liquid. On blowing through the
narrow tube the liquid at o is seen to rise.
If, on the contraiy, the wide tube is blown
into, a depression is produced at o.

To this class of phenomena belongs the
following experiment, which is a simple modi-
fication of one originally described by Cle-
ment and Desormes. A tube is fixed in a
metal disc (fig. 189), its end bemg flush with
the surface. A light disc is held at a little
distance by means of three metal studs.
Holding the tube vertically with the discs
downwards, and blowing into it, the movable
disc is seen to rise until it comes in contact
with the upper one. The current of air
spreads out from the centre of the plate
towards the circumference, and in doing so
it is rarefied ; in consequence of this lessened
pressure in the space, the lower disc is lifted
by the external pressure against the upper
one, where it remains as long as the blowing
continues. The simplest plan of making this
experiment was devised by Faraday. Hold-
ing one hand horizontal, the palm down-
wards and the fingers closed, the space between the index and middle finger
is blown through. If a piece of light paper, of 2 or 3 square inches, is held
against the aperture, it does not fall as long as the blowing continues.

The old water-bellows., still used in mountainous places where there is a
continuous fall, is a further application of the principle. Water falling from
a reservoir down a narrow tube divides and carries air along with it ; and, if
there are apertures in the side through which air can enter, this also is
carried along, and becomes accumulated in a reservoir placed below, from
which by means of a lateral tube it can be directed into the hearth of a
forge.

This may be illustrated by the simple apparatus represented in fig. 190, the
construction of which from glass tubes and corks will be readily intelligible. It
may be remarked that the outer tube at b is represented in section, and that
the part of the tubes ofd and ghk outside the cork are relatively much longer
horizontally and vertically than is here represented.

If the vertical tube fd is fitted to a vessel of boiling water, as soon as
steam issues through f, it not only raises water from a vessel in which the

i88

On Gases.

[207-

Fig. 190.

bottom of the tube gh dips, but drives it through the aperture o. And if a
bent tube, with a narrow opening Hke <?, be fitted at n, and directed upwards,

a continuous jet of
^ water is produced,

often reaching to the
ceihng.

This apparatus
serves well to illus-
trate the principle of
Giffard's t?jjector, an
extremely ingenious
and important appa-
ratus by which steam-boilers are kept supplied with water.

The principle is also applied in a series of machines for moving and
lifting liquids, and even solids such as corn ; in pumping, in blowers,
exhausters, air-pumps, etc. An interesting application is that of the well-
known spray producer ; this principle has further been utilised by Sprengel
in supplying water to sulphuric acid chambers.

By the locomotive steampipe a jet of steam entering the chimney of the
locomotive carries the air away, so that fresh air must arrive through the
fire, and thus the draught be kept up.

208. DCorren's mercury pump. — Figs. 191 and 192 represent a mercu-
rial air-pump, constructed by Alvergniat. It consists of two reservoirs, A
and B, connected by a barometer tube T, and a long caoutchouc tube C.
The reservoir B and the tube T are fixed to a vertical support A, which is
movable and open, and can be alternately raised and lowered through a
distance of nearly 4 feet. This is effected by means of a long wire rope,
which is fixed at one end to the reservoir A, and passes over two pulleys, a
and b, the latter of which is turned by a handle. Above the reservoir B is a
three-way cock n ; to this is attached a tube </, for exhaustion, and on the
left is an ordinary stopcock ni^ which communicates with a reservoir of
mercury t/, and with the air. The exhausting tube d is not in direct com-
munication with the receiver to be exhausted ; it is first connected with a
reservoir 0^ partially filled with sulphuric acid, and designed to dry the gases
which enter the apparatus. A caoutchouc tube, <;, makes communication
with the receiver which is to be exhausted. On the reservoir <? is a small
mercury manometer^.

These details being understood, suppose the reservoir A at the top of its
course (fig. 191), the stopcock m open, and the stopcock n turned as seen in
Z ; the caoutchouc tube C, the tube T, the reservoir B, and the tube above
are filled with mercury as far as v ; closing then the stopcock w, and lower-
ing the reservoir A (fig. 192), the mercury sinks in the reservoir B, and in
the tube T, until the difference of levels in the two tubes is equal to the baro-
metric height, and there is a vacuum in the reservoir B. Turning now the
stopcock «, as shown in fig. X, the gas from the space to be exhausted passes
into the barometric chamber B by the tubes c and d, and the level again
sinks in the tube T. The stopcocks are now replaced in the first position
(fig. Z), and the reservoir A is again lifted, the excess of pressure of mercury
in the caoutchouc tube expels, through the stopcocks n and w, the gas which

-209]

Conciensing Pump.

189

had passed into the chamber B, and, if a few droplets of mercury are carried
along with them, they are collected in the vessel v. The process is repeated
until the mercury is virtually at the same level in both legs.

Like Sprengel's pump, this is very slow in its working, and, like it, is best
employed in completing the exhaustion of a space which has already been par-
tially rarefied ; for a vacuum of j- of a millimetre may be obtained by its means.

Fig. iQi.

Fig. 192.

209. Condensing- pump. — The condensing pump is an apparatus for
compressing air or any other gas. The form usually adopted is the follow-
ing : — In a cyHnder, A, of small diameter (fig. 194), there is a solid piston,
the rod of which is moved by the hand. The cylinder is provided with a
screw which fits into the receiver K. Fig. 193 shows the arrangement of
the valves, which are so constructed that the lateral valve o opens from the
outside, and the lower valve j- from the inside.

When the piston descends the valve 0 closes, and the elastic force of the

190

On Gases,

[209-

compressed air opens the valve s, which thus allows the compressed air to
pass into the receiver. When the piston ascends, s closes and o opens, and

permits the entrance of fresh air, which
in turn becomes compressed by the
descent of the piston, and so on. This
apparatus is chiefly used for charging
liquids with gases. For this purpose
the stopcock B is connected with a re-
servoir of the gas by means of the tube
D. The pump exhausts this gas, and
forces it into the vessel K, in which
the liquid is contained. The artificial
gaseous waters are made by means of
analogous apparatus.

The applications of condensed air are
both numerous and important. In a
certain sense condensed air plays the
part of a metal spring in which is stored
up a greater or less provision of work,
and which can then be utilised by ex-
panding the air at a given moment, and
at a given point in the most favourable
condition for its being applied. In some
cases the expansion is sudden and inter-
'^^ mittent, as in the air-gun, the pneumatic
post, or in air-brakes, and in some cases
\— slow, gradual, and continuous as in

boring machines.

One of the most important applica-

jer boring machines used in tunnelling through the

where steam power would be objectionable

Fig. 194.

tions is that to the lar

Alps and elsewhere. There,

owing to the steam produced, compressed air is of great service, for it not only

supplies the power, but it ventilates the underground spaces.

The principal parts of such machines, which were first employed on a
large scale in the Mont Cenis tunnel, are as follows : — A sheaf of borers or
iron rods with punches on the ends are mounted on a framework. Each of
these .borers is susceptible of three simultaneous motions, one backward and
forward producing repeated shocks against the rock ; a second analogous to
that of a gimlet ; while a third moves the whole framework backwards and
forwards.

This triple motion is effected by a machine like a steam engine, but
driven by compressed air ; the first motion by a piston, the action of which
is regulated by a slide valve (469) ; the other two motions are effected by
means of a separate machine. The air is under a pressure of five atmo-
spheres, the compression being effected by special machines worked by water
power. The air by which all this is effected on expanding serves to cool
and ventilate the mine.

The j)?teiimatic post is of great service in London and other large towns
in forwarding the actual written telegraphic messages from the several re-

-210]

Uses of the Air-pump.

191

ceiving stations to a central telegraph station. The messages are placed in
a carrier (fig. 195), which is a guttapercha cylinder 7 in. long by 2 in.
in diameter, closed at one end ; it is covered with felt, and there is a welt of
that material at one end ; the felt projects at the other, so that it can be
folded down, and held in position by an india-
rubber band, so as to keep the contents in
their place.

Such carriers move air-tight in carefully
turned leaden tubes polished internally and
protected by being incased in iron tubes. Fig. 195.

The propulsion is effected either by pressure

or by exhaustion ; and by suitable valves the tubes can be placed in con-
nection with compressed or rarefied air, so that the carriers may either be
shot in one direction by compressed air, or drawn in the other by rarefied air.
The compression and rarefaction are produced by means of powerful steam
engines to a pressure of about ten pounds, or a vacuum of eight pounds to the
inch. By this means a speed of nearly a mile in a minute may be obtained
in tubes not more than a mile in length.

Other applications of compressed air are in the small pumps used by
plumbers for testing and for clearing gas-pipes, in ventilating mines, in
supplying air to blast-furnaces, in the air-
brakes used in railway trains, and so forth.

210. Uses of the air-pump. — A great
many experiments with the air-pump have
been already described. Such are the mer-
curial rain (13), the fall of bodies in vacuo
(76), the bladder (153), the bursting of a
bladder (159), the Magdeburg hemispheres
(160), and the baroscope (195).

The fountain in vacuo (fig. 196) is an ex-'
periment made with the air-pump, and shows
the elastic force of the air. It consists of a
glass vessel. A, provided at the bottom with
a stopcock, and a tubulure which projects
into the interior. Having screwed this
apparatus to the air-pump, it is exhausted,
and, the stopcock being closed, it is placed
in a vessel of water, R. Opening then the
stopcock, the atmospheric pressure upon the
water in the vessel makes it jet through the
tubulure into the interior of the vessel, as
shown in the drawing.

Fig. 197 represents an experiment illus-
trating the effect of atmospheric pressure on
the human body. A glass vessel, open at
both ends, being placed on the plate of the machine, the upper end of the
cylinder is closed by the hand, and a vacuum is made. The hand then
becomes pressed by the weight of the atmosphere, and can only be taken
away by a great effort. And as the elasticity of the fluids contained in the

192

On Gases. [210-

organs is not counterbalanced by the weight
of the atmosphere, the pahn of the hand
swells, and blood tends to escape from the
pores.

By means of the air-pump it may be
shown that air, by reason of the oxygen it
contains, is necessary for the support of
combustion and of life. For if we place a
lighted taper under the receiver, and begin
to exhaust the air, the flame becomes weaker
as rarefaction proceeds and is finally extin-
guished. Similarly an animal faints and dies
if a vacuum is formed in a receiver under
which it is placed. Mammalia and birds
soon die in vacuo. Fish and reptiles sup-
port the loss of air for a much longer time.
Insects can live several days in vacuo.

Substances liable to ferment may be
kept in vacuo for a long time without
alteration, as they are not in contact with oxygen, which is necessary for
fermentation. Food kept in airtight cases, from which the air had been ex-
hausted, has been found as fresh after years
as on the first day.

211. Hero's fountain. — Hero's fountain,
which derives its name from its inventor,
Hero, who lived at Alexandria, 120 B.C.,
depends on the elasticity of the air. It
consists of a brass dish, D (fig. 198), and of
two glass globes, M and N. The dish com-
municates with the lower part of the globe N
by a long tube, B ; and another tube. A,
connects the two globes. A third tube
passes through the dish D to the lower part
of the globe M. This tube having been
taken out, the globe M is partially filled with
water, the tube is then replaced and water
is poured into the dish. The water flows
through the tube B hito the lower globe,
and expels the air, which is forced into the
upper globe ; the air, thus compressed, acts
upon the water, and makes it jet out as re-
presented in the figure. If it were not for
the resistance of the atmosphere and friction,
the liquid would rise to a height above the
water in the dish equal to the difference of
the level in the two globes.

212. Intermittent fountain. — The in-
termittent fountain depends partly on the
elastic force of the air, and partly on the

-213]

TJie SipJion.

193

atmospheric pressure. It consists of a stoppered glass globe (C, fig. 190),
provided with two or three capillary tubulures, D. A glass tube open at
both ends reaches at one end to the
upper part of the globe C ; the other end
terminates just above a little aperture in
the dish B which supports the whole ap-
paratus.

The water with which the globe C is
nearly two-thirds filled runs out, by the
tubes D, as shown in the figure, the in-
ternal pressure at D being equal to the
atmospheric pressure together with the
weight of the column of water CD, while
the external pressure at that point is only
that of the atmosphere. These condi-
tions prevail so long as the lower end of
the glass tube is open ; that is, so long as
air can enter C and keep the air in C at
the same density as the external air ; but
the apparatus is arranged so that the
orifice in the dish B does not allow so
much water to flow out as it receives from
the tubes D, in consequence of which
the level gradually rises in the dish, and
closes the lower end of the glass tube.
As the external air cannot now enter the
globe C, the air becomes rarefied in pro-
portion as the flow continues, until the
pressure of the column of water CD, togethei with that of the air contained
in the globe, is equal to this external pressure at D ; the flow consequently
stops. But as water continues to flow
out of the dish B, the tubes D become
open again, air enters, and the flow recom-
mences, and so on, as long as there is
water in the globe C.

213. The siphon. — The siphon is
a bent tube open at both ends, and
with unequal legs (fig. 200). It is used
in transferring liquids in the following
manner : — The siphon is filled with some
Hquid, and, the two ends being closed,
the shorter leg is dipped in the liquid,
as represented in fig. 200 ; or, the
shorter leg having been dipped in the ■
liquid, the air is exhausted by applying
the mouth at B. A vacuum is thus pro-
duced, the liquid in C rises and fills the ^'^- ^°°-
tube in consequence of the atmospheric pressure. It will then run out
through the siphon as long as the shorter end dips in the liquid.

194 On Gases. \ [213-

To explain this flow of water from the siphon, let us suppose it filled and
the short leg immersed in the liquid. The pressure then acting on C, and
tending to raise the liquid in the tube, is the atmospheric pressure minus
the height of the column of liquid DC. In like manner, the pressure on
the end of the tube B is the weight of the atmosphere less the pressure of
the column of liquid AB. But as this latter column is longer than CD, the
force acting at B is less than the force acting at C, and consequently a flow
takes place proportional to the difference between these two forces. The
flow will therefore be more rapid in proportion as the difference of level
between the aperture B and the surface of the liquid in C is greater.

It follows from the theory of the siphon that it would not work in vacuo,
nor if the height CD were greater than that of a column of liquid which
counterbalances the atmospheric pressure.

214. The intermittent sipbon. — In the interinitte)it siphon the flow is
not continuous. It is arranged in a vessel, so that the shorter leg is near the

bottom of the vessel, while the longer leg passes

through it (fig. 201). Being fed by a constant

supply of water, the level gradually rises both

in the vessel and in the tube to the top of the

siphon, which it fills, and water begins to flow

out. But the apparatus is arranged so that the

flow of the siphon is more rapid than that of the

tube which supplies the vessel, and consequently

the level sinks in the vessel until the shorter

branch no longer dips in the liquid ; the siphon

"^ . is then empty, and the flow ceases. But as the

'^' "°^" vessel is continually fed from the same source

the level again rises, and the same series of phenomena is reproduced.

The theory of the intermittent siphon explains the natural intermittent
springs which are found in many countries, and of which there is an excel-
lent example near Giggleswick in Yorkshire. Many of these springs fur-
nish water for several days or months, and then, after stopping for a certain
interval, again recommence. In others the flow stops and recommences
several times in an hour.

These phenomena are explained by assuming that there are subterranean
fountains, which are more or less slowly filled by springs, and which are then
emptied by fissures so occurring in the ground as to form an intermittent
siphon.

215. Different kinds of pumps. — Pumps are machines which serve to
raise water either by suction, by pressure, or by both efforts combined ; they
are consequently divided into sitctiofi or lift pumps^fo?-cc piu)ips, and suction
and forcing pumps.

The various parts entering into the construction of a pump are the barrel,
the piston, the valves, and the pipes. The barrel is a cylinder of metal or
of wood, in which is the pisto?i. The latter is a metal or wooden cylinder
wrapped with tow, and working with gentle friction the whole length of the
barrel.

The valves are discs of metal or leather, which alternately close the
apertures which connect the barrel with the pipes. The most usual valves

-216]

Suction-piiDip.

195

_■

are the clack valve (fig. 202) and the conical valve (fig. 203). The former is
a metal disc fixed to a hinge on the edge of the orifice to be closed. In order
more effectually to close it, the lower part of the disc is covered with thick
leather. Sometimes the valve
consists merely of a leather '^i||||l||!|f'll''
disc, of larger diameter than
the orifice, nailed on the
edge of the orifice. Its flexi-
bility enables it to act as a

The conical valve con-
sists of a metal cone fitting in an aperture of the same shape. Below this
is an iron hoop, through which passes a bolt-head fixed to the valve. The
object of this is to limit the play of the valve when it is raised by the water,
and to prevent its removal.

216. Suction-pump. — Fig. 204 represents a model of a suction-pump
such as is used in lectures, but which has essentially the same arrangement
as the pumps in common use. It con-
sists, 1st, of a. glass cylinder B, at the
bottom of which there is a valve S
opening upwards ; 2nd, of a suctiott-
tiibe A, which dips into the reservoir
from which water is to be raised ; 3rd,
of a piston, which is moved up and
down by a rod worked by a handle
P. The piston is perforated by a hole ;
the upper aperture is closed by a
\alve O, opening upwards.

When the piston rises from the
bottom of the cylinder B, a vacuum is
produced below, and the valve O is
kept closed by the atmospheric pres-
sure, while the air in the pipe A, in
consequence of its elasticity, raises the
valve S, and partially passes into the
cylinder. The air being thus rarefied,
water rises in the pipe until the pres-
sure of the liquid column, together
with the pressure of the rarefied air
which remains in the tube, counter-
balances the pressure of the atmo-
sphere on the water of the reservoir.

When the piston descends, the
valve S closes by its own weight, and
prevents the return of the air from the
cylinder into the tube A. The air compressed by the piston opens the valve
O, and escapes into the atmosphere by the pipe C. With a second stroke
of the piston the same series of phenomena is produced, and after a few-
strokes the water reaches the cylinder. The effect is now somewhat modi-

o 2

Fig. 204.

196

071 Gases.

[216-

fied ; during the descent of the piston the valve S closes, and the water
raises the valve O, and passes above the piston by which it is lifted into
the upper reservoir D. There is now no more air in the pump, and the
water forced by the atmospheric pressure rises with the piston, provided
that, when it is at the summit of its course, it is not more than 34 feet above
the level of the water in which the tube A dips, for we have seen (163) that
a column of water of this height is equal to the pressure of the atmosphere.

In practice the height of the tube A does not exceed 26 to 28 feet, for
although the atmospheric pressure can supJDort a higher column, the vacuum
produced in the barrel is not perfect, owing to the fact that the piston does
not fit exactly on the bottom of the barrel. But when the water has passed the
piston, it is the ascending force of the latter which raises it, and the height
to which it can be brought depends on the power which works the piston.

217. Suction and force pump. — The action of this pump, a model of
which is represented in fig. 205, depends both on exhaustion and on pres-
sure. At the base of the barrel, where it is connected with the tube A, there
is a valve S, which opens upwards. Another valve O, opening in the same
direction, closes the aperture of a conduit, which passes from a hole <?, near
the valve S, into a vessel M, which is called the air-chamber. From this

chamber there is another
tube D, up which the
water is forced.

At each ascent of the
piston B, which is solid,
the water rises through
the tube A into the barrel.
When the piston sinks,
the valve S closes, and
the water is forced through
the valve O into the reser-
voir M, and thence into
the tube D. The height
to which it can be raised
in this tube depends
solely on the motive force
which works the pump.

If the tube D were a
prolongation of the tube
]ao, the flow would be in-
termittent ; it would take
place when the piston de-
scended, and would cease
as soon as it ascended.
But between these tubes
there is an interval,
which, by means of the
air in the reservoir M,
ensures a continuous flow. The water forced into the reservoir M divides
into two parts, one of which, rising in D, presses on the water in the reser-

-219] Fire-engine. 1 97

voir by its weight ; while the other, in virtue of this pressure, rises in the
reservoir above the lower orifice of the tube D, compressing the air above.
Consequently, when the piston ascends, and no longer forces the water into
M, the air of the reservoir, by the pressure it has received, reacts on the
liquid, and raises it in the tube D, until the piston again descends, so that
the jet is continuous.

218. Xioad which the piston supports. — In the suction-pump, when
once the water fills the pipe, and the barrel, as far as the spout, the effort
necessary to raise the piston is equal to the weight of a column of water,
the base of which is this piston, a7id the height the vertical distance oti the
spout from the level of the water i?i the reservoir ; that is, the height to
which the water is raised. For if H is the atmospheric pressure, h the
height of the water above the piston, and fi' the height of the column
which fills the suction-tube A (fig. 205), and the lower part of the barrel, the
pressure above the piston is obviously H + //, and that below is H-/;', since
the weight of the column h' tends to counterbalance the atmospheric pressure.
But as the pressure H - h' tends to raise the piston, the effective resistance
is equal to the excess of H -1- >% over H -h', that is to say, to // + h'.

In the suction and force pump it is readily seen that the pressure which
the piston supports is also equal to the weight of a column of water the base
of which is the section of the piston, and the height that to which the water
is raised.

Fig. 206.

219. Fire-engrine. — Thefre-engine is a force-pump in which a steady jet
is obtained by the aid of an air-chamber, and also by two pumps working
alternately (fig. 206). The two pumps fn and n, worked by the same lever
PQ, are immersed in a tank, which is kept filled with water as long as the

198 On Gases. [219-

pump works. P'rom the arrangement of the valves it will be seen that when
one pump, «, draws water from the tank, the other, in, forces it into the air-
chamber R ; whence, by an orifice Z, it passes into the delivery tube, by
which it can be sent in any direction.

Without the air-chamber the jet would be mtermittent. But as the velo-
city of the water on entering the reservoir is less than on emerging, the level
of the water rises above the orifice Z, compressing the air which fills the
reservoir. Hence, whenever the piston stops, the air thus compressed, re-
acting on the liquid, forces it out during its momentary stoppage, and thus
keeps up a constant flow.

-222] 199

BOOK V.

ON SOUND.

CHAPTER I.

PRODUCTION, PROPAGATION, AND REFLECTION OF SOUND.

220. Province of acoustics. — The study of sounds, and that of the
vibrations of elastic bodies, form the province of the science of sounds^ or
acoustics.

Music considers sounds with reference to the pleasurable feeling they are
calculated to excite. Acoustics is concerned with the questions of the pro-
duction, transmission, and comparison of sounds ; to which may be added
the physiological question of the perception of sounds.

221. Sound and noise. — Sound is the peculiar sensation excited in the
organ of hearing by the vibratory motion of bodies, when this motion is
transmitted to the ear through an elastic medium.

Sounds are distinguished from noises. Sound properly so called, or
musical soujid, is that which produces a continuous sensation, and the
musical value of which can be estimated ; while noise is either a sound
of too short a duration to be determined, like the report of a cannon ; or
else it is a confused mixture of many discordant sounds, like the rolling
of thunder or the noise of the waves. Nevertheless the difference between
sound and noise is by no means precise ; Savart showed that there are
relations of height in the case of noise, as well as in that of sound ; and
there are said to be certain ears sufficiently well organised to determine
the musical value of the sound produced by a carriage rolling on the
pavement.

222. Cause of sound. — Sound is always the result of rapid oscillations
imparted to the molecules of elastic bodies, when the state of equilibrium of
these bodies has been disturbed either by a shock or by friction. Such bodies
tend to regain their first position of equilibrium, but only reach it after per-
forming, on each side of that position, very rapid vibratory movements, the
amplitude of which quickly decreases. A body which produces a sound is
called a sonorous or sounding body.

As understood in England and Germany, a vibration comprises a motion
to and fro ; in France, on the contrary, a vibration means a movement to or

200

On Sound.

[222-

Fig. 207.

fro. The French vibrations are with us semi-vibrations, an oscillation or
vibration is the movement of the vibrating molecule in only one direction ;
a double or complete vibration comprises the oscillation both backwards and
forwards. Vibrations of sounding bodies are very readily observed. If a
light powder is sprinkled on a body which is in the act of yielding a musical

sound, a rapid motion is imparted
to the powder, which renders visible
the vibrations of the body ; and, in
the same manner, if a stretched
cord be smartly pulled and let go,
its vibrations are apparent to the
eye.

A bell-jar is held horizontally
in one hand (fig. 207), and made
to vibrate by being' struck with the
other ; if then a piece ot metal is placed in it, it is rapidly raised by the
vibrations of the side ; touching the bell-jar with the hand, the sound ceases,
and with it the motion of the metal.

223. Sounds not propag-ated in v acuo. — The vibrations of elastic bodies
can only produce the sensation of sound in us by the intervention of a
medium mterposed between the ear and the
sonorous body and vibrating with it. This
medium is usually the air ; but all gases,
vapours, liquids, and sohds also transmit
sounds.

The following experiment shows that the
presence of a ponderable medium is neces-
sary for the propagation of sound. A small
metal bell, which is continually struck by a
small hammer by means of clockwork, or
else an ordinaiy musical box, is placed under
the receiver of an air-pump (fig. 208). As
long as the receiver is full of air at the ordi-
nary pressure the sound is transmitted, but
in proportion as the air is exhausted the
sound becomes feebler, and cannot be heard
in a vacuum.

To ensure the success of the experiment,
the bellwork or the musical box must be
placed on wadding ; for otherwise the vibra-
tions would be transmitted to the air through
the plate of the pump.
224. Sound is propag-ated in all elastic bodies. — If, in the above
experiment, any vapour or gas be admitted after the vacuum has been made,
the sound of the bell will be heard, showing that sound is propagated in this
medium as in air.

Sound is also propagated in liquids. When two stones are struck against
each other under water, the shock is distinctly heard ; and a diver at the
bottom of the water can hear the sound of voices on the bank. The sound

Fig. 208.

-225j Propagation of Sound in Air. 201

is, however, enfeebled, as a considerable portion is reflected at the boundary
of the two media.

The conductibility of solids is such that the faint scratching of a pen or
the ticking of a watch at one end of a long horizontal wooden rod is heard
much more distinctly when the ear is directly applied against the other end
of the rod, than when it is at the same distance in the air. Sound may even
reach the ear through solids alone without passing through the air, for if the
ears be closed, and the rod be put between the teeth, the ticking is distinctly
heard. The earth conducts sound so well that at night, when the ear is
applied to the ground, the stepping of horses, or any other noise at a great
distance, is heard.

225. Propagation of sound in air. — In order to simplify the theory of
the propagation of sound in air, we shall first consider the case in which it
is propagated in a cylindrical tube of indefinite length. Let MN, fig. 209,
be a tube filled with air at a constant pressure and temperature, and let P
be a piston oscillating rapidly from A to a. When the piston passes from
A to « it compresses the air in the tube. But in consequence of the great

Fig. 205.

compressibility, the condensation of the air does not take place at once
throughout the whole length of the tube, but solely within a certain length,
rtH, which is called the co7idensed wave.

If the tube MN be supposed to be divided into lengths ecjual to aW, and
each of these lengths divided into layers parallel to the piston, it may be
shown by calculation that, when the first layer of the wave aYi comes to rest,
the motion is communicated to the first layer of the second wave HH', and
so on from layer to layer in all parts of H'H", WW". The condensed wave
advances in the tube, each of its parts having successively the same degree
of velocity and condensation.

When the piston returns in the direction aA, a vacuum is produced
behind it, which causes an expansion of the air in contact with its posterior
face. The next layer expanding in turn brings the first to its original state
of condensation, and so on from layer to layer. Thus when the piston has
returned to A, an expanded wave is produced of the same length as the con-
densed wave, and directly following it in the tube where they are propagated
together, the corresponding layers of the two waves possessing equal and
contrary velocities.

The whole of a condensed and expanded wave forms an undulation;
that is, an undulation comprehends that part of the column of air affected
during the backward and forward motion of the piston. The length of an
U7idulation is the space which sound traverses during a complete \ibration
of the body which produces it. This length is less in proportion as the
vibrations are more rapid.

202 On Sound. [225-

It is important to remark that if we consider a single row of particles,
which when at rest occupy a line parallel to the axis of the cylinder, for
instance, those along AH'^ (fig. 209), we shall find they will have respectively
at the same instant all the various velocities which the piston has had suc-
cessively while oscillating from A to a and back to A. So that if in fig. 38
AH' represents the length of one undulation, the curved line H'PQA will
represent the various velocities which all the points in the line AH' have
sinmltancously : for instance, at the instant the piston has returned to A,
the particle at M will be moving to the right with a velocity represented by
QM, the particle at N will be moving to the left with a velocity represented
by PN, and so on of the other particles.

When an undulatory motion is transmitted through a medium, the
motions of any two particles are said to be in the smne phase when those
particles move with equal velocities in the same direction ; the motions are
said to be in opposite phases \i\i'exv the particles move with the same velocities
in opposite directions. It is plain from an inspection of fig. 38 that when
any two particles are separated by a distance equal to half an undulation,
their motions are always in opposite phases, but if their distance equals the
length of a complete undulation their motions are in the same phase. A
little consideration will show that in the condensed wave the condensation
will be gi^eatest at the middle of the wave, and likewise that the expanded
wave will be most rarefied at its middle.

It is an easy transition from the explanation of the motion of sound-
waves in a cylinder to that of their motion in an unenclosed medium. It is
simply necessary to apply in all directions, to each molecule of the vibrating
body, what has been said about a piston movable in a tube. A series of
spherical waves alternately condensed and rarefied is produced around each
centre of disturbance. As these waves are contained within two concentrical
spherical surfaces, whose radii gradually increase, while the length of the
undulation remains the same, their mass increases with the distance from
the centre of disturbance, so that the amplitude of the vibration of the mole-
cules gradually lessens, and the intensity of the sound diminishes.

It is these spherical waves, alternately condensed and expanded, which
in being propagated transmit sound. If many points are disturbed at the
same time, a system of waves is produced around each point. But all these
waves are transmitted one through the other without modifying either
their lengths or their velocities. Sometimes condensed or expanded waves
coincide with others of the same nature to produce an effect equal to their
sum ; sometimes they meet and produce an effect equal to their difference.
If the surface of still water is disturbed at two or more points, the co-exist-
ence of waves becomes sensible to the eye.

226. Causes which influence the intensity of sound. — Many causes
modify the force or the intensity of sound. These are the distance of the
sounding body, the amplitude of the vibrations, the density of the air at the
place where the sound is produced, the direction of the currents of air, and,
lastly, the neighbourhood of other sounding bodies.

i. The i/iteftsity of souftd is inversely as the square of the distance of the
sonorous body from the ear. This law has been deduced by calculation, but
it may be also demonstrated experimentally. Let us suppose several sounds

-227J Apparatus to Strengthen Sound. 203

of equal intensity — for instance, bells of the same kind, struck by hammers
of the same weight, falling from equal heights. If four of these bells are
placed at a distance of 20 yards from the ear, and one at a distance of 10
yards, it is found that the single bell produces a sound of the same intensity
as the four bells struck simultaneously. Consequently, for double the dis-
tance the intensity of the sound is only one-fourth. A method of com-
paring the intensities of different sounds will be described afterwards (289).
The distance at which sounds can be heard depends on their intensity.
The report of a volcano at St. Vincent was heard at Demerara, 300 miles
off, and the firing at Waterloo was heard at Dover.

ii. The intenstiy of the soundiiicreases with the amplitude of the vibrations
of the so?toroiis body. The connection between the intensity of the sound
and the amplitude of the vibrations is readily observed by means of vibrating
cords. For, if the cords are somewhat long, the oscillations are perceptible
to the eye, and it is seen that the sound is feebler in proportion as the am-
plitude of the oscillations decreases.

iii. The i?itensity of sound depe7tds on the density of the air in the place in
which it is produced. As we have already seen (222), when an alarum moved
by clockwork is placed under the bell-jar of an air-pump, the sound becomes
weaker in proportion as the air is rarefied.

In hydrogen, which is about ^i ^^ density of air, sounds are much
feebler, although the pressure is the same. In carbonic acid, on the con-
trary, whose density is i"529, sounds are more intense. On high mountams,
where the air is much rarefied, it is necessary to speak with some effort in
order to be heard, and the discharge of a gun produces only a feeble sound.
The ticking of a watch is heard in water at a distance of 23 feet, in oil of 16^,
in alcohol of 13, and in air of only 10 feet.

iv. The inte/tsity of sound is modified by the motion of the atmosphere
and the directio/t of the wind. In calm weather sound is always better
propagated than when there is wind ; in the latter case, for an equal distance,
sound is more intense in the direction of the wind than in the contrary
direction.

V. Lastly, sound is strengthened by the neighbourhood of a sonorous body.
A string made to vibrate in free air has but a very feeble sound ; but when it
vibrates above a sounding-box, as in the case of the violin, guitar, or violon-
cello, its sound is much stronger. This arises from the fact that the box and
the air which it contains vibrate in unison with the string. Hence the use of
sounding-boxes in stringed instruments.

Attempts have been made to get a measure of the loudness of sound
which should serve as a standard, by allowing leaden pellets to fall from
various heights on an iron plate of some size. It appears that within
certain limits the loudness is nearly proportional to the square root of the
height from which the pellet falls, and not to the height itself. It thus
appears that only a portion of the energy of the falling body is expended in
producing vibrations of the plate.

227. Apparatus to strengthen sound. — The apparatus represented in
fig. 210 was used by Savart to show the influence of boxes in strengthening
sound. It consists of a hemispherical brass vessel, A, which is set in vibra-
tion by means of a violin bow. Near it there is a hollow cardboard cylinder

204

On Sound.

[227-

B, closed at the further end. By means of a handle this cylinder can be turned
on its support, so as to be inclined at any given degree towards the vessel.
The cylinder is fixed on a slide C, by which means it can be placed at any
distance from A. When the vessel is made to vibrate, the strengthening of
the sound is very remarkable. But the sound loses almost all its intensity if

the cylinder is turned
away, and it becomes
gradually weaker when
the cylinder is removed to
a greater distance, show-
ing that the strengthen-
ing is due to the vi-
bration of the air in the
cylinder.

The cylinder B is
made to vibrate in unison
with the bi^ass vessel by
adjusting it to a certain
depth, which is effected
by making one part slide
into the other.

Vitruvius states that,
in the theatres of the
ancients, resonant brass
^'S- 210- vessels were placed to

strengthen the \-oices of the actors.

228. Influence of tubes on the transmission of sound. — The law
that the intensity of sound decreases in proportion to the square of the
distance does not apply to the case of tubes, especially if they are straight
and cylindrical. The sound-waves in that case are not propagated in the
form of increasing concentrical spheres, and sound can be transmitted to a
great distance without any perceptible alteration. Biot found that in one
of the Paris water-pipes, 1,040 yards long, the voice lost so little of its inten-
sity that a conversation could be kept up at the ends of a tube in a very low
tone. The weakening of sound becomes, however, perceptible in tubes of
large diameter, or where the sides are rough. This property of transmitting •
sounds was first used in England for speaking tubes. They consist of caout-
chouc or metal tubes of small diameter passing from one room to another.
If a person speaks at one end of the tube, he is distinctly heard by a person
with his ear at the other end.

From Biot's experiments it is evident that a communication might be
made between two towns by means of speaking tubes. The velocity of
sound is 1,125 feet in a second at i6°-6 C, so that a distance of 50 miles
would be traversed in four minutes.

229. Reg-nault's experiments.— Theoretically, a sound-wave should be
propagated in a straight cylindrical tube with a constant intensity. Regnault
found, however, that in these circumstances the intensity of sound gradually
diminishes with the distance, and that the distance at which it ceases to be
audible is nearly proportional to the diameter of the tube.

-230] Velocity of Sound in Air. 205

He produced sound-waves of equal strength by means of a small pistol
charged with a gramme of powder, and fired at the open ends of tubes of
various diameters ; and he then ascertained the distance at which the sound
could no longer be heard, or at which it ceased to act on what he calls a
sensitive membrane. This was a very flexible membrane which could be
fixed across the tube at various distances, and was provided with a small
metal disc in its centre. When the membrane began to vibrate, this disc
struck against a metallic contact, and thereby closed a voltaic circuit, which
traced on a chronograph the exact moment at which the membrane received
the sound-wave.

Experimenting in this manner, Regnault found that the report of a pistol
charged as stated is no longer audible at a distance of

1,159 metres in a tube of o™- 108 diameter

3,810 „ ,, o'"-3oo „

9,540 ,, „ ..... i™-ioo „

These numbers represent the limit of distance at which the sound-wave
is no longer heard, but it still acts on the membrane at the distances of
4,156, 11,430, and 19,851 metres respectively.

According to Regnault the principal cause of this diminution of intensity
is the loss of 7//^ 7/zV(^ against the sides of the tube: he found also that sounds
of high pitch are propagated in tubes less easily than those of low ones; a
bass would be heard at a greater distance than a treble voice.

230. Velocity of sound In air. — Since the propagation of sound-waves
is gradual, sound requires a certain time for its transmission from one place
to another, as is seen in numerous phenomena. For example, the sound
of thunder is only heard some time after the flash of lightning has been seen,
although both the sound and the light are produced simultaneously; and in like
manner we see a mason in the act of striking a stone before hearing the sound.

The velocity of sound in air has often been the subject of experimental
determination. The most accurate of the direct measurements was made
by Moll and Van Beck in 1823. Two hills, near Amsterdam, Kooltjesberg
and Zevenboomen, were chosen as stations : their distance from each other
as determined trigonometrically was 57,971 feet, or nearly eleven miles.
Cannons were fired at stated intervals simultaneously at each station, and the
time which elapsed between seeing the flash and hearing the sound was
noted by chronometers. This time could be taken as that which the sound
required to travel between the two stations; for it will be subsequently seen
that light takes an inappreciable time to traverse the above distance. In-
troducing corrections for the barometric pressure, temperature, and hygro-
metric state, and eliminating the influence of the wind, Moll and Van Beck's
results as recalculated by Schroder van der Kolk give 1,09278 feet as the
velocity of sound in one second in dry air at 0° C. and under a pressure of
760 mm. Kendall, in a North Pole expedition, found that the velocity of
sound at a temperature of -40° was 314 metres.

The velocity of sound at zero may be taken at 1,093 feet, or 2>'i'}) metres.
This velocity increases with the increase of temperature; it may be calcu-
lated for a temperature t° from the formula

7/= 1,093 v' (i + 0-003665/)

2o6 On Sound. [230-

where 1,093 is the velocity in feet at 0° C, and 0-003665 the coefficient of ex-
pansion for 1° C. This amounts to an increase of nearly two feet for every
degree Centigrade. For the same temperature it is independent of the density
of the air, and consequently of the pressure. It is the same for the same
temperature with all sounds, whether they be strong or weak, deep or acute.
Biot found, in his experiments on the conductivity of sound in tubes, that
when a well-known air was played on a flute at one end of a tube 1,040 yards
long, it was heard without alteration at the other end, from which he con-
cluded that the velocity of cHfFerent sounds is the same. For the same
reason the tune played by a band is heard at a great distance without altera-
tion, except in intensity, which could not be the case if some sounds travelled
more rapidly than others.

This cannot, however, be admitted as universally true. Earnshaw, by a
mathematical investigation of the laws of the propagation of sound, concludes
that the velocity of a sound depends on its strength ; and, accordingly, that
a violent sound ought to be propagated with greater velocity than a gentler
one. This conclusion is confirmed by an observation made by Captain
Parry on his Arctic expedition. During artillery practice it was found, by
persons stationed at a considerable distance from the guns, that the report
of the cannon was heard before the command to fire given by the officer. And
more recently, Mallet made a series of experiments on the velocity with which
sound is propagated in rocks, by observing the times which elapsed before
blastings, made at Holyhead, were heard at a distance. He found that the
larger the charge of gunpowder, and therefore the louder the report, the more
rapid was the transmission. With a charge of 2,000 pounds of gunpowder
the velocity was 967 feet in a second, while with a charge of 12,000 it was
1,210 feet in the same time.

Jacques made a series of experiments by firing different weights of pow-
der from a cannon, and observing the velocity of the report at different
distances from the gun by means of an electrical arrangement. He thus
found that, nearest the gun, the velocity is least, increasing to a certain
maximum which is considerably greater than the average velocity. The
velocity is also greater with the heavier charge. Thus with a charge of
\\ pound the velocity was 1,187, and with a charge of ^ pound it was 1,032
at a distance of from 30 to 50 feet ; while at a distance of 70 to 80 it was 1,267
and 1,120 ; and at 90 to 100 feet it was 1,262 and 1,1 14 respectively.

Bravais and Martins found, in 1844, that sound travelled with the same
velocity from the base to the summit of the Faulhorn, as from the summit to
the base.

231. Calculation of the velocity of sound in grases. — From theoretical
considerations Newton gave a rule for calculating the velocity of sound in
gases, which may be represented by the formula

in which v represents the velocity of the sound, or the distance it travels in
a second, e the elasticity of the gas, and rt'its density.

This formula expresses that the velocity of the propagation of sound in
gases is directly as the square root of the elasticity of the gas, and inversely

-231] Calculation of the Velocity of Sound in Gases. 207

as the square root of its density. It follows that the velocity of sound is the
same under any pressure ; for although the elasticity increases with increased
pressure, according to Boyle's law, the density increases in the same ratio.
At Quito, where the mean pressure is only 2r8 inches, the velocity is the
same as at the sea-level, provided the temperature is the same.

Now the measure of the elasticity of a gas is the pressure to which it is
subjected ; hence, if g be the force of gravity, h the barometric height
reduced to the temperature zero, and 8 the density of mercury, also at zero,
then for a gas under the standard atmospheric pressure and for zero, e =ghh :
Newton's formula accordingly becomes

^-f""

Now, if we suppose the temperature of a gas to increase from 0° to /°, its.
volume will increase from unity, at zero, to \ + at at /, a being the coefficient
of expansion of the gas. But the density varies inversely as the volume,
therefore d becomes d-^{\ + at). Hence

Substituting in this formula the values in centimetres and grammes,
^ = 981, A = 76, ^=0-001293, we get for the value v a number 29,795 centi-
metres =297-95 metres, which is about one-sixth less than the experimental
result. Laplace assigned as a reason for this discrepancy the heat produced
by pressure in the condensed waves ; and, by considerations based on this
idea, Poisson and Biot found that Newton's formula ought to be written,

V = f^jSl-ii^at)-/, <: being the specific heat of the gas for a constant
pressure, and c' its specific heat for a constant volume (460). The average
value of the constant - is 1-41, and if the formula be modified by the intro-
duction of the value ^i-i\\ or 1-1875 the calculated numbers agree with the
experimental results.

The physical reason for introducing the constant x/- into the ecpation

for the velocity of sound may be understood from the following considera-
tions : — We have already seen (225) that sound is propagated in air by a
series of alternate condensations and rarefactions of the layers. At each
condensation heat is evolved, and this heat increases the elasticity, and thus
the rapidity with which each condensed layer acts on the next ; but in the
rarefaction of each layer the same amount of heat disappears as was deve-
loped by the condensation, and its elasticity is diminished by the cooling.
The effect of this diminished elasticity of the cooled layer is the same as if
the elasticity of an adjacent wave had been increased, and the rapidity with
which this latter would expand upon the dilated wave would be greater.
Thus, while the average temperature of the air is unaltered, both the heating
which increases the elasticity, and the chilling which diminishes it, concur
in increasing the velocity.

Knowing the velocity of sound, we can calculate approximately the dis-
tance at which it is produced. Light travels with such velocity that the

2o8 On Sound. [231-

rtash or the smoke accompanying the report of a gun may be considered to
be seen simultaneously with the occurrence of the explosion. Counting
then the number of seconds which elapse between seeing the flash and
hearing the sound, and multiplying this number by 1,125, we get the distance
in feet at which the gun is discharged. In the same way the distance of
thunder may be estimated.

232. Velocity of sound in various gases.— Approximately the same
results have been ol-»tainetl for the \elocity of sound in air by another method,
by wliich the velocity in other gases could be determined. As the wave-
length A is the distance which sound travels during the time of one oscillation,

that is, - of a second, the velocity of sound or the distance traversed in a

n
second is v = /iK. Now the length of an open pipe is half the wave-length
of the fundamental note of that pipe ; and that of a closed pipe is a quarter
of the wave-length (275). Hence, if we know the number of vibrations of
the note emitted by any particular pipe, which can be easily ascertained by
means of a sirene, and we know the length of this pipe, -we can calculate v.
Taking the temperature into account, Wertheim found in this way 1,086 feet
for the velocity of sound in air at zero.

Further, since in different gases which have the same elasticity, but differ
in density, the velocity of sound varies inversely as the square root of the
density, knowing the velocity of sound in air, we may calculate it for other
gases; thus in hydrogen it will be

/'°^A^Q =4168 feet.
\/o-o6S8

This number cannot be universally accurate, for the coefficient , differs

somewhat in different gases. And when pipes were sounded with different
gases, and the number of vibrations of the notes multiplied with twice the
length of the pipe, numbers were obtained which differed from those cal-
culated by the above formula. \Mien, however, the calculation was made

introducing for each gas its special value of ,, the theoretical results agreed

very well with the observed ones.

By the above method the following values hax^e been obtained : —

Chlorine 677 feet in a second.

Carbonic acid 856 „

Oxygen 1040 „

Air 1093 „

Carbonic oxide ...... 1106 ,,

Hydrogen 4163 „

Zjj- Boppler's principle. — When a sounding body approaches the car,
the tone percei^■ed is somewhat higher than the true one ; but if the source
of sound recedes from the ear, the tone perceived is lower. The truth of
this, which is known as Doppler's principle^ will be apparent from the follow-
ing considerations : — When the source of sound and the ear are at rest, the
ear receives n waves in a second; but if the ear approaches the sound, or
the sound approaches the ear, it receives more; just as a ship meets more

-234] Velocity of Sound in Liquids. 209

waves when it ploughs through them than if it is at rest. Conversely, the ear
receives a smaller number when it recedes from the source of sound. The
effect in the first case is as if the sounding body emitted more vibrations in
a second than it really does, and in the second case fewer. Hence in the
first case the note appears higher ; in the second case lower.

If the distance which the ear traverses in a second towards the source of
sound (supposed to be stationary) is s feet, and the wave-length of the par-
ticular tone is X feet, then there are - waves in a second : or also — , for

A c

\ = ^, where c is the velocity of sound (230). Hence the ear receives not
n

only the ;/ original waves, but also — in addition. Therefore the number

of vibrations which the ear actually receives is

, ns , S-.

?i' = n + - ~ = ?t {i + )

for an ear which approaches a tone ; and by similar reasoning it is

n = n - = « ( I )

for an ear receding from a tone.

To test Dopplei^s theory Buys Ballot stationed trumpeters on the Utrecht
railways and also upon locomotives, and had the height of the approaching-
or receding tones compared with stationaiy ones by musicians. He thus
found both the principle and the formula fully confirmed. Similar conclu-
sive experiments were made by Scott Russell on English railways. The
observation may often be made as a fast train passes a station in which
an electrical alarum is sounding. Independently of the difference in loud-
ness, an attentive ear can detect a difference in pitch on approaching, or on
leaving the station. A speed of about 40 miles an hour sharpens the note
of the whistle of an approaching train by a semitone, and tlattens it to that
extent as the train recedes.

Dopplefs principle may also be established by direct laboratory ex-
periments. Rollmann fixed a long rod on a turning machine, at the end
of which was a large glass bulb with a slit in it, which sounded like a
humming-top when a tangential current of air was blown against the slit.
The uniform and sufficiently rapid rotation of the sphere developed such
a current, and produced a steady note, the pitch of which was higher or
lower in each rotation according as the bulb came nearer, or receded from,
the observer.

The principle may also be illustrated by means of a tuning-fork with wide
branches, and producing a very high note of 2046 vibrations. When this is
loudly sounded, and, being held in front of a smooth wall, is moved towards it
with a velocity of a metre in a second, the direct note and that reflected
from the wall undergo opposite changes, so that an obsen-er hears distinctly
twelve beats in a second (262).

234. Velocity of sound in liquids. — ^The velocity of sound in water
was experimentally determined in 1827 by CoUadon and Sturm. They

2IO On Sound. [234-

moored two boats at a known distance in the Lake of Geneva. The first
supported a bell immersed in water, and a bent lever provided at one end
with a hammer which struck the bell, and at the other with a lighted wick, so
arranged that it ignited some powder the moment the hammer struck the
bell. To the second boat was affixed an ear-trumpet, the bell of which was
in water, while the mouth was applied to the ear of the observer, so that he
could measure the time between the flash of light and the arrival of sound by
the water. By this method the velocity was found to be 4,708 feet in a second
at the temperature 8°-i, or four times as great as in air.

The velocity of sound, which is different in different liquids, can be cal-
culated by a formula analogous to that given above (230) as applicable to

gases, that is, ^' = \/^—, > 'i^ which ^, /?, and 8 have their previous signi-
ficance ; while ^ is the coefficient of the compressibility for the liquid in ques-
tion (97), that is, its diminution in volume by a pressure of one atmosphere —
and ^^s the density. In this way were obtained the numbers given in the
following table. As in the case of gases, the velocity varies with the tem-
perature, which is therefore appended in each case.

River water (Seine)

. 13° c.

= 4714:

feet

in a second.

Artificial sea-water

• 30

. 20

= 5013
- 4761

Mercury

Solution of common

salt

10
. 18

= 4866
= 5132

Absolute alcohol .

• 23

= 3854

Turpentine .
Ether .

• 24

= 3976
= 3801

It will be seen how close is the agreement between the two values for
the velocity of sound in water, the only case in which they have been
directly compared. There is considerable uncertainty about the values for
other liquids, owing to the doubt as to the values for their compressibility.

235. Velocity of sound in solids. — As a general rule, the elasticity of
solids, as compared with the density, is greater than that of liquids, and
consequently the propagation of sound is more rapid.

The difference is well seen in an experiment by Biot, who found that when
a bell was struck by a hammer, at one end of an iron tube 3,120 feet long,
two sounds were distinctly heard at the other end. The first of these was
transmitted by the tube itself with a velocity x ; and the second by the en-
closed air with a known velocity a. The mterval between the sounds was
2-5 seconds. The value of x obtained from the equation

3120_3120^^

a X

shows that the velocity of sound in the tube is nearly 9 times as great as that
in air.

That the report of the firing of cannon is heard at far greater distances
than peals of thunder, is doubtless owing to the fact that the sound in the
former case is mainly transmitted through the earth.

To this class of phenomena belongs the fact that if the ear is held against

-235] Velocity of Sound in Solids. 211

a rock in which a blasting is being made at a distance, two distinct reports
are heard — one transmitted through the rock to the ear, and the other trans-
mitted through the air. The conductivity of sound in sohds is also well
illustrated by the fact that in manufacturing telegraph wires the filing at any
particular part can be heard at distances of miles by placing one end of the
wire in the ear. The toy telephone also is based on this fact.

The velocity of sound in wires has also been determined theoretically

by Wertheim and others, by the formula v = a /^ in which /x is the modulus

of elasticity (89), while d is the mass in unit volume, which is equal to the

specific gravity, or the weight of unit volume divided by the acceleration of

s
gravity, or .

This may be illustrated from a determination by Wertheim of the velocity
of sound in a specimen of annealed steel wire, the specific gravity ^ of which
was 7'63i and its modulus 21,000 (88). That is, a weight of 21,000 kilo-
grammes would double the unit length of a wire i sq. mm. in cross section, if
this were possible without exceeding the limit of elasticity. This is equal to
2,100,000,000, or 21 X 10®, grammes on a wire i sq. cm. in cross section.
Hence

/2 1 00000000 X 98 1 o

^'= V ;763-~-= 519581 cm.

17047 feet.

The following table gives the velocity in various bodies, expressed in feet
per second, mostly from the experimental determinations of Wertheim and
Stefan : —

Caoutchouc . . 100 to 200

Oak .

12622

Tallow .

1 180

Cedar.

13120

Wax

2394

Elm .

13516

Paraffine

4250

Ash .

15314

Lead .

4653

Fir .

15316

Gold

7021

Walnut

15744

Silver .

8806

Glass .

16057

Pine

10900

Steel wire .

16336

Copper .

1 2 194

Wrought ire

nanc

istee

1 16498

The numbers for caoutchouc are of the same order of magnitude as those
for the propagation of a nervous impulse, and suggest that this impulse is
transmitted by longitudinal vibrations like those of sound.

In the case of wood these velocities are in the directions of the fibres,
and are considerably greater than across the rings or along the rings ; thus
with fir the velocities are 4382 and 2572 for these directions respectively.

From a recent determination of the elasticity of ice, Trowbridge and
Macrae have deduced the velocity of sound in it to be 9,600 feet per second,
2,900 metres or about 9 times that of air.

Mallet investigated the velocity of the transmission of sound in various
rocks, and found that it is as follows : —

p 2

212

Ofi Sound.

[235-

Wet sand ......

Contorted, stratified quartz and slate rock
Discontinuous granite ....

Solid g-ranite

825 feet in a second.
1088

1306 „

1664

A direct experimental method of determining the velocity of sound in
solids, gases, and vapours will be described subsequently (277).

If a medium through which sound passes is heterogeneous, the waves of
sound are reflected on the different surfaces, and the sound becomes rapidly
enfeebled. Thus a soft earth conducts sound badly, while a hard ground
which forms a compact mass conducts it well. So also we hear badly
through air spaces which are filled with porous materials, such as shavings,
sawdust, cinders, and the like.

236. Reflection of sound. — So long as sound-waves are not obstructed
in their motion they are propagated in the form of concentric spheres ; but,
when they meet with an olDstacle, they follow the general law of elastic
bodies ; that is, they return upon themselves, forming new concentric waves,
which seem to emanate from a second centre on the other side of the obstacle.
This phenomenon constitutes the reflection of sound.

Fig. 212 represents a series of incident waves reflected from an obstacle
PQ. Taking, for example, the incident wave MCDN, emitted from the
centre A, the corresponding reflected wave is represented by the arc CKD,
of a circle whose centre a is as far behind the obstacle PQ as A is before it.

If any point C of the reflecting surface be joined to the centre of sound,
and if the perpendicular CH be let fall on the surface of this body, the angle
ACH is called the a7igle of incidence, and the angle BCH, formed by the
prolongation of czC, is the angle of reflection.

The reflection of sound is subject to the two following laws : —

I. The angle of reflection is equal to the angle ofificidence.

II. The incident sonorous ray and the reflected 7'ay are in the same plane
perpendicular to the reflecting surface.

From these laws it follows that the wave, which in the figure is propa-

-237] Echoes and Resonances. 213

yated in the direction AC, takes the direction CB after reflection, so that an
observer placed at B hears a second sound, which appears to come from C,
besides the sound proceeding from the point A.

The laws of the reflection of sound are the same as those for light and
radiant heat, and may be demonstrated by similar experiments. One of the
simplest of these is made with conjugate mirrors (see chapter on Radiant
Heat) ; if in the focus of one of these mirrors, which should be rather large,
a watch is placed, the ear placed in the focus of the second mirror hears the
ticking very distinctly even when the mirrors are at a distance of 12 or 13
yards.

In like manner the explosion of fulminating mercury in the focus of one
mirror causes that of iodide of nitrogen placed in that of the other.

237. Echoes and Resonances. — An echo is the repetition of a sound in
the air, caused by its reflection from some obstacle.

A very sharp quick sound can produce an echo when the reflecting
surface is 55 feet distant ; but for articulate sounds at least double that
distance is necessary, for it may be easily shown that no one can pronounce
or hear distinctly more than five syllables in a second. Now, as the velo-
city of sound at ordinary temperatures maybe taken at 1,125 ^^^^ i'^^ second,
in a fifth of that time sound would travel 225 feet. If the reflecting surface
is 112-5 feet distant, in going and returning sound would travel through 225
feet. The time which elapses between the articulated and the reflected
sound would, therefore, be a fifth of a second, the two sounds would not
interfere, and the reflected sound would be distinctly heard. A person
speaking with a loud voice in front of a reflector, at a distance of ii2"5 feet,
can only distinguish the last reflected syllable : such an echo is said to be
vioHosy liable . If the reflector were at a distance of two or three times 112-5
feet, the echo would be dissyllabic^ trisyllabic, and so on.

When the distance of the reflecting surface is less than 112-5 feet, the
direct and the reflected sound are confounded. They cannot be heard
separately, but the sound is strengthened. This is what is often called
reso7iance, and is frequently observed in large rooms. Bare walls and par-
ticularly wood work are very resonant ; they reflect the sound and add to it
the effect of their own vibrations, so that the sound is prolonged and
enforced. In a large meeting room this may considerably aid a speakei-'s
voice ; too great resonance, however, hindeis the distinct perception of the
words. Tapestry and hangings, on the contrary, which are bad reflectors,
deaden the sound. To control or eliminate the effects of resonance is a
difficult problem in the acoustics of the building art.

Multiple ecJioes are those which repeat the same sound several times ;
this is the case when two opposite surfaces (for example two parallel walls)
successively reflect sound. There are echoes which repeat the same sound
20 or 30 times. An echo in the chateau of Simonetta, in Italy, repeats a
sound 30 times. At Woodstock there is one which repeats from 17 to 20
syllables.

As the laws of reflection of sound are the same as those of light and
heat, curved surfaces produce acoustic foci like the luminous and calorific
foci produced by concave reflectors. If a person standing under the arch of
a bridge speaks with his face turned towards one of the piers, the sound is

214 On Sound. [237-

reproduced near the other pier with such distinctness that a conversation
can be kept up in a low tone, which is not heard by anyone standing in the
intermediate spaces.

There is a square room with an elhptical ceihng, on the ground floor of the
Conservatoire des Arts et Metiers, in Paris, which presents this phenomenon
in a remarkable degree when persons stand in the two foci of the ellipse.

Whispering galleries are formed of smooth walls having a continuous
curved form. The mouth of the speaker is presented at one point, and
the ear of the hearer at another and distant point. In this case, the
sound is successively reflected from one point to the other until it reaches
the ear.

In the whispering gallery of St. Paul's, the faintest sound is thus conveyed
from one side to the other of the dome, but it is not heard at any intermediate
points. Placing himself close to the upper wall of the Colosseum, a circular
building 130 feet in diameter, Wheatstone found a word to be repeated a
great many times. A single exclamation sounded like a peal of laughter,
while the tearing of a piece of paper resembled the patter of hail.

It is not merely by solid surfaces, such as walls, rocks, ships' sails, &c.,
that sound is reflected. It is also reflected by clouds, and it has even been
shown by direct experiment that a sound in passing from a gas of one density
into another is reflected at the surface of separation as it would be against
a gas of solid surface. Now, different parts of the earth's surface are un-
equally heated by the sun, owing to the shadows of trees, evaporation of water,
and other causes, so that in the atmosphere there are numerous ascending and
descending currents of air of different density. Whenever a sound-wave
passes from a medium of one density into another it undergoes partial reflec-
tion, which, though not strong enough to form an echo, distinctly weakens
the direct sound. This is doubtless the reason, as Humboldt remarked, why
sound travels further at night than at daytime, even in the South American
forests where the animals, which are silent by day, fill the atmosphere at
night with thousands of confused sounds. To this may be added that at
night and in repose, when other senses are at rest, that of hearing becomes
more acute. This is the case with persons who have become blind.

It has generally been considered that fog in the atmosphere is a great
deadener of sound ; it being a mixture of air and globules of water, at each
of the innumerable surfaces of contact a portion of the vibration is lost.
The evidence as to the influence of this property is conflicting ; recent re-
searches of Tyndall show that a white fog, or snow, or hail, are not important
obstacles to the transmission of sound, but that aqueous vapour is. Expe-
riments made on a large scale, in order to ascertain the best form of fog
signals, gave some remarkable results.

On some days, which optically were quite clear, certain sounds could not
be heard at a distance far inferior to that at which they could be heard even
during a thick haze. Tyndall ascribes this result to the presence in the
atmosphere of aqueous vapour, which forms in the air innumerable stria;
that do not interfere with its optical clearness, but render it acoustically
turbid, the sound being reflected by this invisible vapour just as light is by
the visible cloud.

These conclusions first drawn from observations have been verified by

-238]

Refraction of Sound.

215

laboratory experiments. Tyndall has shown that a medium consisting of
alternate layers of light and heavy gas, such as coal gas and carbon
dioxide, deadens sound, and also that a medium consisting of alternate strata
of heated and ordinary air exerts a similar influence. The same is the case
with an atmosphere containing the vapours of volatile liquids. So long as
the continuity of air is preserved, sound has great power of passing through
the interstices of solids ; thus it will pass through twelve folds of a dry silk
handkerchief, but is stopped by a single layer if it is wetted.

238. Refraction of sound.— It will be found afterwards (536) that refrac-
tion is the change of direction which light and heat experience on passing from
one m.edium to another. It has been shown by Hajech that the laws of the
refraction of sound are the same as those for light and heat : he used tubes
filled with various gases and liquids, and closed by membranes ; the mem-
brane at one end was at right angles to the axis of the tube, while the other
made an angle with it. When these tubes were placed in an aperture in the
wall between two rooms, a sound produced in front of the tube in one room,
that of a tuning-fork for instance, was heard in directions in the other vary-
ing with the inclination of the second membrane, and with the nature of the
substance with which the tube was filled. Accurate measurements showed

that the law held that the sines of the angle of incidence and of refraction
are in a constant ratio, and that this ratio is equal to that of the velocity of
sound in the two media.

Thus the velocity of sound in water is not very different from that in
hydrogen, and they produce deviations which are nearly equal.

Sondhauss confirmed the analogy of the refraction of sound-waves to
those of light and heat. He constructed lenses of gas by cutting equal
segments out of a large collodion balloon, and fastening them on the two
sides of a sheet iron ring a foot in diameter, so as to form a double convex
lens about 4 inches thick in the centre (fig. 212), This was filled with car-
bonic acid, and a watch A was placed in the direction of the axis : the point
was then sought on the other side of the lens at which the sound was most
distinctly heard. It was found that when the ear was removed from the
axis, the sound was scarcely perceptible; but that at a certain point B on the

2i6 On Soiind. [238-

axial line it was very distinctly heard. Consequently, the sound-waves in
passing from the lens had converged towards the axis, their direction had
been changed ; in other words, they had been refracted.

The refraction of sound may be easily demonstrated by means of one of
the very thin india-rubber balloons used as children's toys, inflated by
carbonic acid. If the balloon be filled with hydrogen, no focus is detected ;
it acts like a concave lens, and the divergence of the rays is increased, instead
of their being converged to the ear.

A direct proof of the refraction of sound is given by the experiments of
Schellbach and Bohm. The source of sound was a film of collodion stretched
across a ring ab (fig. 213), and which was put in vibration by electrical sparks
at 0. A disc of paper, sprinkled with fine charcoal powder, was suspended in
the vessel BB'. When this vessel contained air, rings of dust were formed,
the centre of which was at /in the direction of the propagation of the sound.
But if the vessel was filled with carbonic acid the centre of the rings was found
to be at/', showing that the sound had been refracted towards the perpendi-
cular on passing from air into the denser medium ; and measurements showed
that the position of the point /' was in accordance with the law of refraction
for light. Experiments showed that,' when hydrogen was substituted for car-
bonic acid, the sound was bent away from the perpendicular.

It has long been known that sound is propagated in a direction against
that of the wind with less velocity than with the wind. This is probably
due to a refraction of sound on a large scale. The velocity of wind along
the ground is always considerably less than at a greater height ; thus, the
velocity at a height of 8 feet has been observed to be double what it is at a
height of one foot above the ground. Hence the front of a condensed wave
(fig. 209), which was originally vertical, becomes tilted upwards and with the
lower part forward ; and, as the direction of the wave-motion is at right
angles to the front of the wave, the effect of the coalescence of a number of
these rays, thus directed upwards, is to produce an increase of the sound in
the higher regions. The rays which travel with the wind will, for similar
reasons, be refracted downwards, and thus the sound be better heard.

239. Speaking- trumpet. Ear trumpet. — These instruments depend
both on the reflection of sound and on its conductibility in tubes.

The speaking trumpet, as its name implies, is used to render the voice
audible at great distances, more especially on board ship. It consists of a

~^%r~

Fig. 214.

slightly conical tin or brass tube (fig. 214), very much wider at one end (which
is called the bell), and provided with a mouthpiece at the other. They are
as much as 7 feet in length, the bell being i foot in diameter.

The larger the dimensions of this instrument the greater is the distance
at which the voice is heard. Its action is usually ascribed to the .successive

-240]

Stethoscope.

217

reflections of sound-waves from the sides of the tube, by which the waves
tend more and more to pass in a direction parallel to the axis of the
instrument. It has, however, been objected to this explanation that the
sounds emitted by the speaking trumpet are not stronger solely in the
direction of the axis, but in all directions ; that the bell would not tend to
produce parallelism in the sound-wave, whereas it certainly exerts consider-
able influence in strengthening the sound. According to Hassenfratz the bell
acts by allowing a large mass of air to be set in consonant vibration before
it begins to be diffused. This is probably also the reason why sound travels
best in the chief direction of the sounding body ; thus the report of a cannon,
the sound of a wind instrument in the line of the tube, the voice in the
direction of the mouth, etc.

The ear trumpet is used by persons who are hard of hearing. It is
essentially an inverted speaking trumpet, and consists of a conical metallic
tube, one of whose extremities, terminating in a bell^ receives the sound, while
the other end is introduced into the ear. This instrument is the reverse of
the speaking trumpet. The bell serves as a mouthpiece ; that is, it receives
the sound coming from the mouth of the person who speaks. These sounds
are transmitted by a series of reflections to the interior of the trumpet, so
that the waves, which would become greatly diffused, are concentrated on

Fig. 215. Fig. 216.

the ear, and produce a far greater effect than divergent waves would have
done.

240. Stetboscope. — One of the most useful applications of acoustical
principles is the stethoscope. Figs. 215, 216, represent an improved form of
this instrument devised by Konig. Two sheets of caoutchouc, c and cz, are
fixed to the circular edge of a hollow metal hemisphere; the edge is provided
with a stopcock, so that the sheets can be inflated, and then present the ap-
pearance of a double convex lens, as represented in section in fig. 215. To
a tubulure on the hemisphere is fixed a caoutchouc tube terminated by horn
or ivory, (5, which is placed in the ear (fig. 216).

When the membrane c of the stethoscope is applied to the chest of a sick
person the beating of the heart and the sounds of respiration are transmitted
to the air in the chamber «, and from thence to the ear by means of the
flexible tube. If several tubes are fixed to the instrument, as many observers
may simultaneously auscultate the same patient.

2li

On Sound.

[241-

CHAPTER II.

MEASUREMENT OF THE NUMBER OF VIBRATIONS.

241. Savart's apparatus. — Satuirfs toothed zuheel^ so called from the
name of its inventor, is an apparatus by which the absokite number of vibra-
tions corresponding to a given note can be determined. It consists of a
solid oak frame in which there are two wheels, A and B (fig. 217) ; the larger

Fig. 217.

wheel. A, is connected with the toothed wheel by means of a strap and a
multiplying" wheel, thereljy causing the toothed wheel to revolve with great
velocity ; a card, E, is fixed on the frame, and, in revolving, the toothed
wheel strikes against it, and causes it to vibrate. The card, being struck by
each tooth, makes as many vibrations as there are teeth. At the side of the
apparatus there is an indicator, H, which gives the number of revolutions of
the wheel, and consequently the number of vibrations in a given time.

When the wheel is moved slowly, the separate shocks against the card
are distinctly heard ; but if the velocity is gradually increased, the sound
becomes higher and higher. Having obtained the sound whose number of
vibrations is to be determined, the revolution of the wheel is continued with
the same velocity for a certain number of seconds. The number of turns of
the toothed wheel B is then read oft" on the indicator, and this multiplied
by the number of teeth in the wheel gives the total number of \'ibrations.
Dividing this by the corresponding number of seconds, the ciuotient gives
the number of vibrations per second for the given sound.

242. Syren. — The syre/i is an apparatus which, like Sa\art's wheel, is
used to measure the number of vibrations of a body in a given time. The

-242]

Syren.

219

name 'syren' was given to it by its inventor, Cagniard Latour, because it
yields sounds under water.

It is made entirely of brass. Fig. 218 represents it fixed on the table of
a bellows, by which a continuous current of air can be sent through it. Figs.
219 and 220 show the internal details. The lower part consists of a cylin-
drical box, O, closed by a fixed plate, B. On this plate a vertical rod, T, rests,
to which is fixed a disc. A, moving with the rod. In the plate B there are
equidistant circular holes, and in the disc A are an equal number of holes of
the same size, and the same distance from the centre as those of the plate.
These holes are not perpendicular to the disc ; they are all inclined to the
same extent in the same direction in the plate, and are inclined to the same
extent in the opposite direction in the disc, so that when they are opposite
each other they have the appearance represented in w«, fig. 219. Conse-
quently, when a current of air from the bellows reaches the hole, w, it strikes

obliquely against the sides of the hole ;/, and imparts to the disc A a rotatoiy
motion in the direction ?/A.

For the sake of simplicity, let us first suppose that in the movable disc
A there are eighteen holes, and in the fixed plate B only one, which faces
one of the upper holes. The wind from the bellows striking against the
sides of the latter, the movable disc begins to rotate, and the space between
two of its consecutive holes closes the hole in the lower plate. But as the
disc continues to turn from its acquired velocity, two holes are again opposite
each other, a new impulse is produced, and so on. During a complete
revolution of the disc the lower hole is eighteen times open and eighteen
times closed. A series of effluxes and stoppages is thus produced, which
makes the air vibrate, and ultimately produces a sound when the successive
impulses are sufficiently rapid. If the fixed plate, like the moving disc, had
eighteen holes, each hole would separately produce the same effect as a

220 On Sound. [242-

separate one, the sound would be eighteen times as intense, but the number
of vibrations would not be increased.

In order to know the number of vibrations corresponding to the sound
produced, it is necessary to know the number of revolutions of the disc A in
a second. For this purpose an endless screw on the rod T transmits the
motion to a wheel, «, with loo teeth. On this wheel, which moves by one
tooth for eveiy turn of the disc, there is a catch, P, which at each complete
revolution moves one tooth of a second wheel, b (fig. 220). On the axis of
these wheels there are two needles, which move round dials represented in
fig. 218. One of these indices gives the number of turns of the disc A, the
other the number of hundreds of turns. By means of two screws, D and C,
the wheel a can be uncoupled from the endless screw.

Since the pitch of the sound rises in proportion to the velocity of the disc
A, the wind is forced until the desired sound is produced The same current
is kept up for a certain time — two minutes, for example — and the number of
turns read off. This number multiplied by 18, and divided by 120, gives
the number of vibrations in a second. For the same velocity of rotation the
syren gives the same sound in air as in water ; the same is the case with
all gases ; and it appears, therefore, that any given sound depends on the
number of vibrations produced, and not on the nature of the sounding body.

The buzzing and humming noise of certain insects is not vocal, but is
produced by very rapid flapping of the wings against the air or the body.
The syren has been ingeniously applied to count the velocity of the undu-
lations thus produced, which is effected by bringing it into unison with the
sound. It has thus been found that .the wings of a gnat flap at the rate of
1,500 times in a second. If a report is produced in a space with two
parallel walls at no great distance apart, the sound is reflected from one to
the other and reaches the ear at regular and frequent intervals ; that is, the
repetition of the echo acts as a note.

A modification of the syren known as Brown's steam horn, in which high
pressure steam is employed instead of compressed air, is used as ^fog-signal.
Its shrill and penetrating note is better adapted than an ordinary fog-horn,
or even cannon, for being heard over the noise of breakers.

243. Bellows. — In acoustics a bellows is an apparatus by which wind
instruments, such as the syren and organ-pipes, are worked. Between the
four legs of a table there is a pair of bellows, S (fig. 221), which is worked
by means of a pedal, P. D is a reservoir of flexible leather, in which is stored
the air forced in by the bellows. If this reservoir is pressed by means of
weights on a rod, T, moved by the hand, the air is driven through a pipe, E,
into a chest, C, fixed on the table. In this chest there are small holes closed
by leather valves, which can be opened by pressing on keys in front of the
box. The syren or sounding pipe is placed in one of these holes.

244. X>imit of perceptible sounds. — Previous to Savart's researches,
physicists assumed that the ear could not perceive a sound when the number
of vibrations was below 16 for deep sounds, or above 9,000 for acute sounds.
But he showed that these limits were too close, and that the faculty of per-
ceiving sounds depends rather on their intensity than on their height ; so
that when extremely acute sounds are not heard, it arises from the fact that

244]

Limit of perceptible Soimds

221

they have not been produced with sufficient intensity to affect the organ of
hearing.

By increasing the diameter of the toothed wheel, and consequently the
amplitude and intensity of the vibrations, Savart pushed the limit of acute
sounds to 24,000 vibrations in a second.

For deep sounds he substituted for the toothed wheel an iron bar about
two feet long, which revolved on a horizontal axis between two thin wooden
plates, about o-o8 of an inch from the bar. As often as the bar passed, a
grave sound was produced, due to the displacement of the air. As the
motion was accelerated, the sound became continuous, very grave and
deafening. By this means Savart found that, with 7 to 8 vibrations in a
second, the ear perceived a
distinct but very deep sound.

Despretz, howe\'er, who
investigated the same sub-
ject, disputed Savart's results
as to the limits of deep
sounds, and considers that
no sound is audible that is
made by less than 16 vibra-
tions per second. Helm-
holtz holds that the percep-
tion of a sound begins at 30
vibrations, and only has a
definite musical value when
the number is more than 40.
Below 30 the impression of
a number of separate beats
is produced. On the other
hand, acute sounds are audi-
ble up to those correspond-
ing to 38,000 vibrations in a
second. Such sounds, how-
ever, are far from pleasur-
able : they affect the ear as if
it had been pricked with a
pin or needle.

The discordant results obtained by these and other observers for the
limit of audibility of higher notes are no doubt due to the circumstance
that different observers have different capacities for the perception of
sounds. Preyer has investigated this subject by means of experimental
methods of greater precision than any that have hitherto been applied
for this purpose. The minimum limit for the normal ear he found to lie
between 16 and 24 single vibrations in a second; the maximum limit reached
41,000 ; but many persons with average powers of hearing were found to be
absolutely deaf to notes of 16,000, 12,000, or even fewer vibrations.

It appears that the limit of audibility for any particular ear is increased
with the strength of the sound. Paucher examined this by sounding a
powerful syren by steam ; he found that with steam of ^ atmosphere pres-

222 On Sound. [244-

sure the upper limit was at 48,000 vibrations, with li atmospheres it was
60,000, while with steam of 2.^ atmospheres it had not been attained with
72,000 vibrations.

245. Suhamel's graphic method. — When the syren or Sa\art's wheel
is used to determine the exact number of vibrations corresponding to a given
note, it is necessary to bring the sounds which they produce into unison
with the given note, and this cannot be done exactly unless the experi-
menter has a practised ear. Duhamel's graphic method is very simple and
exact, and free from this difificulty. It consists in fixing a fine point to the
body emitting the note, and causing it to trace the vibrations on a properly
prepared surface.

The apparatus consists of a wood or metal cylinder, A (fig. 222), fixed to
a vertical axis, O, and turned by a handle. The lower part of the axis is a
screw working in a fixed nut, so that, according as the handle is turned from
left to right, or from right to left, the cylinder is raised or depressed. Round

Fig. 222.

the cylinder is rolled a sheet of paper covered with an inadhesive film of
lampblack. On this film the vibrations register themselves. This is effected
as follows. Suppose the body emitting the note to be a steel rod. It is held
firmly at one end, and carries, at the other, a fine point which grazes the sur-
faces of the cylinder. If the rod is made to vibrate and the cylinder is at rest,
the point would describe a short line; but, if the cylinder is turned, the point
produces an tindidatino Hue., containing as many undulations as the point
has made vibrations. Consequently, the number of vibrations can be counted..
It remains only to determine the time in which the \'ibrations were made.

-245] Duhainel's Graphic Method. 223

There are several ways of doing this. The simplest is to compare the
curve traced by the vibrating rod with that traced by a tuning-fork (251),
which gives a known number of vibrations per second — for example, 500.
The prong of the fork is furnished with a point, which is placed in contact
with the lampblack. The fork and the rod are then set vibrating together,
and each produces its own undulating trace. When the paper is unrolled,
it is easy, by counting the number of vibrations each has made in the same
distance, to determine the number of vibrations made per second by the
elastic rod. Suppose, for instance, that the tuning-fork made 150 vibrations
while the rod made 165 vibrations. Now we already know that the tuning-
fork makes one vibration in the ^-^ part of a second, and therefore 150
vibrations in \~ of a second. But in the same time the rod makes 165

vibrations ; therefore it makes one vibration in the ^ , , of a second,

500 X 165

and hence it makes per second ^ ^, or 550 vibrations.

^ 150

224 On Sound. [246-

CHAPTER III.

THE PHYSICAL THEORY OF MUSIC.

246. Properties of musical notes. — A simple musical note results from
continuous rapid isochronous vibrations, provided the number of the vibra-
tions falls within the very wide hmits mentioned in the last chapter (244).
Musical notes are in most cases compound. The distinction between a
simple and a compound musical note will be explained later in the chapter.
The tone yielded iDy a tuning-fork furnished with a proper resonance-box is
simple ; that yielded by a wide-stopped organ pipe, or by a flute, is near/v
simple ; that yielded by a musical string is compotind.

Musical notes have three leading qualities, namely, pitcJi., intensity., and
timbre or quality.

i. The pitch of a musical note is determined by the number of vibrations
per second yielded by the body producing the note.

ii. The i?ttensity of the note depends on the extent of the vibrations. It
is greater when the extent is greater, and less when it is less. It is, in fact,
proportional to the square of the extent or amplitude of the vibrations which
produce the note.

iii. The timbre or stamp or quality is that peculiar property of note which
distinguishes a note when sounded on one instrument from the same note
when sounded on another, and which by some is called the colour. Thus
when the C of the treble stave is sounded on a violin, and on a flute, the two
notes will have the same pitch ; that is, they are produced by the same number
of vibrations per second, and they may have the same intensity, and yet the
two notes will have very distinct qualities ; that is, their timbre is different.
The cause of the peculiar timbre of notes will be considered later in the
chapter.

247. IVZusical intervals. — Let us suppose that a musical note, which for
the sake of future reference we will denote by the letter C, is produced by
7/1 vibrations per second ; and let us further suppose that any other musical
note, X, is produced by ;/ vibrations per second, n being greater than in ;
then the interval from the note C to the note X is the ratio ;/ : m, the interval
between two notes being obtained by division, not by subtraction. Although
two or more notes may be separately musical, it by no means follows that
when sounded together they produce a pleasant sensation. On the con-
trary, unless they are concordant, the result is harsh, and usually unpleasing.
We have, therefore, to inquire what 7iotes are fit to be sounded together.
Now, when musical notes are compared, it is found that if they are separated
by an interval of 2 : 1,4: i, &c., they so closely resemble one another that
they may for most purposes of music be considered as the same note. Thus,
suppose c to stand for a musical note produced by 2m vibrations per second,
then C and c so closely resemble each other as to be called in music by

-248] The Musical Scale. 225

the same name. The interval from C to c is called an octave, and c is
said to be an octave above C, and conversely C an octave below c. If we now
consider musical sounds that do not differ by an octave, it is found that
if we take three notes, X, Y, and Z, resulting respectively from /, ^, and r
vibrations per second, these three notes when sounded together will be con-
cordant if the ratio oi p : q : r equals 4:5:6. Three such notes form a
harinojtic triad, and if sounded with a fourth note, which is the octave of
X, constitute what is called in music a major chord. Any of the notes of a
chord may be altered by one or more octaves without changing its distinc-
tive character ; for instance, C, E, G, and c are a chord, and C c, e, g form
the same chord.

If, however, the ratio/ : q : r equals 10 : 12 : 15, the three sounds are
slightly dissonant, but not so much so as to disqualify them from producing
a pleasing sensation. When these three notes and the octave to the lower
are sounded together, they constitute what in music is called a mi?tor chord.

248. The musical scale. — The series of sounds which connects a given
note C with its octave c is called the diatonic scale or gamut. The notes
composing it are indicated by the letters C, D, E, F, G, A, B. The scale
is then continued by taking the octaves of these notes, namely, c, d, e,f.,g, a, b,
and again the octaves of these last, and so on.

The notes are also known by names, viz., do or ut, re, 7ni,fa, sol, la, si,
do. The relations existing between the notes are thiese : — C, E, G form
a major triad, G, B, d form a major triad, and F, A, c form a major triad.
C, G, and F have, for this reason, special names, being called respectively
the tom'c, dovmtant, and sub-dominant, and the three triads the tonic,
domiiiant, and sub-dominant triads or chords respecti\ely. Consequently,
the numerical relations between the notes of the scale will be given by the .
three proportions —

E :

G :

: 4

2D :

: 4

A :

2C :

: 4

Hence, if m denotes the number of double vibrations corresponding to
the note C, the number of vibrations corresponding to the remaining notes
will be given by the following table —

do re mi fa sol la si do
CDEFGAB^
m \m \m \m \m \m ^/ 2w

The intervals between the successive notes being respectively —
C to D D to E E to F F to G G to A A to B B to (T

It will be observed here that there are three kinds of intervals " '^^ and
if ; of these the first two are called a tone, the last a semitone, because it
is about half as great as the interval of a tone. The two tones, however are
not identical, but differ by an interval of |^, which is called a comma. Two
notes which differ by a cofn?na can be readily distinguished by a trained

226 On Sound. [248-

ear. The interval between the tonic and any note is denominated by the
position of the latter note in the scale ; thus the interval from C to G is a
fifth. The scale we have now considered is called the major scale, as being
formed oi major VcxdidA. If the minor triad were substituted for the major,
a scale would be formed that could be strictly called a minor scale. As
scales are usually written, however, the ascending scale is so formed that
the tonic bears a minor triad, the dominant and sub-dominant bear major
triads, while in the descending scale they all bear minor triads. Practically^
in musical composition, the dominant triad is always >najor. If the ratios
given above are examined, it will be found that in the major scale the
interval from C to E equals f, while in the minor scale it equals f. The
former interval is called a major third, the latter a minor third. Hence the
major third exceeds the minor third by an interval of §|. This interval is
called a semitone, though very different from the interval above called by
that name.

249. On semitones and on scales with different key-notes. — It will
be seen from the last article that the term ' semitone ' does not denote a.
constant interval, being in one case equivalent to \i and in another to ||.
It is found convenient for the purposes of music to introduce notes inter-
mediate to the seven notes of the gamut ; this is done by raising or lowering-
these notes by an interval of |f. When a note (say C) is increased by this
mterval, it is said to be sharpened, and is denoted by the symbol CJI , called
' C sharp ;' that is, Cji-=-C = |f. When it is lowered by the same interval, it
is said to \i& flattened, and is represented thus — Bb, called ' B flat ; ' that is,
B-^Bb = §f. If the effect of this be examined, it will be found that the
number of notes in the scale from C up to c has been increased from seven
to twenty-one notes, all of which can be easily distinguished by the ear.
Thus, reckoning C to equal i, we have —

C Cff Db D Dj Eb E &c.

Hitherto we have made the note C the tonic or key-note. Any other of
the twenty-one distinct notes above mentioned, e.g., G, or F, or Cff, &c.,
may be made the key-note, and a scale of notes constructed with reference
to it. This will be found to give rise in each case to a series of notes, some
of which are identical with those contained in the series of which C is the
key-note, but most of them different. And of course the same would be true
for the minor scale as well as for the major scale, and indeed for other scales
which may be constructed by means of the fundamental triads.

250. On musical temperament. — The number of notes that arise from
the construction of the scales described in the last article is so great as to
prove quite unmanageable in the practice of music ; and particularly for
music designed for instruments with fixed notes, such as the pianoforte or
harp. Accordingly, it becomes practically important to reduce the number
of notes, which is done by slightly altering their just proportions. This
process is called temperament. By tempering the notes, however, more or
less dissonance is introduced, and accordingly several different systems of
temperament have been devised for rendering this dissonance as slight as
possible. The system usually adopted is called the system o^ equal tempera-

-251] The Number of Vibrations producing each Note. 227

ment. It consists in retaining the octaves pure, and in substituting between
C and c eleven notes at equal intervals, each interval being, of course, the
twelfth root of 2, or 1-05946. By this means the distinction between the
semitones is abolished, so that, for example, CJt and Db become the same
note. The scale of twelve notes thus formed is called the chroinatic scale.
It of course follows that major triads become slightly dissonant. Thus, in
the diatonic scale, if we reckon C to be i, E is denoted by 1-25000, and G by
1-50000. On the system of equal temperament, if C is denoted by i, E is
denoted by 1-25992, and G by i -49831.

If individual intervals are made pure while the errors are distributed over
the others, such a system is called that of unequal temperament. Of this
class is Kirnbergcr^s, in which nine of the tones are pure.

Although the system of equal temperament has the advantage of afford-
ing the greatest variety of tones with as small a number of notes as possible,
yet it has the drawback that no chord of an equally tempered instrument,
such as the piano, is perfectly pure. And as musical education mostly has
its basis on the piano, even singers and instrumentahsts usually give equally-
tempered intervals. Only in the case of string quartet players, who have
freed themselves from school rules, and in that of vocal quartet singers, who
sing much without accompaniment, does the natural pure temperament assert
itself, and thus produce the highest musical effect.

251. The number of vibrations producing' each note. The tuningr-
fork. — Hitherto we have denoted the number of vibrations corresponding to
the note C by w, and have not assigned any
numerical value to that symbol. In the theory
of music it is frequently assumed that the middle
C corresponds to 256 double vibrations in a
second. This is the note which, on a pianoforte
of seven octaves, is produced by the white key
on the left of the two black keys close to the
centre of the keyboard. This number is con-
venient as being continually divisible by two,
and is therefore frequently used in numerical
illustrations. If is, however, arbitrary. An
instrument is in tune provided the intervals
between the notes are correct, when c is yielded
by any number of vibrations per second not
differing much from 256. Moreover, two instru-
ments are in tune with one another, if, being
separately in tune, they have any one note, for
instance C, yielded by the same number of vibra-
tions. Consequently, if two instruments have
one note in common, they can then be brought
into tune jointly by having their remaining notes
separately adjusted with reference to the funda-
mental note. A tutiing-fork or diapason is an instrument yielding a con-
stant sound, and is used as a standard for tuning musical instruments. It
consists of an elastic steel rod, bent as represented in fig. 223. It is made
to vibrate either by drawing a bow across the ends, or by striking one of

Q 2

Fig. 223.

228 On Soimd. [251-

the legs against a small hammer covered with leather, or by rapidly sepa-
rating the two prongs by means of a steel rod as shown in the figure. The
vibration produces a note which is always the same for the same tuning-fork.
The note is strengthened by fixing the tuning-fork on a box open at one end,
called a sounding or rcso7tance box, adjusted so as to strengthen the special
note of the tuning-fork. The length of this column of air enclosed in the
box is a quarter that of the wave-length of the note which the tuning-fork
emits. The vibrations of the air produce the same note as the fork itself ; the
vibrations of the tuning-fork, being communicated to the column of air in the
box, set it in vibration, by which a strong and pure note is obtained (255).

The standard tuning-fork in any countr}^ represents its accepted concert
pitch.

It has been remarked for some years that not only has the pitch of the
tuning-fork been getting higher in the large theatres of Europe, but also
that it is not the same in London, Paris, Berlin, Vienna, Milan, &c. This is
a source of great inconvenience both to composers and singers, and a com-
mission was appointed in 1859 to establish in France a tuning-fork of uniform
pitch, and to prepare a standard which would serve as an invariable type.
In accordance with the recommendations of that body, a norma! tunifig-fork
has been established, which is compulsory on all musical establishments
in France, and a standard has been deposited in the Conservatory of Music
in Paris. It performs 437'5 double vibrations per second, and gives the
standard note a or la, or the a in the treble stave (252). Consequently, with
reference to this standard, the middle c or do would result from 261 double
vibrations per second.

In England a committee, appointed by the Society of Arts, recommended
that a standard tuning-fork should be one constructed to yield 528 double
vibrations in a second, and that this should represent c' in the treble stave.
This number has the advantage of being divisible by 2 down to 2)3^ and is in
fact the same as the normal tuning-fork adopted in Stuttgart in 1834, which
makes 440 vibrations in the second, and, like the French one, corresponds
to a in the same stave.

In exact determinations of pitch the temperature must be taken into
account. Heat acts on the tuning-fork by expanding it, and also by
diminishing the elasticity of the metal. Both effects concur in lowering
the pitch. Thus Konig found that a tuning-fork which made 512 vibrations
at 20° C. varied by 0*0572 for each degree Centigrade. Stone and McLeod
found the number 0-055.

An international conference at Vienna in 1885 adopted a tuning-fork
of polished mild cast-steel with prismatic prongs, making 435 vibrations in a
second at 1 5° C, as the standard a note.

252. IVXusical notation. IMCusical rangre. — It is convenient to have
some means of at once naming any particular note in the whole range of
musical sounds other than by stating its number of vibrations. ^^Perhaps a
convenient practice is to call the octave, of which the C is produced by an
eight-foot organ pipe, by the capital letters C, D, E, F, G, A, B ; the next
higher octave by the corresponding small letters, c, d, e,f,g, a, b ; and to
designate the octaves higher than this by the index placed over the letter
thus, d , d', e', _/"', g', a', b\ and the higher series in a similar manner. The

-253] Wave-length of a Given Note. 229

same principle may be applied to the notes below C ; thus the octave below
C is C^, and the next lower one C^,.
Hence we have the series

C,^ C^ C c c' c" c"' c".

In musical writing the notes are expressed by signs which indicate the
length of time during which the note is to be played or sung, and are written
on a series of lines called a stave. Thus

stands for the octave in the treble clef, of which the top note is the standard
c' and the bottom is the middle c. When the five lines are insufficient they
are continued above and below the stave by what are called ledger lines.
In order to avoid confusion, a bass clef is used for the lower notes ; and it

may be remarked that tff) l=~ and s^' r:= stand for the same note

Xf -¥-
(251), which is the middle c.

The deepest note of orchestral instruments is the E^ of the double bass,
which makes 41I vibrations, taking the key-note as making 440 vibrations
in a second. Some organs and pianofortes go as low as C^^^ with 32 vibra-
tions in a second, some grand pianos even as low as A^^^ with 27! vibrations.
But the musical character of all these notes below E^ is imperfect, for we
are near the limit at which it is possible for the ear to combine the separate
vibrations to a musical note (244). These notes can only be used musically
with their next higher octave, to which they impart a certain character of
depth and richness.

In the other direction, pianofortes go to a'^ with 3,520 or even c^ with 4,224
vibrations in a second. The highest note of the orchestra is probably the
d" of the piccolo flute, which makes 4,752 vibrations. Although the ear can
distinguish sounds which are still higher, they have no longer a pleasurable
character. And while the notes which are distinguishable by the ear range
between 16 and 38,000 vibrations, or 11 octaves, those which are musically
available range from about 40 to 4,000 vibrations, or within 7 octaves.

253. Wave-Iengtb of a given note. Amplitude of oscillation. —
Knowing the number of vibrations which a sounding body makes in a
second, the corresponding wave-length is easily calculated. For since sound
travels at about 1,120 feet in a second, if a body only made one vibration in
a second its wave-length would be 1,120 feet ; if it made two, the wave-length
would be half of 1,120 feet ; if it made three, the third, and so on — that is,
that the 7vave-le?igth of any note is the quotient obtained by dividing the
velocity of sound by the number of vibrations ; and this whatever the height
of the sound, since the velocity is the same for high and low notes.

Hence, calling zi the velocity of sound, / the wave-length, n the number

of vibrations in a second, we have v = In, from which n = "^ ; that is, that the
number of vibrations is inversely as the wave-length.

230 On Sound. [253-

The amplitude of oscillation which is required for the production of
audible sounds is very small. Lord Rayleigh determined it in the case of
the waves due to a pipe which sounded the note _/"', and which could be
heard at a distance of 820 metres. He found that the amplitude of the oscil-
lation of these waves could not be greater than o-ooooooi of a millimetre.

254. On compound musical tones and harmonics. — When any given
note (say C) is sounded on most musical instruments, not that tone alone is
produced, but a series of tones, each being of less intensity than the one
preceding it. If C, which may be called the primary tone, is denoted by
unity, the whole series is given by the numbers i, 2, 3, 4, 5, 6, 7, &c. ; in
other words, first the primary C is sounded, then its octave becomes audible,
then the fifth to that octave, then the second octave, then the third, fifth,
and a note between the sixth and seventh to the second octave, and so on.
These secondary notes are called the harmonics of the primary note. Though
feeble in comparison with the primary note, they may, with a little practice,
be heard when the primaiy note is produced on most musical instruments ;
when, for instance, one of the lower notes is sounded on the pianoforte.

2 54<:;. Consonance and Resonance. — A singular property of bodies in
a state of vibration is that of setting in vibration bodies at rest. Thus, if
two tuning-forks, tuned so as to give accurately the same note, be at some
distance from each other, and one of them be sounded, the other will be set
in vibration and emit the same note. But, if one of the forks be put slightly
out of tune with the other, by attaching a piece of wax to one prong, for in-
stance, then the excitation of either one will have no effect on the other.

It is remarkable that the successive action of a series of impulses of small
mechanical force should, as in this case, be able to set a relatively very heavy
body — such as a tuning-fork — in vibration ; but for this there are many purely
mechanical analogies. Thus, if a series of pulls be exerted in regular inter-
vals on the rope of a large church bell, the superposition of these small mo-
tions will ultimately set the bell swinging. A regiment of soldiers marching
in step over an iron bridge at Angers set it in such powerful oscillation as to
endanger its stability. In like manner the position of a ship in the trough of
the sea is very dangerous, when the period of vibration of the waves coincides
with that of its own vibration.

This phenomenon, that a body in a state of vibration has the power of
causing an independent body at rest to vibrate in the same period, is called
conso7iance.

If a metal wire freely suspended in the air be tightly stretched and then be
set in vibration, the note which it emits will be feeble, seeing that from its small
surface it can set in vibration only small masses of air. So, too, a tuning-fork
when sounded gives but a feeble note, but if its stem be held on a table the
note becomes far louder.

The reinforcement of a sound by attaching the sounding body to a large,
dry, elastic, wooden plate, called a sound-board, or to a wooden box enclosing
a mass of air, is called resonance ; the vibrations of the sounding body are
transmitted to the sound-board, which, being set in vibration, communicates
its motion to large masses of air.

Although the terms consonance and resonance are sometimes used indis-
crimmately, there are distinctions between them.

-255] HehnJioltd's Analysis of Sound. 231

Consonance is the excitation of an independent body to vibrate in unison
with the sounding body ; it begins later than the sounding body, and con-
tinues after it has become silent. Resonance begins and ends with the sound
of the exciting body. A sound-board strengthens and imparts a general sono-
rity to a complex series of notes. The more a body diverges from the
form of a plate and approaches that of a rod, the more is its resonance
limited to strengthening one or two notes.

In resonance, however, there is a certain amount of tuning. For the loud
and deep notes of the cello a large resonance-box is used, and a smaller
one for the higher notes of the violin. Small enclosed volumes of air also
strengthen one note in preference.

255. Helmholtz's analysis of sound. — For the purpose of experimentally
proving the presence of the harmonics as distinct tones, Von Helmholtz
devised an instrument which he called a resonance-globe. This may be
shown by the following experiment, which is an illustration of what has been
said in the previous article, and is indeed analogous in principle with that
described in article 227 : — If an empty glass cylinder be taken, and a
vibrating tuning-fork be held over the mouth of the vessel, the air will not be
set in vibration unless it be of a certain definite length ; such, indeed, that

Fig. 224. Fig. 225.

the wave-length of the fundamental note corresponds to the wave-length of
the note produced by the tuning-fork. Now, by pouring in water we can
regulate the length of the column of air, and by trial can hit off the exact
length ; when this is attained the note of the tuning-fork will be heard to
be powerfully reinforced (227). A resonance-globe (fig. 224) is a glass globe
tuned to a particular note, furnished with two openings, one of which, a^ is
turned towards the origin of the sound, and the other, b, by means of an
india-rubber tube, is applied to the eai". If the tone proper to the resonance-
globe exists among the harmonics of the compound tone that is sounded,
it is strengthened by the globe, and thereby rendered distinctly audible.
Further, other things being the same, the note proper to a given globe
depends on the diameter of the globe and that of the uncovered opening.
Consequently, by means of a series of such globes, the whole series of
harmonics in a given compound tone can be rendered distinctly audible,
and their existence put beyond a doubt.

Konig, the eminent acoustical instrument maker, has made an important
modification in the resonance-globe, to which he has given the form repre-
sented in fig. 225. The resonator is cylindrical, and the end which receives
the sound can be drawn out, so that the volume maybe increased at pleasure.

232 On Sound. [255-

As the sound thereby becomes deeper, the same resonator may be tuned to a
variety of notes. On the tubulure fits a caoutchouc tube by which the vibra-
tions may be transmitted in any direction.

256. Konigr's apparatus for the analysis of sound. — As the successive
appHcation to the ear of various resonators is both slow and tedious, Konig
devised a remarkable apparatus in which a series of resonators act on mano-
metric flames (288) ; the sounds thus, as it were, become visible, and may
be shown to a large auditory.

Fig. 226.

It consists of an iron frame (fig. 226) on which are fixed in two parallel
lines fourteen resonators tuned so as to give the notes from F^ to c" — that is
to say, four octaves and a half ; or notes of which the highest give the lower
harmonics of the primary. On the right is a chamber C, which is supplied
with coal gas by the caoutchouc tube, D, and on which are placed eight
gas jets, each provided with a manometric capsule (288). Each jet is con-
nected with the chamber C by a special caoutchouc tube, while behind the
apparatus a second tube connects the same jet to one of the resonators.

-257J

Synthesis of Sounds.

233

On the right of the jets is a system of rotating mirrors identical with that
described in article 288.

These details being understood, suppose the largest resonator on the right
tuned to resound with the note i, and seven others with the harmonics of
this note. Let the sound i be produced in part of this apparatus ; if it is
simple, the lower resonator alone answers, and the corresponding flame is
alone dentated ; but if the fundamental note is accompanied by one or more
of its harmonics, the corresponding resonators speak at the same time, which
is recognised by the dentation of their flames ; and thus the constituents of
each sound may be detected.

257. Synthesis of sounds. — Not only has Von Helmholtz succeeded in
decomposing sounds into their constituents ; he has verified the result of his
analysis by performing the reverse operation, the synthesis ; that is, he has

Fig. 227.

reproduced a given sound by combining the individual sounds of which his
resonators had shown that it was composed. The apparatus which he used
for this purpose consists of eleven tuning-forks, the first of which yields the
fundamental note of 256 vibrations, or C, nine others its harmonics, while the
eleventh serves as make and break to cause the diapasons to vibrate by means
of electro-magnets. Each diapason has a special electro-magnet, and more-
over a resonator, which strengthens it.

All these diapasons and their accessories are arranged in parallel lines of
five (fig. 227), the first comprising the fundamental note and its uneven har-
monics, 3, 5, 7, and 9 ; the second the even harmonics, 2, 4, 6, 8, and 10 ;
beyond, there is the diapason break K arranged horizontally. One of its
prongs is provided with a platinum point which grazes the surface of mercury

2 34 On Sound. [257-

contained in a small cup, the bottom of which is connected, by a copper wire,
with an electro-magnet placed in front of the diapason.

The apparatus being thus arranged, a wire from a voltaic battery is con-
nected with the binding screw, c, and this with the electro-magnet E ; which
in turn is connected with those of the nine following diapasons, and then
with the diapason K itself. So long as the diapason does not vibrate, the
current does not pass, for the platinum point does not dip in the mercury
cup which is connected with the other pole of the battery. But when the
diapason is made to vibrate by means of a bow, the current passes. Owing
to their elasticity, the limbs of the tuning-fork soon revert to their original
position, the point is no longer in the mercury, the current is broken, and so
on at each double vibration of the diapason. This intermittence of the
current being transmitted to all the other electro-magnets, they are alternately
active and inactive. Hence they communicate to all the diapasons by their
attraction the same number of vibrations. This is the case with the diapason
I, which is tuned in unison with the diapason break ; but the diapason 3,
being tuned to make three times as many vibrations, makes three vibrations
at each break of the current ; that is to say, the electro-magnet only attracts
it at every third vibration ; in like manner, diapason 5 only receives a fresh
impulse every five vibrations, and so on.

The following is the working of the apparatus : — The resonator of each
■diapason is closed by a clapper O (fig. 228), so that the sounds made by the

diapasons are scarcely
perceptible when the clap-
pers are lowered. Each of
these is fixed to the end of
a bent lever, the shorter
arm of which is worked
by a cord a, which is con-
nected with one of the
keys of a keyboard placed
in front of the apparatus
(fig. 227). When a key is
depressed, the cord moves
the le\er, which raises the
clapper, and the resonator
then acts by strengthening-
its diapason. Hence by
depressing any key we
may add to the funda-
mental sounds any of the nine primary harmonics, and thus reproduce the
sounds, the composition of which has been determined by analysis. Thus by
depressing all the keys at once we obtain the sound of an open pipe in unison
with the deepest diapason. By depressing the key of the fundamental note
and those of its uneven harmonics, we obtain the sound of a closed pipe.

258. Results of Von Helmholtz's researches. —By both his analytical
and synthetical investigations into sounds of the most varied kinds — those
from various musical instruments, the human voice, and even noises — Von
Helmholtz has fully succeeded in explaining the different timbre or quality of

Fig. 22S

-259] Production of Vocal Sounds. 235

sounds. It is due to the different intensities of the harmonics which accom-
pany the primary tones of these sounds. The leading results of these re-
searches into the colour (246) of sounds may be thus stated : —

i. Simple notes, as those produced by a tuning-fork with a resonance-box,
and by wide covered pipes, are soft and agreeable without any roughness,
but weak, and in the deeper notes dull.

ii. Musical sounds accompanied by a series of harmonics, say up to the
sixth, in moderate strength, are full and musical. In comparison with simple
tones they are grander, richer, and more sonorous. Such are the sounds of
open organ-pipes, of the pianoforte, &c.

iii. If only the uneven harmonics are present, as in the case of narrow
stopped pipes, of pianoforte strings struck in the middle, clarionets, &c., the
sound becomes indistinct ; and, when a greater number of harmonics is
audible, the sound acquires a nasal character.

iv. If the harmonics beyond the sixth and seventh are very distinct,
the sound becomes sharp and rough. If less strong, the harmonics are not
prejudicial to the musical usefulness of the notes. On the contrary, they
are useful as imparting character and expression to the music. Of this kind
are most stringed instruments, and most pipes furnished with tongues, &c.
Sounds in which harmonics are particularly strong accjuire thereby a pecu-
. liarly penetrating character ; such are those yielded by brass instruments.

259. Production of vocal sounds. — The trachea or windpipe is a tube
which terminates at one end in the lungs, and at the other in the tatynx,
which is the true organ of vocal sound.

Fig. 229 represents a horizontal section of c p

this organ. It consists of a number of car-
tilaginous structures, bb., which are connected
by various muscles, by which great variety and
control in the motions are attainable. These
muscles are connected with, and move, two
elastic membranes or bands with broad bases
fixed to the larynx, and with sharp edges cc ;
these are called the vocal chords. Accord-
ing to the pressure of the muscles these
chords are more or less tightly stretched, I

and the space between them, the vocal slit,
is narrower or wider accordingly. In ordi-
nary breathing, air passes through the triangular aperture o ; but when in
singing this is closed, the vocal chords are stretched and are put in vibration
by the current of air, and produce tones which are higher the more tightly
the chords are stretched, and the narrower is the vocal slit. These changes
can be effected with surprising rapidity, so that in this respect the human
voice far exceeds anything that can be made artificially.

The notes produced by men are deeper than those of women or boys,
because in them the larynx is longer and the vocal chords larger and thicker ;
hence, though equally elastic, they vibrate less swiftly. The vocal chords
are 18 miUimetres long in men, and 12 millimetres long in women. Chest
notes are due to the fact that the whole membrane vibrates, while the fal-
setto is produced by a vibration of the extreme edges only. The ordinary

!36

On Sound.

[259-

compass of the individual voice is within two octaves, though this is exceeded
by some celebrated singers. Catalani, for instance, is said to have had a
range of 3| octaves.

The wave-length of the sounds emitted by a man's voice in ordinary con-
versation is from 8 feet to 12 feet, and that of a woman's voice is from 2 feet
to 4 feet.

The vowel sounds can be produced in any pitch, and the difference in
them arises from the fact that to form a given vowel sound one or more
characteristic notes, which are always the same, must be added. These
change with the syllable pronounced, but depend neither on the height of
the note, nor on the person who emits them.

The form and cavity of the mouth can be greatly modified by the extent
to which it is opened, by the altered position of the tongue, and so forth. It
thus forms a resonator which can be cjuickly and completely controlled.
When the mouth is adjusted so as to produce the broad A, as in father^ it
has then a sort of funnel shape, with the wide part outward ; for O, as in
more, the effect is like that of a bottle with a wide neck ; and for U, as in
poor, it is that of a similar bottle with a narrow neck. For the other vowels,
such as A, E, and I, the effect is as if the bottle were prolonged by a tube,
formed by contracting the tongue against the palate.

If now, while the mouth is adjusted for the position in which it could
utter the vowel U, on successively holding different vibrating tuning-forks in
front of it, only that emitting the note / will be found to be reinforced by
the enclosed column of air vibrating in unison with it. This is accordingly
the characteristic note of that vowel ; in like manner b' is the note for O,
and b" that for A. The other vowel sounds, such as I, have a higher and
lower characteristic note ; thus those of A as in day are d and a'", of I,/
and rf'"'. In most cases, however, the deeper notes have but little influence.
260. Perception of sounds. The ear. — The organ of hearing in man con-
sists of several structures ;
there is first the outer ear
(fig. 230) by which the
sound is collected and
transmitted through the
auditory passage, a, to
the drum or tympiDtum, t.
This is a delicate tightly
stretched membrane or
skin which separates the
outer ear from the middle
ear or tympanic cavity.
This is a cavity in the
temporal bone in which
are several small bones
whose dimensions are
'^' ~^°' considerably exaggerated

in the figure. One of these, the hammer, d, is attached at one end to the
drum, and at the other is jointed to the attvil, e; the latter is connected by
means of the stirrup bone,f, to the oval tvindow, an aperture closed by a

-262 J Beats. 237

fine membrane and which separates the tympanic cavity from the labyrinth.
The tympanic cavity is also connected by the Eustachian tube., b, with the
cavity of the mouth, so that the air in it is always under the same pressure.

The labyrinth is a complicated structure filled with fluid ; it is entirely of
bone, with the exception of the oval window already mentioned and the
round window, o. The labyrinth consists of three parts : the vestibule,
which is closed by the oval window ; the three semicircular canals, k ; and
the spiral-shaped cochlea or snail shell, s. This is separated throughout its
entire length by a division partly of bony projection and partly of membrane ;
the upper part of this division is connected with the vestibule, and therefore
with the oval window, while the lower part is connected with the round
window. In the labyrinthine fluid of this part the termination of the auditory
nerve is spread, the other end leading to the brain.

The membranous part of this diaphragm is lined with about 3,000
extremely minute fibres, which are the terminations of the acoustic nerve, n.
Each of these, which are called CortVs fibres, seems to be tuned for a
particular note as if it were a small resonator. Thus when the vibrations of
any particular note reach these fibres, through the intervention of the stirrup
bone and the fluid of the labyrinth, one fibre or set of fibres only vibrates in
unison with this note, and is deaf for all others. Hence each simple note
only causes one fibre to vibrate, while compound notes cause several ; just
as when we sing with a piano, only the fundamental note and its harmonics
vibrate. Thus, however complex external sounds may be, these microscopic
fibres can analyse them and reveal the constituents of which they are formed.

261. Interference of sound. — If two waves of sound of the same length,
proceed in the same direction, and if they coincide in their phases, they
strengthen one another ; if, however, their phases differ by half a wave-length,
they neutralise each other, and silence is the result. This is called thezV/Z^r-
ference of sound.

It may be illustrated by a number of experiments, of which that repre-
sented in fig. 231 is one of the simplest and most convenient. Two T-shaped
glass tubes, obac and nedf, are
connected at one end by a
short india-rubber tube ad,
while at the other ends they
are connected by a long
india-rubber tube, cqf. The
end 0 provided with a caout-
chouc tube is held in one
ear, the other ear being „.

" r ig. 231.

closed, and a tuning-fork is •

sounded in front of the long free tube, nrs. If the length of the india-rubber
tube c^/be half the wave-length of the note produced by the fork, the sounds
will reach the ear in completely opposite phases ; they will accordingly
neutralise each other and no sound will be heard. But if this india-rubber
tube is closed by pinching it, the note is at once heard. If the tuning-fork
gives the note c, the note it produces makes 528 vibrations in a second, and
the length of the tube should be 34 centimetres.

262 Beats If the notes are different and are not quite in the same

Fig. 232.

238 On Sound. [262-

phase, they alternately weaken and strengthen each other ; they are said to
beat with one another. This may be explained as follows : — Suppose AB, in
fig. 232, to be a row of particles transmitting the sound : suppose the vibra-
tions producing the one note to be indicated by the continuous curved line ;
then, on the one hand, the ordinates of the different points of AB give the
velocities with which those points are simultaneously moving, and, on the
other hand, each point will have successively the different velocities repre-
sented by the successive ordinates. In like manner let the dotted line show
the vibrations which produce the second note. And, for the sake of distinct-
ness, suppose the number of vibrations in a second producing the former
note to be to that producing the latter in the ratio of 3 : 2. Now. let us con-
sider any point which
f, Q when at rest occupies

the position N ; draw
the ordinate, cutting
the former curve in P
and the latter in Q.
If the notes were
sounded separately,
the velocity of N at a
given distance pro-
duced by the former
note would be PN, and that of N at the same instant produced by the latter
note would be QN. Consequently, as they are sounded together, the actual
velocity of N at the given instant is the sum of these, or PN + QN. If at
the same instant we consider the point «, its velocity will consist q{ j)n and
nq jointly, but, as these are in opposite directions, its actual amount will be
pn- 7jq. Hence the actual velocity resulting from the co-existence of the two
notes will be indicated by the curve in fig. 233, whose ordinates equal the
(algebraical) sum of the corresponding ordinates of the two curves in fig.
232 ; that is, if AN, A«, . . . represent equal distances in both figures, the
curve is described by taking RN equal to PN + QN, rn equal io pn - gft,
and so on. This curve shows by its successive ordinates the simultaneous
velocities of the different particles of AB, and the successive velocities com-
municated to the drum of the ear. An inspection of the figure will shov/
that the velocities are first great, then small, then great, and so on, the drum
being first moved rapidly for a short time, then for a short time nearly brought
to rest, and so on. In short, the effect of the beating of notes on the ear,
as compared with that of a continuous note, is strictly analogous to the effect
produced on the eye by a flickering, as compared with a steady, light.

, It may be proved that when two simple notes are produced by ;« and n
double vibrations per second, they produce m-n beats per second ; thus, if
C is produced by 128, and D by 144, double vibrations per second, on being
sounded together they will produce 16 beats per second. It has been ascer-
tained that the beats produced by two notes are not audible unless the ratio
m : n is less than the ratio 6 : 5. Hence, in the case represented by fig. 232,
though the alternations of intensity exist, they would not be audible. Also,
if the notes have very different intensities, the intensity of the beat is very
much disguised.

-263] Combinational Notes. 239

It IS found that when beats are fewer than 10 per second or more than 70
per second they are disagreeable, but not to the extent of producing discord.
Beats from 10 to 70 per second may be regarded as the source of all discord
in music, the maximum of dissonance being attained when about 30 beats
are produced in a second. For example, if c and B are sounded together
the effect is very discordant, the interval between those notes being 16 : 15,
so that the beats are audible, and the number of beats per second being 16.
On the other hand, if C, E, and G are sounded together there is no disso-
nance ; but if C, E, G, B are sounded together the discord is very marked,
since C produces c, which is discordant with B. It will be remarked that
C, E, G is a major triad, while E, G, B is a minor triad.

A compound musical note, being composed of simple notes represented
by I, 2, 3, 4, 5, 6, 7, &c., does not give rise to any simple notes capable of
producing an audible beat up to the seventh — the sixth and seventh are the
first that produce an audible beat. It is for this reason that there is no
trace of roughness in a compound note, unless the seventh harmonic be
audible.

If we were to represent graphically a compound note, we should proceed
to construct a curve out of simple notes of different intensities in the same
manner as fig. 233 is constructed from two simple notes of equal intensity
represented by fig. 232. It is evident that the resulting curve will take
different y»rw.y according to the presence or absence of different harmonics
and their different intensities ; in other words, the quality or timbre of the
notes produced by different instruments will depend upon the form of the
vibrations producing the sound.

Beats not too fast to be readily counted arise between adjacent notes in
the lower octaves of large organs. They are also met with in the sounds
of church bells, and in those emitted by telegraph wires when vibrating
powerfully in a strong wind. They are heard very distinctly in the latter
case by pressing one ear against a telegraph-post and closing the other.

By means of beats, the notes emitted by two musical instruments may be
brought into very accurate unison, by continuing the tuning until the beats
disappear. In order to make tuning-forks produce the normal number of
440 vibrations, an auxiliary tuning-fork is used which makes 436 vibrations ;
each of the forks under experiment iiiust then make with this 4 beats in a
second, which can be controlled with very great accuracy.

263. Combinational notes. — Besides the beats produced when two
musical notes are sounded together, there is another and distinct pheno-
menon, which may be thus described : — Suppose two simple notes to be
simultaneously produced by n and ;;/ vibrations per second. It has been
shown by Helmholtz that they generate a series of other notes. The prin-
cipal one of these, which may be called the differential note, is produced
hy n-tn vibrations per second. Its intensity is usually very small, but it is
distinctly audible in beats. It has been called the grave harmonic, as its
pitch is generally much lower than that of the notes by which it is generated.
It has been supposed to be caused by the beats becoming too numerous to
be distinguished, and coalescing into a continuous sound, and this supposition
was countenanced by the fact that its pitch is the same as the beat number.
The supposition is shown to be erroneous, first, by the existence of the

240 On Sound. [263-

dififerential tones for intervals that do not beat ; and, secondly, by the fact
that, under certain circumstances, both the beats and the dififerential tones
may be heard together.

264. The physical constitution of musical chords. — Let us suppose
two compound notes to be sounded together, say C and G ; then we obtain
two series of notes each consisting of a primary and its harmonics, namely
denoting C by 4, the two series, 4, 8, 12, 16. . . . and 6, 12, 18, 24, &c. Now,
if, instead of producing the two notes C and G, we had sounded the octave
below C, we should have produced the series, 2, 4, 6, 8, 10, 12, 14, 16, 18, &c.
It is plain that the two former series when joined differ from the last in the
following respects : — {a) The primary note 2 is omitted. (<5) In the case of
the last series, the consecutive notes continually decrease in intensity ;
whereas in the two foniier series, 4 and 6 are of the same intensity, 8 is of
lower intensity, but the two 12's will strengthen each other, and so on.
{c) Certain of the harmonics of the primary 2 are omitted ; for example, 10, i^K
&c., do not occur in either of the two former series. In spite of these dif-
ferences, however, the two compound notes affect the ear in a manner very
closely resembling a single compound note ; in short, they coalesce into a
single note with an artificial colour. It may be added that in the case above
taken C and G produce as a combination note 2 (that is 6 - 4), so that,
strictly speaking, the 2 is not wanted in the series produced by C and G,
only it exists in very diminished intensity. The same explanation will
apply to all possible chords ; for example, in the case of the major chord,
C, E, G, we have a note of artificial colour expressed by the series of simple
tones, 4, 5, 6, 8, 10, 12, 15, 16, 18, t&c, together with the combination notes,

I, I, 2. It will be remarked that in the whole of this series there are no dis-
sonant notes introduced, except 15, 16, and 16, 18, and this dissonance will
be inappreciably slight, since 15 is the third harmonic of 5, and 16 the
fourth harmonic of 4, so that their intensities will be different, as also will be
the intensities of 16 and 18. On the other hand, nearly all the notes which
form a natural compound note are present, namely, there are i, 2, 4, 5, 6, 8,
10, 12, &c., in place of i, 2, 3, 4, -5, 6, 7, 8, 9, 10, 11, 12, &c. In short, the
major triad differs only from a natural compound note in that it consists of
a series of simple notes of different intensities, and omits those which, by
beating with the neighbouring note, would produce dissonance ; for example
7, which would beat with 6 and 8 ; 9, which would beat with 8 and 10 ; and

II, which would beat with lo and 12. It is this circumstance which renders
the major chord of such great importance in harmony. If the constituents
of the minor chord are similarly discussed, namely, three compound tones
whose primaries are proportional to 10, 12, 15, it will be found to differ from
the major chord in the following principal respects : — ia) The primary of the
natural tone to which it approximates' is very much deeper than that of the
corresponding major chord, {b) It introduces the differential notes, 2, 3, 5,
which form a major chord. Now it has already been remarked that when a
major and minor chord are sounded together, they are distinctly dissonant ;
for example, when C, E, G, A are sounded together. Accordingly, the fact
of the dififerential notes forming a major chord shows that an elementary
dissonance exists in every minor chord.

-267j Transverse Vibrations of Strings. 241

CHAPTER IV.

VIBRATIONS OF STRETCHED STRINGS AND OF COLUMNS OF AIR.

265. Vibrations of strings. — By a strmg is meant the string of a
musical instrument, such as a vioHn, which is stretched by a certain force,
and is commonly of catgut, or is a metal wire. The vibrations which
strings experience may be either transverse or lo?tgitudi?ial, but practically
the former are alone important. Transverse vibrations may be produced
by drawing a bow across the string, as in the case of the violin ; or by
striking the string, as in the case of the pianoforte : or by pulling it trans-
versely, and then letting it go suddenly, as in the case of the guitar and harp.

266. Sonometer. — The sonometer is an apparatus by which the trans-
verse vibrations of strings may be studied. It is also called the nionochord .

Fig. 234

because it has often only one string. In addition to the string, it consists
of a box of thin wood which has the effect of strengthening the sound ; this
it does by presenting a far larger area to the air than the string itself.
On this there are two fixed bridges, A and D (fig. 234), over which and
over the pulley ;/, passes the string, which is usually a metal wire. This
is fastened at one end, and stretched at the other by weights, P, which can
be increased at will. By means of a third movable bridge, B, the length of
that portion of the wire which is to be put in vibration can be altered at
pleasure.

267. laws of the transverse vibrations of strings. — If / be the
length of a string— that is, the vibrating part between two bridges, A and B
(fig. 234) — r the radius of the string, d its density, P the stretching weight,
and ;/ the number of vibrations per second, it is found by calculation that

n = '- t, /-4 ; - being the ratio of the circumference to the diameter, <f
2ri'\ Trd

the acceleration of gravity.

242 On Sound. [267-

The above formula expresses the following laws : —

I. The stretching weight or tension being constant, the number of vibra-
tions in a second is inversely as the length.

II. The number of vibrations in a second is inversely as the diameter of
the string.

III. The 7iumber of vibrations in a second is directly as the square root of
the stretchiiig weight or tensiott.

IV. The 7mmber of tnbrations in a second of a string is inversely as the
square root of its de7isity.

These laws are applied in the construction of stringed instruments, in
which the length, diameter, tension, and material of the strings are so
chosen that given notes may be produced from them.

268. Experimental verification of the laws of the transverse vibra-
tion of string's. — Laiu oj the lengths. In order to prove this law, we may call
to mind that the relative numbers of vibrations of the notes of the gamut are
CDEFGABc

T 9 5 4 3 5 1_5 .,

If now the entire length of the sonometer be made to vibrate, and then, by
means of the bridge B, the lengths |, |, f, |, f, ^, |, which are the inverse of
the above numbers, be successively made to vibrate, all the notes of the
gamut are successively obtained, which proves the first law.

Law of the diameters. This law is verified by stretching upon the sono-
meter two cords of the same material, the diameters of which are as 3 to 2,
for instance. When these are made to vibrate, the second cord gives the
fifth above the other ; which shows that it makes three vibrations while the
first makes two.

Latu of the tensions. Having placed on the sonometer two identical
strings, they are stretched by weights which are as 4:9. The second now
gives the fifth of the first, from which it is concluded that the numbers of
their vibrations are as 2 : 3 ; that is, as the square roots of the tensions. If
the two weights are as 16 to 25, the major third or | would be obtained.

Law of the densities. Two strings of the same radius, but different
densities, are fixed on the sonometer. Having been subjected to the same
stretching weight, the position of the movable bridge on the denser one is
altered until it is in unison with the other string. If then ^and d' are the
densities of the two strings, and / and /' the lengths which vibrate in unison,

we find —= ^'^— „. But as we know from the first law that - = '^ , we ha\e
/ s/d V n

= , , which verifies this law. Thus, if a copper wire, whose density is g
n' ^d •' ^'

and a catgut string of the density i, are of equal length and diameter, and

are stretched by the same weight, the vibrations of the copper wire will be

one-third as rapid as those of the string.

The laws of vibrating strings presuppose that they are long, flexible, and

tightly stretched ; but if they are short, stout, and iDut little stretched, the

rigidity of the string comes into play, and the number of vibrations they

make is higher than the theoretical number ; the effect of the rigidity is the

same as if a constant weight were added to the stretching weight. -

-270]

Wind Instrnincnts.

243

269. Nodes and loops. — Let us suppose the string AD (fig. 234) to begin
vibrating, the ends A and D being fixed, and, while it is doing so, let a point
B be brought to rest by a stop, and let us suppose DB to be one-third part
of AD. The part DB must now vibrate about B and D as fixed points in the
manner indicated by the continuous and dotted lines (fig. 235) ; now all parts
of the same string tend to make a vibration in the same time ; accordingly, the
part between "A and B will not perform a single vibration, but will divide into
two at the point C, and vibrate in the manner shown in the figure. If BD
were one-fourth part of AD (fig. 236), the part AB would be subdivided at
C and C into three vibrating portions each equal to BD. The points B, C, C
are called nodes or nodal pohits ; the middle point of the part of the string
between any two consecutive nodes is called a loop or ve7itral segmetit. It
will be remarked that the ratio of BD : BA must be that of some two whole
numbers, for example, i : 2, i : 3, 2 : 3, &c., otherwise the nodes cannot be
formed, since the two portions of the string cannot then be made to vibrate
at the same time, and the vibrations will interfere with and soon destroy one
another.

If now we refer to fig. 235, the existence of the node at C can be easily
proved by bending some light pieces of paper, and placing them as riders
on the string, say

three pieces, one
at C and the others
respectively mid-
way between B and
C, and between C
and A. The one at
C experiences only
a very slight motion,
and remains in its
place, thereby prov-
ing the existence of
a node at C ; the
other two are vio-

Fig. 235.

iiT

Fig. 236.

lently shaken, and in most cases thrown off the string.

When a musical string vibrates between fixed points A and B, its motion
is not quite so simple as might be inferred from the above description. In
point of fact, partial vibrations are soon produced, and superimposed upon
the primary vibrations. The partial vibrations correspond to the half, third,
fourth, &c., parts of the string. It is by these partial vibrations that the
harmonics are produced which accompany the fundamental note due to the
primary vibrations ; they are usually, however, so feeble as to be impercep-
tible to ordinary ears.

270. "Wind instruments.- -In the cases hitherto considered, the sound
results from the vibrations of solid bodies, and the air only serves as a vehicle
for transmitting them. In wind instruments, on the contrary, when the sides
of the tube are of adequate thickness, the enclosed column of air is the sound-
ing body. In fact, the substance of the tubes is without influence on the
fundamental note ; with equal dimensions, it is the same whether the tubes
are of glass, of wood, or of metal. These different materials simply do no

R 2

Fig. 237.

244 Oil Sound. [270-

more than give rise to different harmonics, and thereby impart a different
quahty to the compound tone produced.

In reference to the manner in which the air in tubes is made to vibrate,
wind instruments are divided into iiwiith instruments and reed instruments.

271. iMCouth instruments. — In mouth instruments all parts of the mouth-
piece are fixed. Fig. 238 represents the mouthpiece of an organ pipe, and

fig. 237 that of a whistle, or of a flageolet. In both
figures, the aperture ib is called the mouth ; it is
here that air enters the pipe ; b and o are the lips.,
the upper one of which is bevelled. The mouth-
piece is fixed at one end of a tube, the other end of
which may be either opened or closed. In fig. 238
the tube can be fitted on a wind-chest by means of
the foot P.

When a rapid current of air enters by the mouth,
it strikes against the upper lip, and a shock is pro-
duced which causes the air to issue from bo in an
intermittent manner. In this way, pulsations are
produced which, transmitted to the air in the pipe,
make it vibrate, and a sound is the result. In
order that a pure note may be produced, there must
be a certain relation between the form of the lips
and the magnitude of the mouth ; the tube also
ought to have a great length in comparison with its diameter. The number
of vibrations depends in general on the dimensions of the pipe, and the
velocity of the current of air.

272. Xteed instruments. — In reed instruments a simple elastic tongue
sets the air in vibration. The tongue, which is either of metal or of wood, is
moved by a current of air. The mouthpieces of the oboe, the bassoon, the
clarionet, the child's trumpet, are different applications of the reed, which,
it may be remarked, is seen in its simplest form in the Jew's harp. Some
organ pipes are reed pipes, others are mouth pipes.

Fig. 239 represents a model of a reed pipe as common!)' shown in
lectures. It is fixed on the wind-chest Q of a bellows, and the vibrations of
the reed can be seen through a glass plate, E, fitting into the sides. A
wooden horn, H, strengthens the sound.

Fig. 240 shows the reed out of the pipe. It consists of four pieces : ist,
a rectangular wooden tube closed below and open abo\-e at o ; 2nd, a copper
plate cc forming one side of the tube, and in which there is a longitudinal
aperture, through which air passes from the tube MN to the orifice 0 ; 3rd,
a thin elastic plate, z, called the tongue, which is fixed at its upper end, and
which grazes the edge of the longitudinal aperture, nearly closing it ; 4th, a
curved wire, r, which presses against the tongue, and can be moved up and
down. It thus regulates the length of the tongue, and determines the pitch
of the note. It is by this wire that reed pipes are tuned. The reed being-
replaced in the pipe MN, when a current of air enters by the foot P, the
tongue is compressed, it bends inwards, and affords a passage to air, \\hich
escapes by the orifice o. But, being elastic, the tongue regains its original
position, and performing a series of oscillations successively opens and closes

-274] On the Notes produced by the same Pipe. 245

the orifice. In this way sonorous waves result and produce a note, whose
pitch increases with the velocity of the current.

In this reed the tongue vibrates alternately before and behind the aper-
tuie, and just escapes grazing the edges, as is seen in the harmonium, con-
certina, &c. ; such a reed is called a free reed. But there are other reeds
called beating or striking reeds, in which the tongue, which is larger than
the orifice, strikes against the edges at each oscillation, closing it like a flap.
The reed of the clarionet, repre-
sented in fig. 241, is an example
of this ; it is kept in its place by
the pressure of the lips. The
reeds of the oboe and bassoon
are also of this kind.

273 Of the notes produced
by the same pipe. — Daniel
Bernouilli discovered that the
same organ pipe can be made
to yielr! a succession of notes by
properly varying the force of the
current of air. The results he
arrived at may be thus stated : —

i. If the pipe is open at the
end opposite to the mouthpiece,
then, denoting the fundamental
note by i, we can, by gradually
increasing the force of the cur-
rent of air, obtain successively
the notes 2, 3, 4, 5, &c. ; that is
to say, all the harmonics of the
primary note.

ii. If the pipe is closed at the
end opposite to the mouthpiece,
then, denoting the fundamental note by i, we can, by gradually increasing
the force of the current of air, obtain successively the notes 3, 5, 7, &c. : that
is to say, only the uneven harmo7iics of the primary note.

A closed and an open pipe yield the same fundamental note, if the closed
pipe is half the length of the open pipe, and if in other respects they are the
same ; or, what is an ecjuivalent statement, with a closed and an open pipe
of the same length the former gives a note an octave higher than the latter.

In any case it is impossible to produce from the given pipe a note not
included in the above series respectively.

Although the above laws are enunciated with reference to an organ pipe,
they are true of any other pipe of uniform section.

274. On the nodes and loops of an organ pipe. — The vibrations of
the air producing a musical note take place in a direction parallel to the axis
of the pipe — not transversely, as in the case of the portions of a vibrating
strin* In the former case, however, as well as in the latter, the phenomena
of nodes and loops may be produced. But now by a node must be under-
stood a section of the column of air contained in the pipe, where the particles

Fig. 240.

246

On Sound.

[274-

remain at rest, but where there are rapid alternations of condensation and
rarefactioti. By a loop or ventral segment must be understood a section of
the column of air contained in the pipe where the vibrations of the particles
of air have the greatest amplitudes, and where there is no change of density.
The sections of the column of air are, of course, made at right angles to its
axis. When the column of air is divided into several vibrating portions, it
is found that the distance between any two consecutive loops is constant,
and that it is bisected by a node. We can now consider separately the cases
of the open and closed pipes.

i. In the case of a stopped pipe, the bottom is always a node, for the
layer of air in contact with it is necessarily at rest, and only undergoes
variations in density. At the mouthpiece, on the contrary, where the air has
a constant density (that of the atmosphere), and the vibration is at its maxi-
mum, there is always a loop. In any stopped pipe there is at least one node
and one loop (fig. 242) ; the pipe then yields its fundamental note, and the

Fig.

Fig. 243. Fig. 244.

Fig. 245.

distance VN from the loop to the node is equal to half a condensed or
rarefied wave-length.

If the current of air be forced, the mouthpiece alwaj's remains a loop,
and the bottom a node, the column divides into three equal parts (fig. 243),
and an intermediate node and loop are formed. The sound produced is the
first harmonic. When the second harmonic (5) is produced, there are two
intermediate nodes and two loops, and the tube is then subdivided into five
equal parts (fig. 244), and so on.

ii. In the case of the open pipe, whatever note it produces, there must be
a loop at each end, since the enclosed column of air is in contact with the
external air at those points. When the primary note is produced, there will
be a loop at each end, and a node at the middlesectionof the pipe, the nodes
and loops dividing the column into tzi'o equal parts (fig. 245). When the
first harmonic (2) is produced, there will be a loop at each end, and a loop

-274] On the Nodes and Loops of an Organ Pipe. 247

in the middle, the column being divided into four equal parts by the alternate
loops and nodes (fig. 246). When the second harmonic (3) is produced, the
column of air will be divided into six equal parts by the alternate nodes and
loops, and so on (fig. 247). It will be remarked that the successive modes
of division of the vibrating column are the only ones compatible with the
alternate recurrence at equal intervals of nodes and loops, and with the
occurrence of a loop at each end of the pipe.

There are several experiments by which the existence of nodes and loops
can be shown.

{a) If a fine membrane is stretched over a pasteboard ring, and has

Fig. 24

Fig. 249.

Fig. 250.

Fig. 251.

sprinkled on it some fine sand, it can be gradually let down a tube, as shown
in fig. 250. Now, suppose the tube to be producing a musical note. As the
membrane descends, it will be set in vibration by the vibrating air. But
when it reaches a node it will cease to vibrate, for there the air is at rest.
Consequently, the grains of sand, too, will be at rest, and their quiescence
will indicate the position of the node. On the other hand, when the mem-
brane reaches a loop — that is, a point where the ampUtude of the vibrations

248 On Sound. [274-

of the air attains a maximum — it will be violently agitated, as will be shown
by the agitation of the grains of sand. And thus the positions of the loops
can be rendered manifest.

(/;) Again, suppose a pipe to be constructed with holes bored in one of
its sides, and these covered by little doors which can be opened and shut, as
shown in fig. 248. Let us suppose the little doors to be shut and the pipe to
be caused to produce such a note that the nodes are at N and N' and the
loops at V, V, V". At the latter points the density is that of the external
air, and consecjuently if the door at V is opened no change is produced in
the note. At the former points, N and N', condensation and rarefaction are
alternately taking place. Ifnow the door at N' is opened, this alternation
of density is no longer possible, for the density at this open point must be
the same as that of the external air, and consequently N' becomes a loop,
and the note yielded by the tube is changed. The change of notes, produced
by changing the fingering of the flute, is one form of this experiment.

{c) Suppose A, in fig. 249, to be a pipe emitting a certain note, and sup-
pose P to be a plug, fitting the tube, fastened to the end of a long rod by
which it can be forced down the tube. Now when the plug is inserted,
whatever be its position, there will be a node in contact with it. Conse-
quently, as it is gradually forced down, the note yielded by the pipe will
keep on changing. But every time it reaches a position which was occupied
by a node before its insertion, the note becomes the same as the note
originally yielded. For now the column of air vibrates in exactly the same
manner as it did before the plug was put in.

{d) Fig. 251 shows another mode of illustrating the same point, which is
identical in principle with Konig's manometric flames. The figure repre-
sents an organ pipe, on one side of which is a chest, P, filled with coal gas,
by means of the tube S. The gas from the chest comes out in three jets. A,
B, C, and is then ignited. The manner in which the gas passes from the
chest to the point of ignition is shown in the smaller figure, which is an
enlarged section of A. A circular hole is bored in the side of the pipe and
covered with a membrane r. A piece of wood is fitted into the hole so as
to leave a small space between it and the membrane. The gas passes from
the chest, in the direction indicated by the arrow, into the space between
the membrane and the piece of wood, and so out of the tube, ;;/, at the mouth
of which it is ignited. Now suppose the pipe to be caused to yield its
primary note, then as it is an open pipe there ought to be a node at B,
its middle point. Consequently, there ought to be rapid changes of density
at B ; these would cause the membrane, r, to vibrate, and thereby blow out
the flame, ///, and this is what actually happens. If by increasing the force
of the wind the octave to the primary note is produced, B will be a loop,
and A and C nodes. Consequently the flames at A and C will now be ex-
tinguished, as is, in point of fact, the case. But at B, there being no change
of density, the membrane is unmoved, and the flame continues to burn
steadily.

By each and all of these experiments it is shown that in a given pipe,
whether open or closed, there are always a certain number of nodes, and
midway between any two consecutive nodes there is always a loop ox ventral
seifinent.

-276J Existence of Nodes and Loops in a Musical Pipe. 249

275. Formulae relative to the number of vibrations produced by a

musical pipe It follows from what has been said that the column of air

in stopped pipes is always divided by the nodes and loops into an uneven
number of parts which are equal to each other, and each of which is a quarter
of a complete vibration (figs. 242, 243, and 244), while in an open pipe it is
divided into an even number of such parts (figs. 245, 246, 247). If L be the
length of the pipe, / the wave-length of the sound which it emits, and p any

whole number, then for stopped pipes we have L = (2/ + i) -; and for
open pipes L = 2/- = ^ . Replacing in each of these formula; /by its value
- (2^:;) we have L = (2/) + i) "'' and L =^''' ; from which for stopped pipes

1 {16 + \]V , r M'

we ha\e ;/ = ^^i- — ^, and lor open ones ii = -^.

4L 2L

The laws connecting the length of pipes with the note produced only hold
for narrow pipes, those, for instance, whose length is not less than 12 times
their diameter ; for shorter pipes organ builders have various empirical rules.
AVithin wide limits the formula holds, L' = L - 1^, where L is the theoretical
length, L' the length sought, while ^is the diameter of the round pipe.

If, in the first formula, we give to/ the successive values o, i, 2, 3,4, &c.,

we have n = "-' , 51- ^'^'' that is, the fundamental sound and all its uneven
4L' 4L 4L

harmonics ; and in the formula for the open pipe we get similarly ^ , " ,A^-,

&c., that is, the fundamental note and all its harmonics even and uneven.

276. Sxplanation of the existence of nodes and loops in a musical
pipe The existence of nodes and loops is to be explained by the co-
existence in the same pipe of two equal waves tra\-elling in contrary
directions.

Let A (fig. 252) be a point from which a series of waves sets out towards
B, and let the length of these waves, whether of condensation or rarefaction.

Fig. 252.

be AC, CD, DB. And let B be the point from which the series of exactly
equal waves sets out towards A. It must be borne in mind that in the case
of a wave of condensation originating at A the particles move in the direc-
tion A to B, but in a wave of condensation originating at B they move in the
direction B to A. Now let us suppose that condensation at C, caused by the
wave from A, begins at the same instant that condensation caused by the
wave from B begins at D. Consequently, restricting our attention to the
particles in the hne CD, at any instant the velocities of the particles in CD
due to the former wave will be represented by the ordinates of the curve

2 50 On Sound. [276-

SPRT, while those due to the wave from B will be represented by the co-
ordinates of the curve TQrS. Then, since the waves travel with the same
velocity, and are at C and D respectively at the same instant, we must have,
for any subsequent instant, CR equal to Dr. If, therefore, N is the middle
point between C and D, we must have rN equal to RN, and consequently
PN equal to QN ; that is to say, if the particle at N transmitted only one
vibration, its motion at each instant would be in the opposite phase to that
of its motion if it transmitted only the other vibration. In other words, the
particle N will at every instant tend to be moved with equal velocity in
opposite directions by the two waves, and therefore will be permanently at
rest. That point is therefore a node. In like manner there is a node at N'
midway between A and C, and also at N" midway between B and D. In
regard to the motion of the remaining particles, it is plain that their respec-
tive velocities will be the (algebraical) sum of the velocities they would at
each instant receive from the waves separately. Hence, at the instant indi-
cated by the diagram, they are given by the ordinates of the curve HNK.
This curve will change from instant to instant, and at the end of the time
occupied by the passage of a wave of condensation (or of rarefaction) from
C to D will occupy the position shown by the dotted line Ji^k. It is evident
therefore that particles near N have but small changes of velocity, whilst those
near C and D experience large changes of velocity.

If the curve HK were produced both ways, it would always pass through
N' and N'^ ; the part, however, between N and W would sometimes be on
one side, and sometimes on the other side of AB. Hence all the particles
between N' and N have simultaneously, first a motion in the direction A to
B, and then a motion in the direction B to A, those particles near C having
the greatest amplitude of vibrations. Accordingly near N and N' there will
be alternately the greatest condensation and rarefaction.

This explanation applies to the case in which AB is the axis of an open
organ-pipe, A being the end where the mouthpiece is situated. The waves
from B have their origin in the reflections of the series of waves from A. In
the particular case considered, the note yielded by the pipe is that indicated
by 3 ; that is, the fifth above the octave to the primary note. A similar ex-
planation can obviously be applied to all other cases, and whether the end
be opened or closed. But in the latter case the series of waves from the
closed end must commence at a point distant from the mouthpiece by a
space equal to one half, or three halves, or five halves, &c., of the length of
a wave of condensation or expansion.

277. Kundt's determination of the velocity of sound.^Kundt has
devised a method of determining the velocity of sound in solids and in
gases which can be easily performed by means of simple apparatus, and is
capable of great accuracy. A glass tube, BB', about two yards long (fig. 253)
and two inches in internal diameter, is closed at one end by a movable
stopper, b; the other end is fitted with a cork, KK, which tightly grasps a
glass tube, AA', the same length, but of smaller diameter. This is closed
at one end by a piston, a, which moves with gentle friction in the outer
tube, BB'. Then by rubbing the free end of the tube, AA', with a wet cloth,
it produces longitudinal vibrations, and these transmit their motion to the
air in the tube ab. If the tube ab contain some lycopodium powder, or, still

CJieviical Harinonicon.

251

fii

-278]

better, powdered cork, this is set in active vibration and then arranges itself
in small patches in a certain definite order, as represented in the figure, the
nature and arrangement of which depend on the vibrating part
of the rod and the tube.

These heaps represent the nodes, and the mean distance d
between them can be measured with great accuracy ; it repre-
sents the distance between two nodes, or, half a wave-length ;
that is, the wave-length of the sound in air is id. If the rod
has the length s and is grasped in the middle by the cork KK,
from the law of the longitudinal vibrations of rods (281), the
wave-length of the sound it then emits is twice its length, or 2^.
That is, the wave-length of the vibrating column of air is to
that in the rod as id : is. As the velocity of sound in any
body is equal to the wave-length in that body multiplied by the
number of vibrations in a second ; and since the number of
vibrations is here the same in both cases, for the note is the
same, the velocity of sound in the glass is to the 'velocity of
sound in air as isn : idn, that is, as ^ : ^. Thus when the glass
tube was clamped in the middle by KK, so that the length a^
was equal to half the length of the tube AA', the number of the
ventral segments was found to be eight. This corresponds to
a ratio of wave-length of i to 16 ; in other words, the velocity
of sound in glass is 16 times that in air.

The method is capable of great extension. By means of
the stopcock m, different gases could be introduced instead of
air, and corresponding differences found for the length of the
ventral segments ; from which, by a simple calculation, the cor-
responding velocities were found. Thus the velocities of sound
in carbonic acid, coal gas, and hydrogen were found to be
respectively o'8, r6, and 3"56 that of air, or nearly as the inverse
squares of the densities.

So also, by varying the material of the rod A A', different
velocities are obtained. Thus the velocity in steel was found to
be I5'24, and that in brass 10-87 that of air.

Kundfs figures may also be obtained by providing glass
tubes a yard or two in length with lycopodium powder, as in
the above experiment, and hermetically sealing them at both
ends. The tubes are then put into longitudinal vibrations ;
instead of air they may be filled with hydrogen or any other gas.

Using this method, with iron filings instead of lycopodium, Kundt and
Lehmann determined the velocity of sound in water contained in glass tubes
of various diameters and thicknesses ; the thicker the tubes and the smaller
their diameter, the more nearly do the results agree with those required by
theory and with those obtained by Colladon and Sturm (234).

278. Chemical barmonicon. — The air in an open tube may be made to
give a sound by means of a luminous jet of hydrogen, coal gas, &c. When
a glass tube about 12 inches long is held over a lighted jet of hydrogen
(fig. 254), a note is produced, which, if the tube is in a certain position, is the
fundamental note of the tube. The sounds are considered to arise from the

r-K

Fig. 253.

On Sound.

[278-

successive, exceedingly rapid explosions produced by the periodic combina-
tions of the atmospheric oxygen with the issuing jet of hydrogen. The
apparatus is called the chemical Jiarmonicon.

Coal gas may be used in this experiment instead of hydrogen, and
indeed from its brighter flame is more advantageous. A thin metal pipe
about 8 inches in length and with a narrow aperture is fitted to an ordinary
burner, which is supplied with gas through a caoutchouc tube connected with
a reservoir of the gas which is under rather higher pressure than usual.

The note depends on the size of the flame and the length of the tube :
with a long tube, by varying the position of the
jet in the tube, the series of notes, in the ratio
I : 2 : 3 : 4 : 5, is obtained.

If, while the tube emits a certain sound, the
voice or the syren (242) be gradually raised to the
same height, as soon as the note is nearly in
unison with the harmonicon, the flame becomes
agitated, jumps up and down, and is finally steady
when the two sounds are in unison. If the note
of the syren is gradually heightened the pulsations
again commence ; they are the optical expressions
of the beats (262) which occur near perfect unison.
If, while the jet burns in the tube and produces
a note, the position of the tube is slightly altered,
a point is reached at which no sound is heard. If
now the voice, or the syren. Or the tuning-fork, be
pitched at the note produced by the jet, it begins
to sing, and continues to sing even after the syren
is silent. A mere noise, or shouting at an incorrect
pitch, agitates the flame, but does not cause it to
sing.

These effects may be conveniently studied by
p;,, means of a gas-burner, over which, at a distance

of four inches, a ring covered with fine wire gauze
is fixed. The gas is lighted above the gauze, and forms a very sensitive
flame, especially when a moderately wide tube is held over the gauze. If
the gauze is raised with the tube, the flame becomes duller and smaller, but
begins to sound with a uniform loud tone. If now the gauze is lowered so
that the flame is just silent, it begins at once when a sound is produced,
but ceases with the sound.

If a metal tube 4 cm. wide and 15 to 20 cm. high, closed at the bottom by
a wire gauze, is held vertically over a Bunsen's jet, an acute sound is heard,
almost as loud as the whistle of a locomotive, on lighting the gas inside the
tube.

279. String-ed instruments. — Stringed musical instruments depend on
the production of transverse vibrations. In some, such as the piano, the
sounds are constant, and each note requires a separate string ; in others,
such as the violin and guitar, the sounds are 7'aried by the fingering, and
can be produced by fewer strings.

In the piano the vibrations of the strings are produced by the stroke of

-279] Stringed Instruments. 253

the /uiiiiiucr, which is moved by a series of bent levers communicating with
the ke\s. The sound is strengthened by the vibrations of the air in the
sounchng board on which the strings are stretched. Whenever a key is
struck, a damper is raised which falls when the finger is removed from the
key, and stops the vibrations of the corresponding string. By means of a
pedal all the dampers can be simultaneously raised, and the vibrations then
last for some time.

The karp is a sort of transition from the instruments with constant to
those with variable sounds. Its strings correspond to the natural notes of the
scale ; by means of the pedals the length of the vibrating parts can be
changed, so as to produce sharps and flats. The sound is strengthened by
the sounding-box, and by the vibrations of all the strings harmonic with
those played.

In the violin and guitar each string can give a great number of sounds
according to the length of the vibrating part, which is determined by the
pressure of the fingers of the left hand while the right hand plays the bow,
or twitches the strings themselves. In both these instruments the vibra-
tions are communicated to the upper face or belly of the sounding-box by
means of the bridge over which the strings pass. These vibrations are
communicated from the upper to the lower face or back of the box either by
the sides or by an intermediate piece called the sound-post. The air in the
interior is set in vibration by both faces, and the strengthening of the sound
is produced by all these simultaneous vibrations. The value of the instru-
ment consists in the perfection with which all possible sounds are intensified,
which depends essentially on the quality of the wood, the mellowness of
which increases with age, and on the relative arrangement of the parts.

The number and strength of the harmonics produced in a twitched or
stroked string varies with the manner in which it is sounded and with the
nature of the string. The sharper the edge of the exciting body the shorter
and broader are the waves, and therefore the higher and stronger are the
harmonics and the shriller the clang ; if the strings are struck with a metal
rod the harmonics are so predominant that the fundamental note is scarcely
heard, and thus what is called a hollow sound is produced. The tone is
fullest when struck with the finger, and somewhat less so with a soft hammer,
as in the piano. The deeper harmonics are often stronger than the funda-
mental note, so that the note is not so strong but is richer ; all the har-
monics, whose nodes are in the place struck, are wanting. If a string is struck
in the middle, none of the even harmonics are produced, and therefore all the
octaves of the fundamental note are wanting ; the tone is nasal and hollow.
This is the characteristic of a note which is wanting in the harmonics nearer
and most allied to the fundamental note. If the string is struck near one end,
the clang has a jingling character. Instrument makers, led by practised
ears, have long found it advantageous that the piano be struck at about
one-seventh of the length of the string ; the reason for this advantage lies in
the fact that in this way the seventh and ninth harmonics, which are unhar-
monic with each other, are deadened, while the deeper harmonics — the
octaves, fifths, thirds— preponderate, and the clang is rich and harmonious-

The higher harmonics fade away in gut-strings more rapidly than in
metal wires ; hence the guitar and the harp are not so jingling as the zither.

2 54 On Sound. [280-

280. "Wind instruments. — All wind instruments may be referred to the
different types of sounding tubes which have been described. In some, such
as the organ, the notes ax&Jixed, and require a separate pipe for each note,
in others the notes are variable, and are produced by only one tube : the
flute, horn, &c., are of this class.

In the organ the pipes are of various kinds ; namely, mouth pipes, open
and stopped, and reed pipes with apertures of various shapes. By means of
stops the organist can produce any note by both kinds of pipe.

In the/iute, the mouthpiece consists of a simple lateral circular aperture;
the current of air is directed by means of the lips, so that it grazes the edge
of the aperture. The holes at different distances are closed either by the
fingers or by keys ; when one of the holes is opened, a loop is produced in
the corresponding layer of air, which modifies the distribution of nodes and
loops in the interior, and thus alters the note. The whistling of a key is
similarly produced.

The pandccan pipe consists of stopped pipes of different lengths corre-
sponding to the different notes of the gamut.

In the trumpet, the horn, the trombone, cornet-a-piston, and ophicleide,
the lips form the reed, and vibrate in the mouthpiece. In the //<7r«, different
notes are produced by altering the distance of the lips. In the trombone^
one part of the tube slides within the other, and the performer can alter
at will the length of the tube, and thus produce higher or lower notes. In
the cornet-a-piston, the tube forms several convolutions ; pistons placed at
different distances can, when closed, cut off communication with other parts
of the tube, and thus alter the length of the vibrating column of air.

-281]

Vibration of Rods.

255

CHAPTER V.

VIBRATION OF RODS, PLATES, AND MEMBRANES.

281. Vibration of rods. — The term rods is applied in acoustics to solids
whose length is considerable in proportion to their breadth and thickness ;
they are nevertheless so broad and thick that, while they have not the
llexibility of strings, they have yet elasticity enough to vibrate without being
stretched like strings. They are ordinarily of wood, glass, metal, and more
particularly of tempered steel. Like strings, they have two kinds of vibra-
tions, lo7tgitudinal and transverse. The latter are produced by fixing the
rods at one end, and passing a bow across the free part. Longitudinal
vibrations are produced by fixing the rod at any part, and rubbing it length-
wise with a piece of cloth sprinkled
with resin. But in the latter case
the sound is only produced when
the rod has been fixed at some
aliquot part of its length from the
end, as a half, a third, or a quarter.

It is shown by calculation that
tJie number of transverse vibratioiis
made in a given time by rods and
thin plates of the same material is
directly as their thickness and ift-
versely as the square of their length.
The width of the plate does not
affect the number of vibrations. A
wide plate, however, requires a
greater force to set it in motion than
a narrow one. It is, of course, pre-
supposed that one end of the vibrat-
ing plate is clamped or is otherwise
held firmly.

The laws of the longitudinal vi-
brations of strings are expressed in

the formula « * , ,

2r/ V -nd
ti, r, /, d, and g have all the same
meaning as in the formula for the
transverse vibrations, while /x is the F^s- -55-

modulus of elasticity of the string,

the number which expresses the weight by which it must be stretched in
order to elongate by its own length (88).

— A / eT, in which

;r/ V 71

2 56 On Sound. [281-

Fig. 255 represents an instrument invented by Marloye, and known as
Marloye's Jim-p, based on the longitudinal vibration of rods. It consists of
a solid wooden pedestal, in which are fixed twenty thin deal rods, some
coloured and others white. They are of such a length that the white rods
give the diatonic scale, while the coloured ones give the semitones and
complete the chromatic scale. The instrument is played by rubbing the
rods in the direction of their length between the finger and thumb, which
have been previously covered with powdered resin. The notes produced
resemble those of a pandasan pipe.

The tuning-fork., the triangle., and musical boxes, are examples of the
transverse vibrations of rods. In musical boxes, small plates of steel of
dititerent dimensions are fixed on a rod, like the teeth of a comb. A cylinder
whose axis is parallel to this rod, and whose surface is studded with steel
teeth, arranged in a certain order, is placed near the plates. By means of
a clockwork motion, the cylinder rotates, and the teeth striking the steel
plates set them in vibration, producing a tune, which depends on the arrange-
ment of the teeth on the cyhnder.

If a given rod be clamped either in the middle, or at both ends, the
wave-length of the note produced by making it vibrate longitudinally is
double its own length ; and if it be clamped at one end only, and made to
vibrate longitudinally, the wave-length of the sound is four times its own
length. Thus the former case is analogous to an open pipe, and the latter to
a stopped pipe, in respect of the notes produced.

The velocity of sound in any solid may be determined experimentally by
clamping it at one end and putting it in longitudinal vibrations. The length
of a stopped pipe is next ascertained which gives the same note. The
velocity of sound in the material in question is thus to its velocity in air in
the same ratio as the length of the rod to the length of the stopped pipe.
Thus a rod of alder a metre in length was found to give the same longitudinal
note as a stopped pipe 7 cm. in length ; the velocities are accordingly as
100 : 7, or the velocity of sound in this wood is 14-3 times that in air.

Stefan has determined the velocity of sound in soft bodies by attaching
them, in the form of rods, to long glass or wooden rods. The compound
rod was made to vibrate and the number of vibrations of the note was de-
termined. Knowmg this, and also the velocity of sound in the longer rod,
the velocity in the shorter rod was at once obtained. By this method some
of the numbers in the table in article 235 were obtained.

Scratching and scraping sounds are pi^oduced by moving a i^od over a
smooth surface ; the rod is thereby put in vibration, which vibrations are
regular for a short interval, but frequently change their period during the
motion.

282. Vibration of plates. — In order to make a plate vibrate, it is fixed
in the centre (fig. 256), and a bow rapidly drawn across one of the edges ;
or else it is fixed at any point of its surface, and caused to vibrate by
rapidly drawing a string covered with resin against the edges of a central
hole (fig. 257).

Vibrating plates contain nodal lines (269), which vary in number and
position according to the form of the plates, their elasticity, the mode of
excitation, and the number of vibrations. These nodal lines may be made

-282] Vibrations of Plates. 257

visible by covering the plate with fine sand, before it is made to vibrate.
As soon as the vibrations commence, the sand leaves the vibrating parts,
and accumulates on the nodal lines, as seen in figs. 256 and 257.

The position of the nodal lines may be determined by touching the
points at which it is desired to produce them. Their number increases with
the number of vibrations ; that is, as the note given by the plates is higher.
The nodal lines always possess great symmetry of form, and the same form

Fig. 256.

Fig. 257.

is always produced on the same plate under the same conditions. They
were discovered by Chladni, and the plates are known as Chladni's plates.

The vibrations of plates are governed by the following law : — In plates
of the same kind and shape, atid giving the same system of nodal lines, the
number of vih'ations i?i a second is directly as the thickness of the plates, and
inversely as their area.

Gongs and cymbals are examples of instruments in which sounds are
produced by the vibration of metal plates. The glass and the steel harmo-
nicon depend on the vibrations of glass and of steel plates respectively.

Bells, which are to be regarded as curved plates, never vibrate as a whole
but when they give their fundamental note in four equal parts which are
separated by nodal lines. This can be shown by suspending pith balls by
silk threads from the ends of glass rods arranged crosswise, so that the pith
balls just rest against the rim of a bell jar held vertically with the mouth
upwards. When this is made to sound by drawing a bow across the edge,
the balls are powerfully repelled from the ventral segments, but with far less
force from the nodes.

Bells are also capable of vibrating in 6, 8, 10, or 12 parts, producing thus
a corresponding series of over-tones. The note of a bell is higher in pro-
portion as the surface is smaller and the substance thicker.

If water is poured into a bell jar which is made to vibrate by means of a
violin bow, the surface of the water forms a series of nodes and segments,
and water is projected in the form of spray from the ventral segments. If
alcohol or ether be used instead of water, a number of droplets form and
group themselves into beautiful starlike figures.

258

On Sound.

[283-

283. Vibration of membranes. — In consequence of their flexibility,
membranes cannot vibrate unless they are stretched, like the skin of a drum.
The sound they give is more acute in proportion as they are smaller and
more tightly stretched. To obtain vibrating membranes, Savart fastened
gold-beater's skin on wooden frames.

In the drum., the skins are stretched on the ends of a cylindrical box.
When one end is struck, it communicates its vibrations to the internal
column of air, and the sound is thus considerably strengthened. The cords
stretched against the lower skin strike against it when it vibrates, and pro-
duce the sound characteristic of the drum.

Membranes either vibrate by direct percussion, as in the drum, or they
may be set in vibration by the vibrations of the air, as Savart has observed,,

provided these vibrations are sufficiently intense. Fig. 258 shows a mem-
brane vibrating under the influence of the vibrations in the air caused by
a sounding bell. Fine sand strewn on the membrane shows the formation
of nodal lines just as upon plates.

Membranes are eminently fitted for taking up the vibrations of the air,
on account of their small mass, their large surface, and the readiness with
which they subdivide. With a pretty strong whistle, nodal lines may be
produced in a membrane stretched on a frame, even at the distant end of a
large room.

The phenomenon so easily produced in easily-moved bodies is also found
in larger and less elastic masses ; all the pillars and walls of a church vibrate
more or less while the bells are being rung.

284]

Method of making Vibrations apparent.

259

CHAPTER VI.

GRAPHICAL METHOD OF STUDYING VIBRATORY MOTIONS.

284. lissajous'inelhodof making: vibrations apparent.— The method
of Lissajous exhibits the vibratory motion of bodies either directly or by
projection on a screen. It has also the great advantage that the vibratory
motions of two sounding bodies maybe compared without the aid of the ear.,
so as to obtain the exact relation between them.

This method, which depends on the persistence of visual sensations on
the retina (625), consists in fixing a small mirror on the vibrating body, so as
to vibrate with it, and impart to a luminous ray a vibratory motion similar
to its own.

Lissajous uses tuning-forks, and fixes to one of the prongs a small
metal mirror, m (fig. 259), and to the other a counterpoise, ;?, which is

^^XAAAi:

Fig 259

necessary to make the tuning-fork vibrate regularly for a long time. At a
few yards' distance from the mirror there is a lamp surrounded by a dark
chimney, in which is a small hole giving a single luminous point. The
tuning-fork being at rest, the eye is placed so that the luminous point is seen
at o. The tuning-fork is then made to vibrate, and the image elongates so
as to form a persistent image, fz, which diminishes in proportion as the

26o On Sound. [284-

amplitude of the oscillation decreases. If, during the oscillation of the
mirror, it is made to rotate by rotating the tuning-fork on its axis, a sinuous
line, oix., is produced instead of the straight line oi. These different effects
are explained by the successive displacements of the luminous pencil, and
Ijy the duration of these luminous impressions on the eye after the cause
has ceased — a phenomenon to which we shall revert in treating of
vision.

If, instead of viewing these effects directly, they are projected on a
screen, the experiment is arranged as shown in fig. 260 ; the pencil reflected

from the vibrating mirror is reflected a second time from the fixed mirror, ;;/,
which sends it towards an achromatic lens, /, placed so as to project the
images on the screen.

285. Combination of two vibratory motions intbe same direction. —

Lissajous resolved the problem of the optical combination of two vibratory
motions — vibrating at first in the same direction, and then at right angles to
each other.

Fig. 261 represents the experiment as arranged for combining two
parallel motions. Two tuning-forks provided with mirrors are so arranged
that the light reflected from one of them reaches the other, which is almost
parallel to it, and is then sent towards a screen after having passed through
a lens.

If now the first tuning-fork alone vibrates, the image on the screen is
the same as in figure 261 ; but if they both vibrate, supposing they are in
unison, the elongation increases or diminishes according as the simultaneous
motions imparted to the image by the vibrations of the mirrors do or do not
coincide.

optical Combination of Tzvo Vibratory Motions. 261

If the tuning-forks pass their position of equihbrium in the same time
and in the same direction, the image attains its maximum ; and the image
is at its minimum when they pass at the same time but in opposite direc-
tions. Between these two extreme cases, the ampHtude of the image varies
according to the time which elapses between the exact instant at which the
tuning-forks pass through their position of rest respectively. The ratio of

this time to the time of a double vibration is called a differeitce of phase of
the vibration.

If the tuning-forks are exactly in unison, the luminous appearance on the
screen experiences a gradual diminution of length in proportion as the ampli-
tude of the vibration diminishes ; but if the pitch of one is very little altered,
the magnitude of the image varies periodically, and, while the beats resulting

g. 262.

from the imperfect harmony are distinctly heard, the eye sees the concomi-
tant pulsations of the image.

286. Optical combination of two vibratory motions at rigrht angles
to each other. — The optical combination of two rectangular vibratory
motions is effected as shown in figure 262 ; that is, by means of two tuning-
forks, one of which is horizontal and the other vertical, and both provided

262 On Sound. [286-

with mirrors. If the horizontal fork first vibrates alone, a horizontal luminous
outline is seen on the screen, while the vibration of the other produces a
vertical image. If both tuning-forks vibrate simultaneously, the two motions
combine, and the reflected pencil describes a more or less complex cui-ve,
the form of which depends on the number of vibrations of the two tuning-
forks in a given time. This curve gives a valuable means of comparing the
number of vibrations of two sounding bodies.

Fig. 263.

Fig. 263 shows the luminous image on the screen when the tuning-forks
are in unison ; that is, when the number of vibrations is equal.

The fractions below each curve indicate the differences of phase between
them. The initial form of the curve is determined by the difference of phase.
The curve retains exactly the same form when the tuning-forks are in unison,
provided that the amplitudes of the two rectangular vibrations decrease in
the same ratio.

Fig. 264.

If the tuning-forks are not quite in unison, the initial difference of phase
is not preserved, and the curve passes through all its variations.

Fig. 264 represents the different appearances of the luminous image
when the difference between the tuning-forks is an octave : that is, when the

-287]

Leon Scott's PJionautograph.

263

numbers of their vibrations are as 1:2; and fig. 265 gives the series of
curves when the numbers of the vibrations are as 3 : 4.

It will be seen that the curves are more complex when the ratios of the

Fig. 265.

numbers of vibrations are less simple. Lissajous examined these curves
theoretically, and has calculated their general equations.

When these experiments are made with the electric light, instead of an
ordinary lamp, the phenomena are remarkably brilliant.

287. Iieon Scott's Phonautograpta. — This apparatus registers not only
the vibrations produced by solid bodies, but also those produced by wind in-
struments, by the voice in singing, and even by any noise whatsoever ; for

264

On Sound.

[287-

instance, that of thunder, or the report of a cannon. It consists of an elhp-
soidal barrel, AB, about a foot and a half long and a foot in its greatest dia-
meter, made of plaster of Paris. The end A is open, but the end B is
closed by a solid bottom, to the middle of which is fixed a brass tube a, bent
at an elbow and terminated by a ring, on which is fixed a flexible membrane
which, by means of a second ring, can be stretched to the required extent.
Near the centre of the membrane, fixed by sealing-wax, is a hog's bristle,
which acts as a style, and, of course, shares the movements of the membrane.
In order that the style shall not be at a node^ the stretching ring is fitted
with a movable piece, z, or subdivider, which, being made to touch the mem-
brane first at one point and then at another, enables the experimenter to
alter the arrangements of the nodal lines at will. By means of the sub-
divider, the point is made to coincide with a loop ; that is, a point where the
vibrations of the membrane are at a maximum.

When a sound is produced near the apparatus, the air in the ellipsoid,
the membrane, and the style will vibrate in unison with it, and it only remains
to trace on a sensitive surface the vibrations of the style, and to fix them.
For this purpose there is placed in front of the membrane a brass cylinder,
C, turning round a horizontal axis by means of a handle, ;;/. On the pro-

Fig. 267.

P ig. 268.

longed axis of the cylinder a screw is cut which works in a nut ; conse-
quently, when the handle is turned, the cylinder gradually advances in the
direction of its axis. Round the cylinder is wrapped a sheet of paper
covered with a thin layer of lampblack.

The apparatus is used by bringing the prepared paper into contact with
the point of the style, and then setting the cylinder in motion round its axis.
So long as no sound is heard, the style remains at rest, and merely removes
the lampblack along a line which is a helix on the cylinder, but which be-
comes straight when the paper is unwrapped. But when a sound is heard,
the membrane and the style vibrate in unison, and the line traced out is no
longer straight, but undulates, each undulation corresponding to a double

-288]

Koniz's Mano metric Flames.

>6s

vibi-ation of the style. Consequently, the figures thus obtained faithfully
denote the number, amphtude, and isochronism of the vibrations.

Fig. 267 shows the trace produced when a simple note is sung, and
strengthened by means of an upper octave. The latter note is represented
by the curve of lesser amplitude. Fig. 268 represents the sound produced
jointly by two pipes whose notes ditfer by an octave. The lower line ot
fig. 269 represents the rolling sound of the letter R when pronounced with
a ring.

The upper line of fig. 269 represents the perfectly isochronous vibrations
of a tuning-fork placed near the ellipsoid. This line was traced by a fine
point on one branch of the fork, which was thus found to make exactly 500
vibrations per second. Hence, each undulation of the upper line corresponds
to the 5^^ part of a second ; and thus these lines become very exact means
of measuring short intervals of time. For example, in fig. 269 each of the
separate shocks producing the rolling sound of the letter R corresponds to
about 18 double vibrations of the tuning-fork, and consequently lasts about
i*- or about J^ of a second.

288. Konigr's manometric flames. — Konig's method consists in trans-
mitting the motion of the waves which form a sound to gas flames, which,
by their pulsations, indicate the nature of the sounds. For this purpose a

^:T

^--kk-

.^jaJ

Fig. 270.

metal capsule, represented in section at A, fig. 270, is divided into two com-
partments by a thin membrane ot caoutchouc ; on the right of the figure
is a gas jet, and below it a tube conveying coal gas ; on the left is a tubu-
lure, to which may be attached a caoutchouc tube. The other end of this

266 On Sound. [288-

may be placed at the node of an organ-pipe (274), or it terminates in a
mouthpiece in front of which a given note may be sung ; this is the arrange-
ment represented in fig. 270.

Fig. 271.

Fig. 272.

When the sound-waves enter the capsule by the mouthpiece and the
tube, the membrane yielding to the condensation and rarefaction of the
waves, the coal gas in the compartment on the right is alternately contracted
and expanded, and hence are produced alternations in the length of the

Fig. 273.

flame, which are, however, scarcely perceptible when the flame is observed
directly. But to render them distinct they are received on a mirror with
four faces, M, which may be turned by two cog-wheels and a handle. As

-289]

Dcterini)iation of the Intensity of Sotuids.

267

long as the flame burns steadily, there appears in the mirror, when turned, a
continuous band of light. But, if the capsule is connected with a sounding
tube yielding the fundamental note, the image of the flame takes the form
represented in fig. 271, and that of the figure 272 if the sound yields the
octave. If the two sounds reach the capsule simultaneously, the flame has
the appearance of fig. 273 ; in that case, however, the tube leading to the
capsule must be connected by a T-pipe with two sounding-tubes, one giving
the fundamental note, and the other the octave. If one gives the funda-
mental note and the other the third, the flame has the appearance of figure 274.
If the vowel E be sung in front of the mouthpiece first upon f, and then

K,g. .70.

upon c' , the rotating mirror gives the flames represented in figs. 275 and
276.

289. Determination of the intensity ot sounds. — Meyer has devised
a plan by which the intensities of two sounds of the same pitch may be
directly compared. The two sounds are separated from each other by a
medium impervious to sound, and in front of each of them is a resonance
globe (255) accurately tuned to the sound. Each of these resonance globes
is attached by means of caoutchouc tubes of equal length to the two ends of
a U-tube, in the middle of the bend of which is a third tube provided with a
manometric capsule.

If the resonance globes are each at the same distance from the sounding
bodies, and if the note of only one of them is produced, the flame vibrates.
If both sounds are produced, and they are of the same intensity, and in the
same phase, they interfere completely in the tube, so that the flame of the
manometric capsule is quite stationary', and appears in the turning mirror as
a straight luminous band.

If, however, the sounds are not of the same intensity, the interference
will be incomplete, and the luminous band will be jagged at the edge. The
distance of one of the sounds from the resonance globes is altered until the

268

On Sound.

[289-

flame is stationary. The intensities of the two sounds are thus directly as
the squares of their distances from the resonators.

290. Acoustic attraction and repulsion. — It was observed by Guyot,
and afterwards independently by Guthrie and by Schellbach, that a sound-
ing body, one in a state of vibration therefore, exercises an action on a
body in its neighbourhood which is sometimes one of attraction and some-
times of repulsion. The vibrations of an elastic medium attract bodies
which are specifically heavier than itself, and repel those which are specifi-
cally lighter. Thus a balloon of goldbeater's skin filled with carbonic acid
is attracted towards the opening of a resonance-box on which is a vibrating
tuning-fork ; while a similar balloon filled with hydrogen and tied down by
a thread is repelled. This result always follows, even when the hydrogen
balloon is made heavier than air by loading it with wax.

A light piece of cardboard suspended and held near a tuning-fork moves
towards it when the fork is made to vibrate. If the tuning-fork is suspended
and is then made to vibrate, it moves towards the card if the latter is fixed.
Two suspended tuning-forks in a state of vibration move towards each
other. The flame of a candle placed near the end of a sounding tuning-
fork was repelled if held near it ; if held underneath it was flattened out to a
disc. A gas flame near the end of the tuning-fork was divided into two arms.
Guthrie found that, when one prong of a tuning-fork is enclosed in a tube
provided with a capillary tube dipping into a liquid, and is set in vibration
by bowing the free prong, the air around the en-
closed prong is expanded, and he thence con-
cluded that the approach, above described, of a'
suspended body to the sounding-fork is due to
the diminution of the pressure of the air between
the fork and the body below that on the other
side of the body.

A cylindrical resonator of stiff drawing-paper
is fastened to a strip of wood, which is provided
with a glass cap and counterpoise, and thus can
be made to turn on a needle point. If the open
end of the sounding-box of a tuning-fork vibrating
in unison with the resonator is brought near this,
it is repelled even at a distance of some inches.
When a small mill with four arms (fig. 277), each
provided with a small resonator, is placed near
the open end of the sounding-box, the repulsion
is so strong as to produce a uniform rotation.
These phenomena do not seem to be due to the aspirating action of cur-
rents of air, nor are they caused by any heating effect ; and it must be con-
fessed that the phenomena require further elucidation ; they are of special
interest as furnishing a possible clue to the solution of the problem of attrac-
tion in general.

291. Phonograph. Craphophone — In the year 1877 Edison devised the
apparatus known as the ///cW(^_o"r<:7//^ for recording and reproducing sound,
which is equally remarkable for the simplicity of its construction and for the
striking character of the results which it produces.

Fig. 277.

-291]

Edison's Phonograph.

269

This instrument is illustrated in fig. 278, and it consists generally of a
cylinder C, mounted on a horizontal axis AA', which can be rotated beneath
a mouthpiece E, by means of a winch-handle M, the speed of rotation being
controlled by a fly-wheel attached to one end of the spindle AA', and the
whole is supported by a base-board L. Upon the cylindric surface of C is
cut a helical groove, and one end of the spindle A' is formed into a screw the
pitch of which is equal to that of the groove upon the cylinder. This screw
works in a correspondingly screwed bearing, so that on turning the handle the
cylinder not only rotates upon its axis but also travels from end to end in a
direction parallel to its axis.

Fig. 279.

The mouthpiece is closed with a diaphragm or membrane P, to the
centre of which is attached, by means of a caoutchouc tube, a small style S
directed towards the cylinder, and which is caused
to vibrate longitudinally by the vibratoiy action of the
diaphragm P, and the position of the mouthpiece is so
adjusted that the point of the style is always directed
to the centre of the helical groove in the cylinder. On
this grooved cylinder is stretched a sheet of tinfoil
which bridges over the grooves, being supported by
the ridges and the position of the mouthpiece, and its
distance from the cylinder is adjusted by the handle ;«,
which can be fixed in its place by the set screw v.
Their position and distance are so adjusted that
when the apparatus is at rest the point of the style
is within the groove and a little lower than the top of the ridge.

If, while the cylinder is being rotated, sounds or words be uttered into
the mouthpiece, the diaphragm attached thereto will be set into vibration
and will cause the style to indent on the foil a groove of varying depth, the
bottom of which is a mechanical record of the vibration of the diaphragm,
and therefore of the sounds by which those vibrations were set up, and as
the tinfoil is a very imperfectly elastic material it is able to retain the record
so made.

If now this record be passed again beneath the style the varying indenta-
tions on the foil will cause the style to vibrate as it did when it produced the
indentations, and the diaphragm will be similarly set into vibration, and will
reproduce the sound by which it was in the first instance set into vibi'ation.

In this way sound may be reproduced so as to be audible to a large
audience ; the articulation is distinct though feeble ; it reproduces the
voice of a person who speaks into it, but with a nasal intonation. Speech

270 On Sound [291-

may thus be stored up on a sheet of tinfoil and kept for an indefinite period,
and the sound may be reproduced more than once from the same record,
but after a second reproduction the clearness is greatly diminished.

If the velocity of rotation be greater than before, the pitch of the sound
is raised; and if it be not uniform, then, m the case of a song, the reproduc-
tion is incorrect. In order to produce a uniform velocity the instrument may
with advantage be driven by clockwork.

There is great difference in the distinctness with which the various con-
sonants and vowels are reproduced, the most distinct are words containing
the vowels A, O, and U, and the consonants /, k, and r ; the s and similar
consonants, on the contrary, are seldom distinct. If the phonograph be
rotated in the reverse direction, the sounds of which the words are made
up retain their character, but are produced in the reverse order.

If the instrument be reset to the starting-point of the phonographic
record of a song, and be again sung into, it will reproduce both series of
sounds, as if two persons were singing at the same time ; and, by repeating
the same process, a third or fourth succession of sounds may be added,
and the whole will be heard together and without the one record destroying
the other.

The impressions on the tinfoil appear at first sight as a series of successive
points or dots, but when examined under a microscope they are seen to have
a distinct form of their own. When a cast is taken by means of fusible
metal and a longitudinal section made, the outline closely resembles the
jagged edge of a Konig's flame. Mr. Edison states that as many as 40,000
words can be registered on a space not exceeding 10 square inches.

The phonograph has been used with great advantage by Jenkins and
King for the analysis of vocal sounds, for which purpose it is better suited
than Konig's flames.

The graphophone, invented by Mr. Sumner Tainter, in conjunction with
Professor Graham Bell and Dr. Chichester Bell, consists essentially of three
parts : the recorder, the cylinder on which the record is made, and the
reproducer.

The cylinder is a hollow cone of cardboard coated with a composition of
wax and paraffin ; it is mounted horizontally and is rotated by means of a
treadle underneath the table, which supports the whole apparatus. Between
the treadle and the cylinder is interposed a very ingenious governor by which
the speed of rotation of the cylinder may be regulated to perfect uniformity,
the force required for this rotation being very small.

On a bar parallel to and in front of the cylinder is clamped the recorder,
which consists of an exceedingly minute cutting point, or rather chisel, fixed to
a mica diaphragm. This diaphragm is at the end of a flexible tube provided
with a mouthpiece. If this be spoken into, the diaphragm vibrates with a
to and fro motion, and if at the same time the cylinder rotates at a uniform
speed the style cuts or carves out a groove in the surface of the wax, forming
a very irregular outline which is the exact reproduction of the sound wave.
Therein lies the difference between the graphophone and the phonograph,
for in the latter the record is produced by a process of indentation, while in
the former the record of the sound waves is engraved in a waxy material.
The grooves are so excessively minute that their variations in depth cannot

-291] GraphopJione. 27 1

be recognised by the naked eye ; they are not more than the ^h^ of a" inch in
diameter, and there are 160 to the inch.

The reproducer consists of a hght ebonite tube, at one end of which is the
enlargement containing the diaphragm, which, hke that of the recorder, is of
mica, but is somewhat smaller. The diaphragm is connected by means of a
fine waxed silk thread with a fine steel point or hook which rocks on a pivot
at the end of the tube. There is an arrangement by which this reproducer
can be clamped in front of the recorder, so that when the cylinder is rotated
the reproducer travels at a proportionate speed, allowing the small point to
rest in the groove forming the sound record, and along which it rides and
vibrates ; and these vibrations are transmitted to the mica diaphragm, and,
being communicated to the ear, faithfully reproduce the sound.

Notwithstanding what appears the very yielding character of the wax,
the sounds, and even elaborate pieces of music, are reproduced with great
fidelity, and it is stated that the same record will reproduce the original
sound some thousand times.

272

071 Heat. [292-

BOOK VI.

ON HEAT.

CHAPTER I.

PRELIMINARY IDEAS. THERMOMETERS.

292. Heat. Hypotheses as to its nature. — In ordinary language the
term Jieat is used not only to express a particular sensation, but also to de-
scribe that particular state or condition of matter which produces this sensa-
tion. Besides producing this sensation, heat acts variously upon bodies ; it
melts ice, boils water, makes metals red-hot, produces electrical currents,
decomposes compound bodies, and so forth.

Two theories as to the cause of heat have been propounded : these are,
the theory of emission., and the theo7y of undulation.

On the first theory, heat is caused by a subtle imponderable fluid, which
surrounds the molecules of bodies, and which can pass from one body to
another. These heat atjnospheres., which thus surround the molecules, exert
a repelling influence on each other, in consequence of which heat acts in
opposition to the force of cohesion. The entrance of this substance into our
bodies produces the sensation of warmth, its egress the sensation of cold.

On the second hypothesis the heat of a body is caused by an extremely
rapid oscillating or vibratory motion of its molecules ; and the hottest bodies
are those in which the vibrations have the greatest velocity and the greatest
amplitude. At any given time the whole of the molecules of a body possess
a sum of vis viva, which is the heat they contain. To increase their tempera-
ture is to increase their ins viva ; to lower their temperature is to decrease
their vis viva. Hence, on this view, heat is not a substance but a condition
of matter., and a condition which can be transferred from one body to another.
When a heated body is placed in contact with a cooler one, the former cedes
more molecular motion than it recei\es ; but the loss of the former is the
equivalent of the gain of the latter.

It is also assumed that there is an imponderable elastic ether, which per-
vades all matter and infinite space. A hot body sets this in rapid vibration,
and the vibrations of this ether being communicated to material objects set
them in more rapid vibration ; that is, increase their temperature. Here we
have an analogy with sound ; a sounding body is in a state of vibration, and

292] Heat. Hypotheses as to its Nature. 273

its vibrations are transmitted by atmospheric air to the auditoiy apparatus
in which is produced the sensation of sound.

This hypothesis as to the nature of heat is now admitted by the most
distinguished physicists. It affords a better explanation of all the phenomena
of heat than any other theory, and it reveals an intimate connection between
heat and light. It will be subsequently seen that by the friction of bodies
against each other an indefinite quantity of heat is produced. Experiment
has shown that there is an exact equivalence between the motion thus de-
stroyed and the heat produced. These and many other facts are utterly
inexplicable on the assumption that heat is a substance, and not a form of
motion.

In what follows, however, the phenomena of heat will be considered, as
far as possible, independently of either hypothesis ; but we shall subsequently
return to the reason for the adoption of the latter hypothesis.

Assuming that the heat of bodies is due to the motion of their particles,
we may admit the following explanation as to the nature of this motion in
the various forms of matter : —

In solids the molecules have a kind of vibratory motion about certain
fixed positions. This motion is probably veiy complex ; the constituents of
the molecule may oscillate about each other, besides the oscillation of the
molecule as a whole ; and this latter again may be a to-and-fro motion, or it
may be a rotatoiy motion about the centre. In cases in which external
forces, such as violent shocks, act upon the body, the molecules may per-
manently acquire fresh positions.

In the liquid state the molecules have no fixed positions. They can
rotate about their centres of gravity, and the centre of gravity itself may
move. But the repellent action of the motion, compared with the mutual
attraction of the molecules, is not sufficient to separate the molecules from
each other. A molecule no longer adheres to particular adjacent ones ; but
it does not spontaneously leave them except to come into the same relation
to fresh ones as to its previous adjacent ones. Thus in a liquid there is a
vibratory, rotatory, and progressive motion.

In Xh^ gaseous state the molecules are entirely without the sphere of their
mutual attraction. They fly forward in straight lines according to the ordi-
nary laws of motion, until they impinge against other molecules or against
a fixed envelope which they cannot penetrate, and then return in an opposite
direction, with, in the main, their original velocity. If the molecules were in
space, where no external force could act upon them, they would fly apart, and
disappear in infinity. But if contained in any vessel, the molecules con-
tinually impinge in all directions against the sides, and thus arises the pres-
sure which a gas exerts on its vessel.

The perfection of the gaseous state implies that the space actually
occupied by the molecules of the gas be infinitely small compared with the
entire volume of the gas ; that the time occupied by the impact of a mole-
cule either against another molecule, or against the sides of the vessel, be
infinitely small in comparison with the inter\-al between any two impacts ;
and that the influence of molecular attraction be infinitely small. . When
these conditions are not fulfilled the gas partakes more or less of the nature
of a liquid, and exhibits certain deviations from Boyle's law (180). This is the

274 On Heat. [292-

case with all gases ; to a very slight extent with the less easily condensable
gases, but to a far greater extent with vapours and the more condensable
gases, especially near their points of liquefaction.

293. Dynamical theory of g-ases. — We have seen that in the gaseous
condition the particles are assumed to fly about in right lines in all possible
directions. A rough illustration of this condition of matter is afforded by
imagining the case of a number of bees enclosed in a box.

Let us suppose a cubical vessel to be filled with air under standard con-
ditions of temperature and pressure. Let the length of the sides be a. We
will for the present suppose that each particle moves freely in the space
without striking against another particle. All possible motions may be con-
ceived to be resolved into motions in three directions which are parallel to
the faces of the cube. Conceive any single particle, of mass in ; it will strike
against one face with such a velocity, //, as not only to annul its own motion,
but to cause it to rebound in the opposite direction with the same velocity ;
hence the measure of the momentum with which it strikes against the side
will be imu. Now, by their rapid succession and their uniform distribution,
the total action of these separate impacts is to produce a pressure against
the sides of the vessel which is the elastic force of the gas ; and, to measure
the pressure on the side, we must multiply the momentum of each individual
impact by the total number of such impacts.

Since the length of the side is a, if there are n molecules in the unit

of space, there will be ncv' in the volume of the cube, of which will be

3
moving in a direction parallel to each one of the sides. To get the number
of impacts on one face, we must remember that they succeed each other,,
after the interval of time recjuired for a particle to fly to the opposite side
and back again. Hence, u being the velocity, the number of impacts which

each particle makes in the unit of time, a second, will be -^' ,and the number

7. a

of all such which strike against one side will be ^nd^^- - pta'-u.

Now, since each one exerts a pressure represented by 2mu, we shall have
for the total pressure p on the surface n~

pd^ = \a-nmir.,

and therefore the pressure on the unit of surface will be

p = ^ntnu^.

Now, if N is the number of molecules in the volume 7/, N = nv, ancll
therefore

p = ^ — mtr ; that is, pv = ^Nmu'~.

But, for any given mass of gas, N, w, and z/ are constant quantities, and the
product /2/ must therefore also be constant ; this, however, is only one form
of expressing Boyle's law (180).

294. Molecular velocity. — In the formula p = ^n;/nr, nnt represents the
mass in unit volume which we may designate as the density p, of the gas.

-294] Molecular Velocity of Gases. 275

referred to that of water, and which can be directly measured ; and, since the
pressure^ is also capable of direct measurement, we can calculate the third
magnitude u in absolute measure.

The pressure jZ^ on a gas is equal to the action of gravity on a column of
mercury of given height h ; so that, if S is the density of mercury = I3'596,
and_^ the acceleration of gravity,^ = bgh and

u- = ^-^-.

•Now, if a be the specific gravity of the gas as compared with air, which is

lighter than water, p x 773"3 = o-, or p = — - — ,

773'3 773'3

^■2 ^ 3 X 13-596 X 076 X 9'8i[5 X yyy^
<r

which gives u = ''- ; that is, that for atmospheric air the mean velocity of

the particles is 485 metres in a second. For other gases we have, expressed
in the same units,

O - 461

N = 492
H = 1844

In a gas the velocities of the particles are unequal ; since, even supposing
that they were all originally the same, it is not difficult to see that they would
soon alter. For imagine a particle to be moving parallel to one side, and to
be struck centrically by another moving at right angles to the direction of
its motion, the particle struck would proceed on its new path with increased
velocity, while the striking particle would rebound in a different direction
with a smaller velocity.

Notwithstanding the accidental character of the velocity of any individual
particle in such a mass of gas as we have been considering, there will, at any
one given time, be a certain average distribution of velocities. Now, from
considerations based on the theory of probabilities, it follows that some
velocities will be more probable than others — that there will, indeed, be one
velocity which is more probable than any other. This is called the most
probable velocity. The mean velocity oi ^ho. particle, as found above, is
not this, nor is it the same as the arithmetical mean of all the velocities ; it
may be defined to be that velocity which, if all the molecules possessed it,
would give rise to the same mean energy of the molecular impacts against
the side as that which actually exists. This mean velocity is about j^- greater
than the arithmetical mean velocity, and is \\ that of the most probable
single velocity.

Theoretical as well as experimental observations render it possible to
determine with great probability not only the average length of the path
which a molecule traverses before it encounters another, but also the number
of impacts in a given time. Thus, in air, measured under standard con-
ditions, the length of the mean path of a molecule is calculated to be 0-000095
mm., and the number of impacts in a second 4,700 millions. For hydrogen
these numbers are 0-0001855 mm. for the length of path, and 9,480 millions

2/6 On Heat. [294-

for the number of impacts. Hence it is that, notwithstanding these enormous
velocities, gases diffuse but slowly, as is observed in the case of those with
strong odours.

It follows from the above equation that

u : u^ = ^/'oT : ^-^

that is, that the molecular velocities are inversely as the square roots of the
densities or the molecular weights. This is confirmed by experiments on
diffusion (190).

The magnitudes of the molecules themselves have been calculated by
several observers from different methods based on various physical pheno-
mena. Loschmidt found, for instance, that the diameter of the molecule of
hydrogen was 41, oxygen 7, and nitrogen 8 hundred millionths of a centi-
metre. The results of other calculations agree remarkably with these.

295. General effects of heat. — The general effects of heat upon bodies
may be classed under three heads. One portion is expended in raising the
temperature of the body ; that is, in increasing the vis viva of its molecules.
In the second place, the molecules of bodies have a certain attraction for
each other, to which is due their relative position ; hence a second portion
of heat is consumed in augmenting the amplitude of the oscillations, by
which an increase of volume is produced, or in completely altering the
relative positions of the molecules, by which a change of state is effected.
These two effects are classed as internal work. Thirdly, since bodies are
surrounded by atmospheric air which exerts a certain pressure on their sur-
face, this has to be overcome or lifted through a certain distance. The heat
or work required for this is called the exterftal work.

If Q units of heat are imparted to a body, and if A be the quantity of

heat which is equivalent to the unit of work ; then if W is the amount of

heat which serves to increase the temperature, I that required to alter the

position of the molecules, and if L be that expended in external work, then

Q = A (W + I -t- L).

296. Expansion. — All bodies expand by the action of heat. As a general
rule, gases are the most expansible, then liquids, and lastly solids.

Fig. 280.

In solids which have definite figures, we can either consider the expan-
sion in one dimension, or the linear expansion ; in two dimensions, the
superficial expansion ; or in three dimensions, the cubical expansion or the

-296]

Expansion.

expansion of volume, although one of these never takes place without the
other. As liquids and gases have no definite figures, the expansions of
volume have in them alone to be considered.

To show the linear expansion of solids, the apparatus represented in fig.
280 may be used. A metal rod. A, is fixed at one end by a screw, B, while
the other end presses against the short arm of an index, K, which moves on
a scale. Below the rod there is a sort of cylindrical lamp in which alcohol
is burned. The needle K is at first at the zero point, but as the rod becomes
heated it expands, and moves the needle along the scale.

The cubical expansion of solids is shown by a Graiiesande' s ring. This
consists of a brass ball a (fig. 281), which at the ordinary temperature passes

Fig. 28

Fig. 282. Fig. 2S3.

freely through a ring, 111, almost of the same diameter. But when the ball
has been heated, it expands and no longer passes through the ring.

In order to show the expansion of liquids, a large glass bulb provided
with a capillary stem is used (fig. 282). If the bulb and a part of the stem
contain some coloured liquid, the liquid rapidly rises in the stem when heat
is applied, and the expansion thus observed is far greater than in the case
of solids.

The same apparatus may be used for showing the expansion of gases.
Being- filled with air, a small thread of mercury is introduced into the capillary
tube to serve as index (fig. 283). When the globe is heated in the slightest
degree, even by approaching the hand, the expansion is so great that the
index is driven to the end of the tube, and is finally expelled. Hence, even
for a very small degree of heat, gases are highly expansible.

In these different experiments the bodies contract on cooling, and when
they have attained their former temperature they resume their original
volume. Certain metals, however, especially zinc, form an exception to this
rule, and it appears also to be the case with some kinds of glass.

2/8 On Heat. [297-

MEASUREMENT OF TEMPERATURE. THERMOMETRY.

297. Temperature. — The temperature or hotness of a Ijody, indepen-
dently of any hypothesis as to the nature of heat, may be defined as being
the greater or less extent to which it tends to impart sensible heat to other
bodies. The temperature of a body must not be confounded with the quati-
tity of heat it possesses : a body may have a high temperature and yet
have a very small quantity of heat, and, conversely, a low temperature and yet
possess a large amount of heat. If a cup of water be taken from a bucketful,
both will indicate the same temperature, yet the quantities they possess will
be diffei-ent. This subject of the quantity of heat will be afterwards more
fully explained in the chapter on Specific Heat.

298. T\xeTm.ometeTS.— Thermometers are instruments for measuring
temperatures. Owing to the imperfections of our senses we are unable to
measure temperatures by the sensation of heat or cold which they produce
in us, and for this purpose recourse must be had to the physical actions of
heat on bodies. These actions are of various kinds, but the expansion of
bodies has been selected as the easiest to observe. But heat also produces
electrical phenomena in bodies ; and on these the most delicate methods
of observing temperatures have been based, as we shall see in a subsequent
chapter.

Liquids are best suited for the construction of thermometers^the ex-
pansion of solids being too small, and that of gases too great. Mercury and
alcohol are the only licjuids used — the former because it only boils at a very
high temperature, and the latter because it does not solidify at the greatest
known cold.

The mercurial thermometer is the most extensively used. It consists of
a capillary glass tube, at the end of which is blown the bulb, a cylindrical
or spherical reservoir. Both the bulb and a part of the stem are filled with
mercury, and the expansion is measured by a scale graduated either on the
stem itself, or on a frame to which it is attached.

Besides the manufacture of the bulb, the construction of the thermometer
comprises three opeiations : the calibration of the tube, or its division into
parts of equal capacity ; the introduction of the mercury into the reservoir ;
and the graduation.

299. Division of the tube into parts of equal capacity. Calibration.
As the indications of the thermometer are only correct when the divisions
of the scale correspond to equal expansions of the mercury in the reservoir,
the scale must be graduated, so as to indicate parts of equal capacity in the
tube. If the tube were quite cylindrical, and of the same diameter through-
out, it would only be necessaiy to divide it into equal lengths. But as the
diameter of glass tubes is usually greater at one end than another, parts of
equal capacity in the tube are represented by unequal lengths of the scale.

In order, therefore, to select a tube of uniform bore, it is calibrated; for
this purpose, a thread of mercury about an inch long is introduced into the
capillary tube, and moved in different positions in the tube, care being taken
to keep it at the same temperature. If the thread is of the same length in
every part of the tube, it shows that the capacity is everywhere the same ;

Determmation of the Fixed Points of a Thermometer. 279

but if the thread occupies different lengths the tube is rejected, and another
one sought.

300. Filling- the thermometer. — In order to fill the thermometer with
mercury, a small funnel, C (fig. 284), is blown on at the top, and is filled
with mercury ; the tube is then slightly inclined, and the air in the bulb
expanded by heating it with a spirit lamp. The expanded air partially
escapes by the funnel, and, on cooling, the air which remains contracts, and
a portion of the mercury passes into the bulb D. The bulb is then again
warmed, and allowed to cool, a fresh quantity of mercury enters, and so on,
until the bulb and part of the tube are full of

mercury. The mercury is then heated to boiling ;
the mercurial vapours in escaping carry with them
the air and moisture which remain in the tube.
The tube, being full of the expanded mercury and
of mercurial vapour, is hermetically sealed at one
end. When the thermometer is cold, the mercury
ought to fill the bulb and a portion of the stem.

301. Graduation of the thermometer. — The
thermometer being filled, it requires to be gradu-
ated ; that is, to be provided with a scale to which
variations of temperature can be referred. And,
first of all, two points must be fixed which repre-
sent identical temperatures, and which can always
be easily reproduced.

Experiment has shown that ice constantly melts
at the same temperature, whatever be the degree of
heat, and that distilled water under the same pres-
sure and in a vessel of the same kind always boils
at the same temperature. Consequently, for the
first fixed point, or zero, the temperature of melting
ice has been taken : and for a second fixed point,
the temperature of boiling water in a metal vessel
under the normal atmospheric pressure of 760
millimetres.

This interval of temperature — that is, the range
from zero to the boiling point — is taken as the unit for comparing tempera-
tures ; just as a certain length, a foot or a metre for instance, is used as a
basis for comparing lengths.

302. Determination of the fixed points. — To obtain zero, snow or
pounded ice is placed in a vessel in the bottom of which is an aperture by
which water escapes (fig. 285). The bulb and a part of the stem of the
thermometer are immersed in this for about a quarter of an hour, and a
mark made at the level of the mercury, which represents zero.

According to Bunsen it is doubtful whether a very accurate determination
is obtained by placing a thermometer in melting ice, for some slight admix-
tures lower the freezing point considerably. The best plan is to let water, in
which is the thermometer, be over-cooled (345) and then made to freeze by
shaking ; the point to which the mercury rises is the true melting point.

The second fixed point is determined by means of the apparatus repre-

Fig 284.

2 So

On Heat.

[302-

sented in the figures 286 and 287, of which fig. 287 represents a vertical sec-
tion. In both, the same letters designate the same parts. The whole of the
apparatus is of metal. A central tube, A, open at both ends, is fixed on a
cylindrical vessel containing water ; a second tube,
B, concentric with the first, and surrounding it,
is fixed on the same vessel, M. In this second
cylinder, which is closed at both ends, there are
three tubulures, a, E, D. A cork, in which is the
thermometer /, fits in a. To E, a glass tube, con-
taining mercury, is attached, which serves as a
manometer for measuring the pressure of the vapour
in the apparatus. D is an escape tube for the
vapour and condensed water.

The apparatus is placed on a furnace and heated
till the water boils ; the vapour produced in M rises
in the tube A, and, passing through the two tubes
in the direction of the arrows, escapes by the tubu-
lure D. The thermometer / being thus surrounded
with vapour, the mercury expands, and, when it
has become stationary', the point at which it stops
is marked. This is the point sought for. The
object of the second case, B, is to avoid the cooling
of the central tubulure by its contact with the air.
The determination of the point 100 (see next Article) would seem to
require that the height of the barometer during the experiment should be

Fig. 285.

Fig. 2S6.

Fig. 287.

760 millimetres, for, when the barometric height is greater or less than this
quantity, water boils either above or below 100 degrees. But the point 100

-303]

Construction of the Scale of a Thermometer.

may always be exactly obtained, by making a suitable correction. For
every 27 millimetres difference in height of the barometer there is a differ-
ence in the boiling point of i degree. If, for example, the height of the
barometer is 778— that is, iS millimetres, or two-thirds of 27, above 7.60 —
water would boil at 100 degrees and two-thirds. Consequently ioo§ would
ha\e to be marked at the point at which the mercury stops.

Gay-Lussac observed that water boils at a somewhat higher temperature
in a glass than in a metal vessel ; and as the boiling point is raised by any
salts which are dissolved, it has been assumed that it was necessary to use
a metal vessel and distilled water in fixing the boiling point. Rudberg
showed, however, that these latter precautions are superfluous. The nature
of the vessel "and salts dissolved in ordinary water influence the tempei'ature
of boiling water, but not that of the vapour which is formed. That is to
say, that if the temperature of boiling water from any of the above causes
is higher than 100 degrees, the temperature of the vapour does
not exceed 100, provided the pressure is not more than 760
millimetres. Consequently, the higher point may be determined
in a vessel of any material, provided the thermometer is quite
surrounded by vapour, and does not dip in the water.

Even with distilled water, the bulb of the thermometer must
not dip in the liquid, for, strictly speaking, it is only the upper
layer that really has the temperature of 100 degrees, since the
temperature increases from layer to layer towards the bottom, in
consequence of the increased pressure.

303. Construction of the scale. — Just as the foot-rule
which is adopted as the unit of comparison for length, is divided
into a number of equal divisions called inches for the purpose of
having a smaller unit of comparison, so likewise the unit of com-
parison of temperatures, the range from zero to the boiling point,
must be divided into a number of parts of equal capacity called
degrees. On the Continent, and more especially in France, this
space is divided into 100 parts, and this division is called the
Centigrade or Celsius scale ; the latter being the name of the
inventor. The Centigrade thermometer is almost exclusively
adopted in foreign scientific works, and, as its use is gradually
extending in this country, it has been and will be adopted in
this book.

The degrees are designated by a small cypher placed a little
above on the right of the number which marks the temperature,
and to indicate temperatures below zero the minus sign is placed
before them. Thus, — 15° signifies 15 degrees below zero.

In accurate thermometers the scale is marked on the stem
itself (fig. 288). It cannot be displaced, and its length remains
fixed, as glass has very little expansibility. The graduation is
effected by covering the stem with a thin layer of wax, and
then marking the divisions of the scale, as well as the corre- Fig. i>ss.
spending numbers, with a steel point. The thermometer is
then exposed for about ten minutes to the vapours of hydrofluoric acid,
which attacks the glass where the wax has been removed. The rest

282 On Heat. [303-

of the wax is then removed, and the stem is found to be permanently
etched.

Besides the Centigrade scale two others are frequently used — FaJii'enheif s
scale and Reaumur'' s scale.

In Reaumur's scale the fixed points are the same as on the Centigrade
scale, but the distance between them is divided into 80 degrees, instead of
into 100. That is to say, 80 degrees Reaumur are equal to 100 degrees
Centigrade ; one degree Reaumur is equal to ^~° or | of a degree Centigrade,
and one degree Centigrade equals ^^-^ or | degrees Reaumur. Consequently,
to convert any number of Reaumui-'s degrees into Centigrade degrees (20, for
example), it is merely necessary to multiply them by | (which gives 25).
Similarly, Centigrade degrees are converted into Reaumur by multiplying
them by |.

The thermometric scale invented by Fahrenheit in 17 14 is still much
used in England, and also in Holland and North America. The higher fixed
point is, like that of the other scales, the temperature of boiling water ; but
the null point of zero is the temperature obtained by mixing equal weights
of sal-ammoniac and snow, and the interval between the two points is
divided into 212 degrees. The zero was selected because the temperature
was the lowest then known, and was thought to represent absolute cold.
When Fahrenheit's thermometer is placed in melting ice it stands at 32 de-
grees, and therefore 100 degrees on the Centigrade scale are equal to 180
degrees on the Fahrenheit scale, and thus i degree Centigrade is equal to f
of a degree Fahrenheit, and, inversely, i degree Fahrenheit is equal to | of a
degree Centigrade.

If it be required to convert a certain number of Fahrenheit degrees (95,
for example) into Centigrade degrees, the number 32 must first be subtracted
in order that the degrees may count from the same part of the scale. The
remainder in the example is thus 63, and, as i degree Fahrenheit is equal
to I of a degree Centigrade, 63 degrees are equal to 63 x § or 35 degrees
Centigrade.

If F be the given temperature in Fahrenheit degrees and C the corre-
sponding temperature in Centigrade degrees, the former may be converted
into the latter by means of the formula

(F-32)| = C,

and, conversely, Centigrade degrees may be converted into Fahrenheit by
means of the formula

f C + 32 = F.

The formuke are applicable to all temperatures of the two scales, pro-
vided the signs are taken into account. Thus, to convert the temperature
of 5 degrees Fahrenheit into Centigrade degrees, we have

(5-32)1==^^= -15 C.

In like manner we ha\'e, for converting Reaumur into Fahrenheit degrees,
the formula

f R + 32 = F,

-307j Conditions of the Delicacy of a Thermometer. 283

and, conversely, for changing Fahrenheit into Reaumur degrees, the formula

(F-32)| = R.

304. Displacement of zero.- — Thermometers, even when constructed
with the greatest care, are subject to a source of error which must be taken
into account ; that is, that in course of time the zero tends to rise, the dis-
placement sometimes extending to as much as two degrees ; so that when
the thermometer is immersed in melting ice it no longer sinks to zero.

This is generally attributed to a diminution of the volume of the bulb and
also of the stem, occasioned by the pressure of the atmosphere. It is usual
with very accurate thermometers to fill them two or three years before they
are graduated. Joule once observed that even after twenty-five years a deli-
cate thermometer indicated a displacement of zero.

Besides this slow displacement, there are often variations in the position
of the zero, when the thermometer has been exposed to temperatures above
60°, caused by the fact that the bulb and stem do not contract on cooling to
their original volume (294) ; these differences are greater the thicker the glass
sides, and hence it is necessary from time to time to verify the position of
zero when a thermometer is used for delicate determinations.

Regnault noticed that some mercurial thermometers, which agree at 0°
and at 100°, differ between these points, and that these differences frequently
amount to several degrees. Regnault ascribed this to the unequal expansion
of different kinds of glass.

305. Iiimits to the employment of mercurial thermometers.- — Of all
thermometers in which liquids are used, the one with mercury is the most
useful, because this liquid expands most regularly, and is easily obtained
pure, and because its expansion between -36° and 100° is regular ; that is,
proportional to the degree of heat. It also has the advantage of having a
very low specific heat. But for temperatures below — 36° C. the alcohol
thermometer must be used, since mercury solidifies at — 40° C. Above 100
degrees the coefficient of expansion mcreases, and the indications of the
mercurial thermometer are only approximate, the error rising sometimes to
several degrees. Mercury thermometers also cannot be used for temperatures
above 350°, for this is the boiling point of mercuiy.

306. Alcohol thermometer. — The alcohol thermoineter differs from the
mercury thermometer in being filled with coloured alcohol. But as the
expansion of liquids is less regular in proportion as they are near the boiling
point, alcohol, which boils at 78° C., expands y&xy irregularly. Hence,
alcohol thermometers are usually graduated by placing them in baths at
different temperatures together with a standard mercurial thermometer, and
marking on the alcohol thermometer the temperature indicated by the
mercury thermometer. In this manner the alcohol thermometer is compar-
able with the mercury one ; that is to say, it indicates the same temperatures
under the same conditions. The alcohol thermometer is especially used for
low temperatures, for it does not solidify at the greatest known cold.

307. Conditions of the delicacy of a thermometer. — A thermometer
may be delicate<.in two ways : — 1. When it indicates very small changes of
temperature. 2. When it quickly assumes the temperature of the surround-
ing medium.

284

On Heat.

[307-

The first object is attained by having a very narrow capillary tube and a
very large bulb ; the expansion of the mercury on the stem is then limited
to a small number of degrees, from lo to 20 or 20 to 30 for instance, so that
each degree occupies a great length on the stem, and can be subdivided into
very small fractions. The second kind of delicacy is obtained by making
the bulb very small, for then it rapidly assumes the temperature of the liquid
in which it is placed.

A good mercury thermometer should answer to the following tests : —
When its bulb and stem, to the top of the column of mercury, are immersed
in melting ice, the top of the mercury should exactly indicate 0° C. ; and
when suspended with its bulb and scale immersed in the steam of water
boiling in a metal vessel (as in fig. 286) the barometer standing at 760 mm.,
the mercury should be stationary at 100° C. When the instrument is
inverted, the mercury should fill the tube, and fall with a metallic click, thus
showing the complete exclusion of air. The value of the degrees should be
uniform ; to ascertain this a little cylinder of mercury may be detached from
the column by a slight jerk, and on inclining the tube it may be made to
pass from one portion of the bore to another. If the scale be properly
graduated, the column will occupy an equal number of degrees in all parts
of the tube.

308. 3>ifferential thermometer. — Sir John Leslie constructed a ther-
mometer for showing the difference of temperature of two neighbouring

Fig. 290.

places, from which it has received the name of the differe7itial ihcrinoiiicter.
A modified form of it is that devised by Matthiessen (fig. 289), which has
the advantage of being available for indicating the temperature of liquids.
It consists of a bent glass tube, each end of which is bent twice, and
terminates in a bulb ; the bulbs being pendent can be readily immersed in

-310] RutJierford's Maximum and Minimum Thermometers. 285

a liquid. The bend contains some coloured liquid, and in a tube which
connects the two limbs is a stopcock, by which the liquid in each limb is
easily brought to the same level. The whole is supported by a frame.

When one of the bulbs is at a higher temperature than the other, the
liquid in the stem is depressed and rises in the other stem. The instru-
ment is now only used as a thennoscope ; that is, to indicate a difference
of temperature between the two builds, and not to measure its amount.

309. Breg'uet's metallic thermometer. — Breguet invented a ther-
mometer of considerable delicacy, which depends on the unequal expansion
of metals. It consists of three strips of platinum, gold, and silver, which are
passed through a rolling mill so as to form a very thin metallic ribbon. This
is then coiled in a spiral form, as seen in fig. 290, and, one end being fixed to
a support, a light needle is fixed to the other, which is free to move round a
graduated scale.

Silver, which is the most expansible of the metals, forms the inner face
of the spiral, and platinum the outer. When the temperature rises, the
silver expands more than the gold or platinum, the spiral unwinds itself, and
the needle moves from left to right of the above figure. The contrary effect
is produced when the temperature sinks. The gold is placed between the
other two metals because its expansibility is intermediate between that of
the silver and the platinum. Were these two metals employed alone, their
rapid unequal expansion might cause a fracture. Breguet's thermometer is
empirically graduated in Centigrade degrees, by comparing its indications
with those of a standard mercury thermometer.

On this principle depend several forms of pocket thermometers, and it is
also applied in some registering thermometers.

310. Xtutberford's maximum and minimum thermometers. — It is
necessary, in meteorological observations, to know the highest temperature

Fig. 291.

of the day and the lowest temperature of the night. Ordinary thermometers
could only give these indications by a continuous observation, which would
be impracticable. Several instruments have accordingly been invented for
this purpose, the simplest of which is Rutherford's. On a rectangular piece
of plate-glass (fig. 291) two thermometers are fixed, whose stems are bent
horizontally. The one. A, is a mercury, and the other, B, an alcohol
thermometer. In A there is a minute piece of iron wire. A, moving freely in
the tube, which serves as an index. The thermometer being placed hori-

286 On Heat. [310-

zontally, when the temperature rises the mercury pushes the index before it.
But as soon as the mercury contracts, the index remains in that part of the
tube to which it has been moved, for there is no adhesion between the iron
and the mercury. In this way the index registers the highest temperature
which has been attained ; in the figure this is 32°. In the minimum ther-
mometer there is a small hollow glass tube which serves as index. When it
is at the end of the column of liquid, and the temperature falls, the column
contracts, and carries the index with it, in consequence of adhesion, until it
has reached the greatest contraction. When the temperature rises the alcohol
expands, and, passing between the sides of the tube and the index, does not
displace B. The position of the index gives therefore the lowest temperature
which has been reached ; in the figure this is 8-5 degrees below zero.

311. Pyrometers. — The name pyrometers is given to instruments for
measuring temperatures so high that mercurial thermometers could not be
used. The older contrivances for this purpose — Wedgwood's, Daniell's
(which in principle resembled the apparatus in fig. 280), Brongniart's, &c. —
have gone entirely out of use. None of them give an exact measure of tem-
perature. The arrangements now used for the purpose are either based on
the expansion of gases and vapours, on the specific heat of solids, or on the
electrical properties of bodies, and will be subsequently described.

312. Different remarkable temperatures. — The following table gives
some of the most remarkable points of temperature. It may be observed
that it is easier to produce very high temperatures than very low degrees of
cold.

Greatest artificial cold produced by a bath of bisulphide

of carbon and liquid nitrous acid .... - 140° C.

Greatest cold produced by ether and liquid carbonic acid . -no

Greatest natural cold recorded in Arctic expeditions . - 587

Mercury freezes — 39'4

Mixture of snow and salt . . . . . . . - 20

Ice melts .......••• o

Greatest density of water +4

Mean temperature of London 9'9

Blood heat 36"6

Water boils 100

Mercury boils 35°

Sulphur boils 44°

Red heat (just visible) . (Daniell) .... 526

Silver melts ... „ .... 1000

Zinc boils .... „ .... 1040

Cast iron melts ... „ .... 1530

Highest heat of wind furnace „ .... 1800

Platinum melts 2000

Iridium „ 2700

-314] Expansion of Solids, 287-

CHAPTER II.

EXPANSION OF SOLIDS.

313. Iiinear expansion and cubical expansion. Coefficients of
expansion. — It has been already explained that in solid bodies the expansion
may be according to three dimensions — linear, superficial, and cubical.

The coefficient of Ihiear expansiojt is the elongation of the unit of length
of a body when its temperature rises from zero to i degree ; the coefficiefit of
superficial expa?ision is the increase of the surface in being heated from zero
to I degree, and the coefficient of cubical expansion is the increase of the
unit of volume under the same circumstances.

These coefficients vary with different bodies, but for the same body the
coefficient of cubical expansion is three times that of the linear expansiofi, as
is seen from the following considerations : — Suppoae a cube, the length of
whose side is i at zero. Let k be the elongation of this side in passing from
zero to I degree, its length at i degree will be i + k, and the volume of the
cube, which was i at zero, will be {i + kf, or i + 3/^ + 3^'- + z^''. But as the
elongation k is always a very small fraction (see table. Art. 316), its square,
k', and still more its cube, P, are so small that they may be neglected, and
the value at i degree becomes very nearly i + 3/^. Consequently, the increase
of volume is 2)k, or thrice the coefficient of linear expansion.

In the same manner it may be shown that the coefficient of superficial
expansion is double the coefficient of linear expansion.

314. Measurement of the coefficient of linear expansion. Xiavoisier
and Dbaplace's metbod. — The apparatus used by Lavoisier and Laplace for
determining the coefficients of linear expansion (fig. 292), consists of a brass

'lliiiliii(liiiiiiii(iiiiiimnlnl(inilinnnil!ii1iriniminiiltii[

■liiiiiii

Fig. 292.

trough, placed on a furnace between four stone supports. On the two sup-
ports on the right hand there is a horizontal axis, at the end of which is a
telescope ; on the middle of this axis, and at right angles to it, is fixed a
glass rod, turning with it, as does also the telescope. The other two supports

288 On Heat. [314-

are joined by a cross-piece of iron, to which another glass rod is fixed, also
at right angles. The trough, which contains oil or water, is heated by a fur-
nace not represented in the figure, and the bar whose expansion is to be
determined is placed in it.

Fig. 293 represents a section of the apparatus ; G is the telescope, KH
the bar, whose ends press against the two glass rods F and D. As the rod

- l:^

=.■«:

K H

Fig. 293.

F is fixed, the bar can only expand in the direction KH, and in order to
eliminate the effects of friction it rests on two glass rollers. Lastly, the
telescope has a cross-wire in the eyepiece, which, when the telescope moves,
indicates the depression by the corresponding number of divisions on a
vertical scale, AB, at a distance of 220 yards.

The trough is first filled with ice, and the bar being at zero, the division
on the scale AB, corresponding to the wire of the telescope, is read ofif. The
ice having been removed, the trough is filled with oil or water, which is
heated to a given temperature. The bar then expands, and when its tempe-
rature has become stationaiy, which is determined by means of thermometers,
the division of the scale, seen through the telescope, is read ofif.

From these data the elongation of the bar is determined ; for since it has
become longer by a quantity, CH, and the optical axis of the telescope has
become inclined in the direction GB, the two triangles, GHC and ABG,
are similar, for they have the sides at right angles each to each, so that
FTG G FT
AT? ="ar' ^^ ^^ same way, if HC' were another elongation, and AB' a

corresponding deviation, there would still be .-„>= r^\ from which it.

follows that the ratio between the elongation of the bar and the deflection

G FT

of the telescope is constant, for it is always equal to . A preliminary

FTG

measurement has shown that this ratio was ^\-^. Consequently, -— = =:ij,

AB
whence HC = — ; that is, the total elongation of the bar is obtained by

744
dividing the length on the scale traversed by the cross-wire by 744. Divid-
ing this elongation by the length of the bar, and then by the temperature of
the bath, the quotient is the dilatation for the unit of length and for a single
degree — in other words, the coefificient of linear dilatation.

315. Roy and Ramsden's method. — Lavoisier and Laplace's method is
founded on an artifice which is frequently adopted in physical determinations,
and which consists in amplifying by a known amount dimensions which, in
themselves, are too small to be easily measured. Unfortunately, this plan is

315]

Roy mid Raiiisdcifs Method.

289

often more fallacious than profitable, for it is first necessary to determine
the ratio of the motion measured to that on which it depends. In the pre-
sent case, it is necessary to know the lengths of the arms of the lever in the
apparatus. But this preliminary operation may introduce errors of such
importance as partially to counterbalance the advantage of great delicacy.
The following method, used by General Roy in 1787, and which was devised
by Ramsden, depends on another principle. It measures the elongations
directly, and without amplifying them ; but it measures them by means of a
micrometric telescope, which indicates very small displacements.

The apparatus (fig. 294) consists of three parallel metal troughs about 6
feet long. In the middle one there is a bar of the body whose expansion is

j«J*|I95iJiqi||iu|^V;;jj^^ ^l^ ^ri»l«OUM!*JJI

nv^Eiiiii I

Fig. 294.

to be determined, and in the two others are cast-iron bars of exactly the
same length as this bar. Rods are fixed vertically on both ends of these
three bars. On the rods in the troughs A and B there are rings with cross-
wires like those of a telescope. On the rods in the trough C are small tele-
scopes, also provided with cross-wires.

The troughs being filled with ice, and all three bars at zero, the points of
intersection of the wires in the disc, and of the wires in the telescope, are
all in a line at each end of the bar. The temperature in the middle trough
is then raised to 100° C. by means of spirit lamps placed beneath the trough;
the bar expands, but as it is in contact with the end of the screw, a, fixed on
the side, all the elongation takes place in the direction jim, and, as the cross-
wire n remains in position, the cross-wire m is moved towards B by a quan-
tity equal to the elongation. But since the screw a is attached to the bar,
by turning it slowly from right to left, the bar is moved in the direction mn,
and the cross-wire fn regains its original position. To effect this, the screw

290 On Heat. [315-

has been turned by a quantity exactly equal to the elongation of the bar,
and, as this advance of the screw is readily deduced from the number of
turns of its thread (ii), the total expansion of the bar is obtained, which,
divided by the temperature of the bath, and this quotient by the length of
the bar at zero, gives the coefficient of linear expansion.

316. Coefficients of linear expansion. — By one or the other method
the following- results have been obtained : —

Coefficients of ,

linear expansioii

I for 1° between 0°

and 100^ C.

Diamond .

o-oooooii8o

Bronze .

0-000018167

Pine .

0-000006080

Brass

0-000018782

Graphite

0-000007860

Silver

0-000019097

Marble

0-000008490

Tin .

0-00002 1 730

White glass

0-000008613

Aluminium

0-000023130

Platinum .

0-000008842

Lead

0-000028575

Untempered steel

0-000010788

Zinc

0-000029417

Cast iron .

0-000011250

Sodium chloride

0-000040390

Sandstone .

0-0000 1 1740

Ice .

0-000052000

Wrought iron

0-000012204

Sulphur' .

0-000064130

Tempered steel .

0-000012395

Ebonite (17° to 3

5°) 0-000080600

Gold .

0-000014660

Paraffin .

0-000278540

Copper

0-000017182

Guttapercha .

0-000598000

From what has been said about the Hnear expansion (313), the coefficients
of cubical expansion of solids are obtained by multiplying those of hnear
expansion by 3.

The coefficients of the expansion of the metals vary with their physical
condition, being different for the same metal according as it has been cast
or hammered and rolled, hardened or annealed. As a general rule, opera-
tions which increase the density increase also the rate of expansion. But
even for substances in apparently the same condition, different observers
have found very unequal amounts of expansion ; this may arise in the case
of compound substances, such as glass, brass, or steel, from a want of uni-
formity in chemical composition, and in simple bodies from slight differences
of physical state.

The expansion of amorphous solids, and of those which crystallise in the
regular system, is the same for all dimensions, unless they are subject to a
strain in some particular direction. A fragment of such a substance varies
in bulk, but retains the same shape. Crystals not belonging to the regular
system when heated, exhibit an unequal expansion in the direction of their
different axes, in consequence of which the magnitude of their angles, and
therefore their form, is altered. In the dimetric system the expansion is the
same in the direction of the two equal axes, but different in the third. In
crystals belonging to the hexagonal system the expansion is the same in the
direction of the three secondary axes, but different from that according to
the principal one. In the trimetric system it is different in all three directions.

To the general law that all bodies expand by heat there is an important
exception in the case of iodide of silver, which contracts somewhat when

-318] FornmlcB relative to the Expansion of Solids. 291

heated. Between -60° and + 142° C. it has a negative coefficient of expan-
sion, the vahie of which is 0*000001 39 for 1° C.

Fizeau determined the expansion of a great number of ciystaUised bodies
by an optical method. He placed thin plates of the substance on a glass
plate and let yellow light pass through them. He thus obtained alternately
yellow and dark Newton's rings {q.ii.). On heating, the plate of the substance
expanded, the thin layer of air became thinner, and the position of the rings
was altered. From the alteration in their position the amount of the expan-
sion could be deduced. Among the results he has obtained is the curious
one that certain crystallised bodies, such as diamond, emerald, and cuprous
oxide, contract on being cooled to a certain temperature, but as the cooling
is continued below this temperature they expand. They have thus a tem-
perature of maximum density, as is the case with water (329). In the case
of emerald and cuprous oxide this temperature is at — 4-2°, in the case of
diamond at —42-3°.

317. The coefficients of expansion increase with the temperature. —
According to Matthiessen, who determined the expansion of some metals and
alloys by weighing them in water at different temperatures, the coefficients
of expansion are not quite regular between o^ and 100°. He found the fol-
lowing values for the linear expansion between 0° and 100° : —

Zinc . . . L^= Lq ( I -1-0-00002741 / + 0-0000000235 /-)

Lead . . . Lj= L^ (i -1- 0-00002716 / -1- 0*0000000074 ^')

Silver . . Lj= L(t -f 0-00001809 /-i- 0-0000000135 /-)

Copper. . . Lj= Ly ( I -1-0-00001408 /-I- 0-0000000264 /-)

Gold . . . Lj= L^ (i -I- 0-00001358 /-1-0-0000000112 /-)

Matthiessen further found that the coefficients of expansion of an alloy are
very nearly equal to the mean of the coefficients of expansion of the volumes
of the metals composing it.

3 1 8. Formulae relative to the expansion of solids, — Let / be the length
of a bar at zero, /' its length at the temperature f C, and a its coefficient of
linear expansion. The tables usually give the expansion for 1° between 0°
and 100° as in Art. 316, or for 100°; in this latter case a is obtained by
dividing the number by 100.

The elongation corresponding to / is / times a or at for a single unit of
length, or atl for / units. The length of the bar which is / at zero is I + afl
at i, consequently,

r = l + atl=l{\\at).

This formula gives the length of a body /' at /'', knowing its length / at
zero, and the coefficient of expansion a ; and by simple algebraical transforma-
tions we can obtain from it formulae for the length at zero, knowing the
length /' at /°, and also for finding a, the coefficient of linear expansion,
knowing the lengths /' and / at t° and zero respectively.

The formulas for cubical expansion are entirely analogous to the preceding.

The following are examples of the application of these formulae : —

(i.) A metal bar has a length /' at t'° ; what will be its length / at /° ?

From the above formula we first get the length of the given bar at zero,

u 2

292 On Heat. [318-

which is ; by means of the same formula we pass from zero to /'" in

multiplying by i + at., which gives for the desired length the formula
lJ\^^(it)
I + at'
(ii.) The density of a body being ^at zero, required its density d' at t°.
If I be the volume of the body at zero, and D its coefficient of cubical
expansion, the volume at t will be i + D/ ; and as the density of a body is in
inverse ratio of the volume which the body assumes in expanding, we get
the inverse proportion,

d' : d=\ : i + D/

d' I ,, d

or d ■

d i+Dt i+Dt

Consequently, when a body is heated from o to /^, its density, and therefore
its weight for an equal volume, is inversely as the expression, i + Dt.

319. A.ppIications of the expansion of solids. — In the arts we meet
with numerous examples of the influence of expansion, (i.) The bars of
furnaces must not be fitted tightly at their extremities, but must, at least,
be free at one end, otherwise in expanding they would split the masonry.
(ii.) In making railways a small space is left between the successive rails, for,
if they touched, the force of expansion would cause them to curve or would
break the chairs, (iii.) Water-pipes are fitted to one another by means of
telescope joints, which allow room for expansion, (iv.) If a glass vessel is
heated or cooled too rapidly, it cracks, especially if it be thick ; this arises
from the fact that, since glass is a bad conductor of heat, the sides become un-
equally heated, and consequently unequally expanded, which causes a fracture.
(v.) The cracking off of a portion of a glass tube by red-hot charcoal is due
to the expansion of the heated parts, which detach themselves from the rest.

When bodies have been heated to a high temperature, the force pro-
duced by their contraction on cooling is very considerable ; it is equal to
the force which is needed to compress or expand the material to the same
extent by mechanical means. According to Barlow, a bar of malleable iron
a square inch in section is stretched xooUo^^"^ ^^ '^^ length by a weight of a
ton ; the same increase is experienced by about 9'^ C. A difference of 45°
C. between the cold of winter and the heat of summer is not unfrequently
experienced in this country. In that range, a wrought-iron bar ten inches
long will vary in length by ^^^^^ '^^ ^'^ inch, and will exert a strain, if its ends
are securely fastened, of fifty tons. It has been calculated from Joule's data
that the work done by heat in expanding a pound of iron between 0° and 100°,
during which it increases about ^so of i*^s bulk, is equal to 16,000 foot-
pounds ; that is, it could raise a weight of over 7 tons through a height of one
foot.

(i.) An application of this contractile force is seen in the mode of secur-
ing tires on wheels. The tire being made red-hot, and thus considerably
expanded, is placed on the circumference of the wheel and then cooled.
The tire, when cold, embraces the wheel with such force as not only to
secure itself on the rim but also to press home the joints of the spokes into
the felloes and nave, (ii.) Another interesting application was made in the

-320] Compensation Penduhini. 293

case of a gallery at the Conservatoire des Arts at Metiers in Paris, the walls
of which had begun to bulge outwards. Iron bars were passed across the
building and screwed into plates on the outside of the walls. Each alternate
bar was then heated by means of lamps, and when the bar had expanded
it was screwed up. The bars being then allowed to cool contracted, and in
so doing drew the walls together. The same operation was performed on
the other bars.

320. Compensation pendulum. — An important application of the ex-
pansion of metals has been made in the compensation pcnduliun. This is
a pendulum in which the elongation, when the
temperature rises, is so compensated that the
distance between the centre of suspension and
the centre of oscillation (80) remains constant,
which, from the laws of the pendulum (81), is
necessary for isochronous oscillations, and in
order that the pendulum may be used as a
regulator of clocks.

In fig. 295, which represents the gridiron
pendulum, one of the commonest forms of com-
pensation pendulum, the ball, L, instead of
being supported by a single rod, is supported
by a framework, consisting of alternate rods of
steel and brass. In the figure, the shaded rods
represent steel ; including a small steel rod, b,
which supports the whole of the apparatus,
there are six of them. The rest of the rods,
four in number, are of brass. The rod /, which
supports the ball, is fixed at its upper end to a
horizontal cross-piece ; at its lower end it is
free, and passes through the two circular holes
in the lower horizontal cross-pieces.

Now it is easy to see from the manner in
which the vertical rods are fixed to the cross-
pieces, that the elongation of the steel rods can
only take place downward, and that of the
brass rods upward. Consequently, in order
that the pendulum may remain of the same :
length, it is necessary that the elongation of
the brass rods shall tend to make the ball
rise, by exactly the same quantity that the '^' ^^^'

elongation of the steel rod tends to lower it ; a result which is attained
when the sum of the lengths of the steel rods A is to the sum of the lengths
of the brass rods B in the inverse ratio of the coefficients of expansion of
steel and brass, a and b ; that is, in the proportion \:^ = b:a.

The elongation of the rod may also be compensated for by means of
compensating strips. These consist of two blades of copper and iron
soldered together and fixed to the pendulum rod, as represented in fig. 296.
The copper blade, which is more expansible, is below the iron. When the
temperature sinks, the pendulum rod loecomes shorter, and the ball rises. But

294

On Heat.

[320

at the same time the compensating strips become curved, as seen in fig. 297,
in consequence of the copper contracting more than the iron, and two
metal balls at their extremities become lower. If they have the proper size

Fig. 296.

in reference to the pendulum ball, the parts which tend to approach the
centre of suspension compensate those which tend to remove from it, and the
centre of oscillation is not displaced. If the temperature rises, the pendu-
lum ball descends; but at the same time the small balls ascend, as shown in
fig. 298, so that there is always compensation.

One of the most simple compensating pendulums is the mercury pendii-
luni, invented by an English watchmaker, Graham. The ball of the pendu-
lum, instead of being solid, consists of a glass cylinder, containing pure
mercury, which is placed in a sort of stirrup, supported by a steel rod.
When the temperature rises the rod and stirrup become longer, and thus
lower the centre of gravity; but at the same time the mercury expands, and,
rising in the cylinder, produces an inverse effect, and as mercury is much
more expansible than steel, a compensation may be effected without making
the mercurial vessel of undue dimensions.

The same principle is applied in the coinpc?tsati?ig balattces of chronometers
(fig. 299). The motion here is regulated by a balance or wheel, furnished with
a spiral spring not represented in the figure, and the time
of the chronometer depends on the force of the spring, the
mass of the balance, and on its circumference. Now
when the temperature rises the circumference increases,
and the chronometer goes slower ; and to prevent this
part of the mass must be brought nearer the axis. The
circumference of the balance consists of compensating
strips BC, of which the more expansible metal is on the
outside, and towards the end of these are small masses
of metal D, which p'ay the same part as the balls in the above case. When
the radius is expanded by heat, the small masses are brought nearer the
centre in consequence of the curvature of the strips ; and as they can be
fixed in any position, they are easily arranged so as to compensate for the
expansion of the balance. It may, however, here be observed that the chief
action of heat on chronometers is to expand and soften the spring, and
thereby lessen its elasticity; this action produces five times the effect on the
rate that the expansion of the balance-wheel does.

Fig. 299.

-321]

Apparent and Real Expansion.

'-9S

CHAPTER III.

EXPANSION OF LIQUIDS.

321. Apparent and real expansion. — A hollow space enclosed by a
solid expands as if it were wholly occupied by the solid ; for consider a
section of a glass tube ; we may regard this
as made up of a series of innumerable con-
centric circles ; when the tube is heated each
of these glass circles becomes longer, and in
doing so must press outwards, and these
expansions and elongations are the same
whether there is another circle within it or
not ; the hollow space will become larger
just as if it were a solid glass rod. This may
be illustrated by the following experiment.
If a flask of thin glass, provided with a nar-
row stem, the flask and part of the stem
being filled with some coloured liquid, be
immersed in hot water (fig. 300), the column
of liquid in the stem at first sinks from 3 to
a, but then immediately after rises, and con-
tinues to do so until the liquid inside has the
same temperature as the hot water. The
first sinking of the liquid is not due to its '^' ^°°'

contraction ; it arises from the expansion of the glass, which becomes heated
before the heat can reach the liquid ; but the expansion of the liquid soon
exceeds that of the glass, and the liquid then ascends.

Hence in the case of liquids we must distinguish between the apparent
and the real or absolute expansion. The apparent expansion is that which
•is actually observed when liquids contained in vessels are heated ; the abso-
lute expansion is that which would be observed if the vessel did not expand ;
or, as this is never the case, it is the apparent expansion corrected for the
simultaneous expansion of the containing vessel.

As has been already stated, the cubical expansion of liquids is alone con-
sidered ; and as in the case of solids, the coeffidettt of expansion of a liquid
is the mcrease of the unit of volume for a single degree ; but a distinction
is here made between the coefficient of absolute expa?ision and the coefficient
of apparefit expansion. Of the many methods which have been employed
for determining these two coefficients, we shall describe that of Dulong and
Petit.

296

On Heat.

[322-

322. Coefficient of the absolute expansion of mercury. — In order to
determine the coefificient of the absolute expansion of mercury, the influence
of the envelope must be eliminated. Dulong and Petit's method depends on
the hydrostatical principle that in two communicating vessels, the heights
of two columns of liquid in equilibrium are inversely as their densities (108),
a principle independent of the diameters of the vessels, and therefore of
their expansions.

The apparatus consists of two glass tubes, A and B (fig. 301), joined by
a capillary tube and kept vertical on an iron support, KM, the horizontality
of which is adjusted by means of two levelling screws and two spirit levels,
;// and 7i. Each of the tubes is surrounded by a metal case, of which the

Fig. 30X.

smaller, D, is filled with ice ; the other, E, containing oil, can be heated by
the furnace, which is represented in section so as to show the case. Mercuiy
is poured into the tubes A and B ; it remains at the same level in both, as
long as they are at the same temperature, but rises in B in proportion as it
is heated, and expands.

Let h and d be the height and density of the mercury in the leg A, at
the temperature zero, and h' and d' the same quantities in the leg B. From
the hydrostatical principle previously cited we have hd = h'd'. Now from

the problem in Art. 318, d' ■■

. , D being the coefficient of absolute

expansion of mercury ; substituting this value of d' in the equation, we

have — ^--, =hd. {xom which we get D = —-"— ,
I + D/ ' *" ht

The coefficient of absolute expansion of mercury is obtained from this

formula, knowing the heights h' and /;, and the temperature / of the bath in

which the tube B is immersed. In Dulong and Petit's experiment this tem-

-324] Weight Thermometer. 297

perature was measured by a weight thermometer, P (323), the mercury of
which overflowed into the basin, C, and by means of an air thermometer, T
(334) ; the heights // and h were measured by a cathetometer, K (88).

Dulong and Petit found by this method that the coefficient of absohite
expansion of mercury between 0° and 100° C. is ■~^, But they found that
the coefficient increased with the temperature. Between 100° and 200°
it is ^Jj5,'and between 200° and 300° it is ^3. The same observation
has been made in reference to other hquids, showing that their expansion
is not regular. It has been found that this expansion is less regular in
proportion as liquids are near a change in their state of aggregation ; that
is, approach their freezing or boiling points. Dulong and Petit found that
the expansion of mercury between — 36° and 100° is practically quite uniform.

Regnault, who determined this important physical constant, found that
the mean coefficient between 0° and 100° is 5555, between 100° and 200°,
^^Vj, and between 200° and 300°, j-^-^.

323. Coefficient of the apparent expansion of mercury. — The co-
efficient of apparent expansion of a liquid varies with the nature of the
envelope. That of mercury in glass

was determined by means of the
apparatus represented in fig. 302.
It consists of a glass cylinder to
which is joined a bent capillary
glass tube, open at the end. 3^

The apparatus is weighed first
empty, and then when filled with F,^ ^o„

mercury at zero : the difference

gives the weight of the mercury, P. It is then raised to a known tempera-
ture, /; the mercury expands, a certain quantity passes out, which is received
in the capsule and weighed. If the weight of this mercury be/, that of the
mercury remaining in the apparatus will be P -p.

When the temperature is again zero, the mercury in cooling produces an
empty space in the vessel, which represents the contraction of the weight ot
mercury P — /, from t° to zero, or, what is the same thing, the expansion
of the same weight from o to /f° ; that is, the weight p represents the ex-
pansion of the weight P-/, for f. If this weight expands in glass by a

quantity p for f, a single unit of weight would expand -—^ — - for /°, and

^ — for a single degree ; consquently, for D', the coefficient of ap-

{V-p)t

parent expansion of mercury in glass, we have D' = — — 2^ Dulong

and Petit found the coefficient of apparent expansion of mercuiy in glass to
be -i-

'-"- 6480-

324. 'Weight thermometer. — The apparatus represented in fig. 302 is
called the lueight thermometer, because the temperature can be deduced
from the weight of mercury which overflows.

The above experiments have placed the coefficient of apparent e.xpansion

at , 1-- ; we have therefore the equation - ^ = j:^\;-, from which we get

298 On Heat. [324-

t = -^ — ^, a formula which gives the temperature /when the weights P and
F-p

p are known.

325. Coefficient of the expansion of g^lass. — As the absolute expansion
of a liquid is the apparent expansion, //«^.y the expansion due to the envelope,
the coefficient of the cubical expansion of glass is obtained by taking the
difference between the coefficient of absolute expansion of mercury in glass
and that of its apparent expansion. That is, the coefficient of cubical expan-
sion of glass is

55'oS - 6i08 = 38f 00 = 0-00002 584.

Regnault found that the coefficient of expansion varies with different
kinds of glass, and further with the shape of the vessel. For ordinary
chemical glass tubes, the coefficient is 0-0000254.

326. Coefficients of expansion of various liquids. — The coefficient of
apparent expansion of liquids may be determined by means of an application
of the principle of the weight thermometer, and the absolute expansion is
obtained by adding to this coefficient the expansion of the glass.

Mean coefficieiifs of absolute expansioji of liquids for 1° C.

Mercury .

. o-oooiS

Fixed oils .

. o-ooo8o

Water saturated with

Nitric acid .

. o-ooiio

salt

. 0-00050

Alcohol

. 0-00104

Sulphuric acid .

. 0-00063

Bisulphide of carbon

. 0-00114

Oil of turpentine

. 0-00090

Chloroform .

. o-ooiii

Ether

. 0-00015

Bromine

. 0-00104

The numbers here given only hold for moderate temperatures. The co-
efficient of expansion of almost all liquids increases gradually from zero, and
can only be expressed with accuracy by a somewhat comphcated formula

in which / is the temperature, and o, /3, and 7 are constants specially deter-
mined for each liquid. The expansion of mercury is practically Constant
between —36° and 100° C, while water contracts from zero to 4°, and then
expands.

For many physical experiments a knowledge of the exact expansion of
water is of great importance. This physical constant was determined with
great care by Matthiessen, who found that between 4" and 30° it may be
expressed by the'formula

V/= I -0-00000253 (/- 4) -1- 0-0000008389 (^'- 4)- +0-00000007173(^-4)^;

and between 30 and 100 by V/ = 0-999695 + 0-0000054724/- -t- o-oooooooi 126/^
Many liquids, with low boiling points, especially condensed gases, have very
high coefficients of expansion. Thilorier found that liquid carbonic acid
expands four times as much as air. Drion confirmed this observation and
has obtained analogous results with chloride of ethyle, liquid sulphurous
acid, and liquid hyponitrous acid.

-329] Maximum Density of Water. 299

327. Correction of the barometric Iieigrbt. — It has been already ex-
plained under the barometer (164), that, in order to make the indications of
this instrument comparable in different places and at different times, they
must be reduced to a uniform temperature, which is that of melting ice. The
correction is made in the following manner : —

Let H be the barometric height at /f°, and h its height at zero, d the
density of mercury at zero, and d' its density at t°. The heights H and h

are inversely as the densities rfand d' ; that is, - = -. If we call one the

H d

volume of mercury at zero, its volume at t° will be i + D/, D being the co-
efficient of absolute expansion of mercury. But these volumes, i -f- D/ and i,

are inversely as the densities d and d' ; that is = —p. ,• Consequently,

A I , , H

-- = =:^, whence h = .

H I + D/' I + D/

/ 5508 + /
■-5558

In this calculation, the coefficient of absolute expansion of mercury is
taken, and not that of apparent expansion ; for the value H is the same as
if the glass did not expand, the barometric height being independent of the
diameter of the tube, and therefore of its expansion.

328. Correction of tbermometric readiD§rs. — If the whole column of
mercury of a thermometer is not immersed in the space whose temperature
is to be determined, it is necessary to make a correction, which in the
accurate determination of jDoiling points, for instance, is of great import-
ance, in order to arrive at the true temperature which the thermometer
should show. That part of the stem which projects will have a tempera-
ture which must be estimated, and which may roughly be taken as some-
thing over that of the surrounding air.

Supposing, for instance, the actual reading is 160° and that the whole of
the part over 80° is outside the vessel, while the temperature of the surround-
ing air IS 1 5°. We will assume that the mean temperature of the stem is 25°,
and that a length of 160° -80° is to be heated through 160-25 = 135° ; this

gives 80 X -i^ = 1-66 (taking the coefficient of apparent expansion of

6480
mercury) ; so that the true reading is 161 -66.

329. Force exerted by liquids in expanding:. — The force which liquids
exert in expanding is very great, and equal to that which would be required
in order to bring the expanded liquid back to its original volume. Now we
know what an enormous force is required to compress a liquid to even a
veiy small extent (97). Thus between 0° and 10°, mercury expands by
0-0015790 of its volume at 0° ; its compressibility is 0-00000295 of its volume
for one atmosphere ; hence a pressure of more than 600 atmospheres would
be requisite to prevent mercury expanding when it is heated from 0° to 10°.
In like manner a pressure of 140 atmospheres would be required to prevent
water from expanding when its temperature was raised from 4° to 14°.

300 On Heat. [330-

330. Maximum density of water. — Water presents the remarkable
phenomenon that when its temperature sinks it contracts up to 4° ; but
from that point, although the cooling continues, it expands up to the freezing
point, so that 4° represent the point of greatest contraction of water.

Many methods have been used to determine the maximum density of
water. Hope made the following experiment : — He took a deep vessel
with two apertures in the sides, in which he fixed thermometers, and
having filled the vessel with water at 0°, he placed it in a room at a tem-
perature of 15°. As the layers of liquid at the sides of the vessel became
heated they sank to the bottom, and the lower thermometer marked 4° while
the upper one was still at zero. Hope then made the inverse experiment ;
having filled the vessel with water at 15°, he placed it in a room at zero.
The lower thermometer having sunk to 4° remained stationary for some
time, while the upper one cooled down until it reached zero. Both these
experiments prove that water is heavier at 4° than at 0°, for in both cases it
sinks to the lower part of the vessel.

This last experiment may be adapted for lecture illustration by using a
cylinder containing water at 15° C, partially surrounded by a jacket contain-
ing bruised ice (fig. 303).

Hallstrom made a determination of the maximum density of water in the
following manner : — He took a glass bulb, loaded with sand, and weighed it

in water of different temperatures. Allow-
ing for the expansion of glass, he found
that 4-1° was the temperature at which it
lost most weight, and consequently this
was the temperature of the maximum
density of water.

Despretz arrived at the temperature
4° by another method. He took a water
thermometer — that is to say, a bulbed
tube containing water — and, placing it in
a bath, the temperature of which was in-
dicated by an ordinary mercury thermo-
meter, found that the water contracted to
the greatest extent at 4°, and that this
therefore is the point of greatest density.
This phenomenon is of great import-
ance in the economy of nature. In winter
the temperature of lakes and rivers falls,
from being in contact with the cold air
i.;.^. 30,. and from other causes, such as radiation.

The cold water sinks to the bottom, and
a continual series of currents goes on until the whole has a temperature of
4°. The cooling on the surface still continues, but the cooled layers being
lighter remain on the surface, and ultimately freeze. The ice formed thus
protects the water below, which remains at a temperature of 4°, even in the
most severe winters, a temperature at which fish and other inhabitants of
the water are not destroyed.

Salt dissolved in water lowers the temperature of the maximum density,

-330]

Maxiinuin Density of Water.

301

this

so that sea water exhibits such a maximum. According to Rosetti,
temperature is between 3°-2 and 3°-9 in the Adriatic.

The following table of the density of pure water at various temperatures
is based on several sets of observations : —

Density of water between 0° and 30°.

Tempe-

Densities

Tempe-

Densities

Tempe-

Densities

ratures

0-99988

0-99955

0-99738

0-99993

0-99943

0-99704

0-99997

0-99930

0-99689

0-99999

0-99915

0-99662

I -00000

0-99900

0-99635

0-99999

0-99884

0-99607

0-99997

1 18

0-99800

0-99579

0-99994

i 19

0-99847

0-99226

0-99988

; 20

0-99807

0-98320

0-99982

0-99806

0-98232

0-99974

0-99785

0-97796

0-99965

0-99762

0-97191

?02

On Heat.

[331-

CHAPTER IV.

EXPANSION AND DENSITY OF GASES.

331. Gay-Xussac's method. — Gases are the most expansible of all
bodies, and at the same time the most regular in their expansion. The co-
efficients of expansion, too, of the several gases differ only by very small
quantities. The cubical expansion of gases need alone be considered.

Gay-Lussac first determined the coefficient of the expansion of gases by
means of the apparatus represented in fig. 304.

In a rectangular metal bath, about 16 inches long, was fitted an air
thermometer, which consisted of a capillary tube, AB with a bulb, A, at one

end. The tube
'^ was divided into

parts of equal
capacity, and the
contents of the
bulb ascertained
ni terms of these
parts. This was
effected by weigh-
ing the bulb and
tube full of mer-
cury at zero,
and then heating
slightly to expel
a small quantity

Fig. 304.

of mercury, which was weighed. The apparatus being again cooled down
to zero, the vacant space in the tube corresponded to the weight of mercury
which had overflowed ; the volume of mercury remaining in the apparatus,
and consequently the volume of the bulb, was determined by calculations
analogous to those made for the piezometer (98).

In order to fill the thermometer with dry air it was first filled with
mercury, which was boiled in the bulb itself A tube, C, filled with chloride
of calcium, was then fixed on to its end by means of a cork. A fine platinum
wire having then been introduced into the stem AB, through the tube C, and
the apparatus being slightly inclined and agitated from time to time, air
entered, having been previously well dried by passing through the chloride
of calcium tube. The whole of the mercury was displaced, with the excep-
tion of a small thread, which remained in the tube AB as an index.

The air thermometer was then placed in the box filled with melting ice,
the index moved towards A, and the point was noted at which it became

-332] Problems on the Expansion of Gases. 303

stationary. This gave the volume of air at zero ; for the capacity of the
bulb was known. Water or oil was then substituted for the ice, and the
bath successively heated to different temperatures. The air expanded and
moved the index from A towards B. The position of the index in each case
was noted, and the corresponding temperature was indicated by means of
the thermometers D and E.

Assuming that the atmospheric pressure did not vary during the experi-
ment, and neglecting the expansion of the glass as being small in comparison
with that of the air, the total expansion of the air is obtained by subtracting
from its volume at a given temperature its volume at zero. Dividing this by a
given temperature, and then by the number of units contained in the volume
at zero, the quotient is the coefficient of expansion for a single unit of volume
and a single degree ; that is, the coefficiejit of expansion. It will be seen,
further on, how corrections for pressure and temperature may be intro-
duced.

By this method Gay-Lussac found that the coefficient of expansion of air
was 0-00375 ; the two following laws hold in reference to the expansion of
gases : —

I. All gases have the same cofficient of expaiision as air.

II. This coefficient is the same whatever be the pressure sipported by
the gas.

These simple laws are not, however, rigorously exact (333) ; they only
express the expansion of gases in an approximate manner. These laws were
discovered independently by Dalton and by Gay-Lussac, and are usually
ascribed to them. The first discoverer of the former law was, however,
Charles.

332. Problems on the expansion of gases. — Many of the problems
relative to the expansion of gases are similar to those on the expansion of
liquids. With obvious modifications, they are solved in a similar manner.
In most cases the pressure of the atmosphere must be taken into account
in considering the expansion of gases. The following is an example of the
manner in which this correction is made : —

i. The volume of a gas at t°, and under the pressure H, is V; what will
be the volume V of the same gas at zero, and under the normal pressure
760 millimetres ?

Here there are two corrections to be made ; one relative to the tempera-
ture, and the other to the pressure. It is quite immaterial which is taken
first. If a be the coefficient of cubical expansion for a single degree, by
reasoning similar to that in the case of linear expansion (318), the volume of

the gas at zero, but still under the pressure H, will be . This pressure

is reduced to the pressure 760 in accordance with Boyle's law (180), by

putting V X 760 = X H : whence V = — — j .

"^ I+a/ ' 760 (I -t- a/)

ii, A volume of gas weighs P' at t° ; what will be its weight at zero?

Let P' be the desired weight, a the coefficient of expansion of the gas,

d' its density at /°, and d its density at zero. As the weights of equal

volumes are proportional to the densities, we have — = — . If i be the

304

On Heat.

[332-

volume of a gas at

are inversely as the volumes

\t : but as the densities

and therefore

From this equation we get

hence P =P'(i + at).

which gives the weight at t, know-

zero, its \'olume at / will be i

'^'= '^
d~ \ + at'
I
+ at

P _
I + at

ing the weight at zero, and which further shows that the weight P' is inversely
as the binomial of expansion i + at.

333. Reg-nault's method.— Regnault used successfully four different
methods for determining the expansion of gases. In some of them the
pressure was constant and the volume variable, as in Gay-Lussac's method ;
in others the volume remained the same while the pressure varied. The
first method will be described. It is the same as that used by Rudberg and
Dulong, but is distinguished by the care with which all sources of error are
avoided.

The apparatus consisted of a pretty large cylindrical reservoir, B (fig.
305), terminating in a bent capillary tube. In order to fill the reservoir with

Fig. 305-

dry air, it was placed in a hot-water bath, and the capillary tube connected
by a caoutchouc tube with a series of drying tubes. These tubes were
joined to a small air-pump, P, by which a vacuum could be produced in the
reservoir while at a temperature of 100°. The reservoir was first exhausted,
and air afterwards admitted slowly ; this operation was repeated a great
many times, so that the air in the reservoir became quite dry, for the mois-
ture adhering to the sides passed off in vapour at 100°, and the air which
entered became dry in its passage through the U tubes.

The reservoir was then kept for half an hour at the temperature of boil-
ing water ; the air-pump having been detached, the diying tubes were then
disconnected, and the end of the tube hermetically sealed, the height H of
the barometer being noted. When the reservoir B was cool, it was placed

-333]

Regnaiilfs MetJiod.

305

in the apparatus represented in fig. 306. It was there quite surrounded
with ice, and the end of the tube dipped in the mercury bath, C. After the
air in the reservoir B had sunk to zero, the
point b was broken off by means of a forceps ;
the air in the interior became condensed by
atmospheric pressure, the mercury rising to a
height cG. In order to measure the height of
this column, Gf, which will be called h^ a mov-
able rod, go, was lowered until its point, <?, was
flush with the surface of the mercury in the
bath ; the distance between the point 0 and the
level of the mercury G was measured by means
of the cathetometer. The point b was finally
closed with wax by means of the spoon «, and
the barometric pressure noted at this moment.
If this pressure be H', the pressure in the reser-
voir is W -h.

The reservoir was now weighed to ascertain
P, the weight of the mercury which it con-
tained. It was then completely filled with mer-
cury at zero, in order to have the weight P' of __

the mercury in the reservoir and in the tube. ^ ,.

If S be the coefficient of the cubical expan-
sion of glass, and D the density of mercury at zero, the coefficient a of
the cubical expansion of air is determined in the following manner: —

P'
The volume of the reservoir and of the tube at zero is , from the formula

P = VD (126) ; consequently, this volume is

at the temperature /°, assuming, as is the case, that the reservoir and tube
expand as if they were soUd glass (321). But from the formula P = VD, the
volume of air in the reservoir at zero, and under the pressure H' — //, is

D ■

P^-P
D

(i+S/) (I)

At the same pressure, but at /°, its volume would be

(l+n/)

and by Boyle's law (180), at the pressure H, at which the tube was sealed,
this volume must have been

(P'

(2)

Now the volumes represented by these formulte, (i) and (2), are each
equal to the volume of the leservoir and the tube at t° ; they are therefore
equal. Removing the denominators, w^e have

P'(i+5/)H = (P'-P)(i+«/)(H'-/2) (3)

from which the value of a is deduced.

3o6 On Heat. [333-

The means of a great number of experiments between zero and ioo° and
for pressure between 300 millimetres and 500 millimetres, gave the following
numbers for the coefficients of expansion for a single degree : —

Air .

. 0-003667

Carbonic acid .

. 0-003710

Hydrogen .

. 0-003661

Nitrous oxide .

. 0-003719

Nitrogen .

. 0-003661

Cyanogen

. 0-003877

Carbonic oxide .

. 0-003667

Sulphurous acid

. 0-003903

These numbers, with which the results obtained by Magnus closely agree,
show that the coefficients of expansion of the permanent gases differ very
little ; but that they are somewhat greater in the case of the more easily
condensable gases, such as carbonic and sulphurous acids. Regnault has
further found that, at the same temperature, the coefficient of expansion of
any gas increases with the pressure which it supports. Thus, while the
coefficient of expansion of air under a pressure of i lo-mm. is 0-003648, under
a pressure of 3655 mm., or nearly five atmospheres, it is 0-003709.

The number found by Regnault for the coefficient of the expansion of
air, 0-003667, is equal to :^^ = ^ig nearly ; and if we take the coefficient of ex-
pansion at 0-0036666 ... it may be represented by the fraction jii^,
which is convenient for purposes of calculation.

The small differences in the expansibility of various gases may be ascribed
to the circumstance that when a gas is heated the relative positions of the
atoms in the molecules are thereby altered ; and a certain amount of internal
work is required for this, which is different for different gases.

334. Air thermometer. — The air thermometer is based on the expan-
sion of air. When it is used to measure small differences of temperature, it
has the same form as the tube used by Gay-Lussac in determining the ex-
pansion of air (fig. 304), that is, a capillary tube with a bulb at the end. The
reservoir being filled with dry air, an index of coloured sulphuric acid is
passed into the tube ; the apparatus is then graduated in Centigrade degrees
by comparing the positions of the index with the indications of a mercurial
thermometer. Of course the end of the tube must remain open ; otherwise,
the air above the index condensing or expanding at the same time as that in
the bulb, the index would remain stationary. A correction must be made
at each observation for the atmospheric pressure.

When considerable variations of temperature are to be measured, the
tube has a form hke that used in Regnault's experiments (figs. 305 and 306).
By experiments made as described in Art. 333, P, P', H, H', and h may
be found, and the coefficients a and S being known, the temperature t to
which the tube has been raised is readily reduced from the equation (3).

Regnault found that the air and the mercurial thermometer agree up to
260°, but above that point mercury expands relatively more than air. In
cases where very high temperatures are to be measured, the reservoir is
made of platinum. The use of an air thermometer is seen in Dulong and
Petit's experiment (322) ; it was by such an apparatus that Pouillet measured
the temperature corresponding to the colours which metals take when heated
in a fire, and found them to be as follows : —

335J

Incipient red
Dull red
Cherry red .

Density of Gases.

525° C. Dark orange ,
. 700 White .

. 900 Dazzling white

307

1100° C

1500

In the measurement of high temperatures Deville and Trpost used with
advantage the vapour of iodine instead of air, and, as platinum has been
found to be permeable to gases at high temperatures, they employed porce-
lain instead of that metal.

The expansion of gases has been determined by Jolly by means of a
form of apparatus which is also a convenient form of air thermometer (fig,
^yO'j). A quadrangular post rests on a tripod ; on one side
of this post is a graduated glass scale, while in the two
others are grooves in which screw-blocks A and A' can be
slid up and down and adjusted at any height.

A glass bulb a is prolonged in a tube bent twice, the
end of which is provided with a stopcock, not shown in
the figure, and in which can be fitted a glass tube R sup-
ported by the block A. This again is fitted to a flexible
india-rubber tube, at the other end of which is an open
glass tube R' fixed to the block A'. This tube contains
mercury.

The bulb a having been filled with dry air, the stopcock
is closed, the tube R fixed, and the stopcock opened.
The bulb a is then immersed to the stem in melting ice,
and when it is supposed that the temperature is stationary,
the tube R' is moved up and down until the mercury in
the other limb is at a mark S. The difference betv/een
the levels of the mercury at S and at R' is noted. If the
latter is higher the difference is added to, and if lower
subtracted from, the barometric height at the time, to give
the pressure h in the vessel a.

The bulb a is then placed in a space at any constant
temperature, and the same operation repeated to get the
pressure /;, From the ratio of the total pressures in the two cases we get
the coefficient of expansion a from the formula h : h^ = i +ai : i + ai\ By
means of this apparatus Jolly found 0-00366957 for the value of a.

335. Density of g-ases. — The relative density of a gas, or its specific
gravity, is the ratio of the weight of a certain volume of the gas to that of
the same volume of air ; both the gas and the air being at zero and under a
pressure of 760 millimetres.

In order, therefore, to find the specific gravity of a gas, it is necessary to
determine the weight of a certain volume of this gas at a pressure of 760
millimetres, and a temperature of zero, and then the weight of the same
volume of air under the same conditions. For this purpose a large globe of
about two gallons' capacity is used, the neck of which is provided with a
stopcock, which can be screwed to the air-pump. The globe is first weighed
empty, and then full of air, and afterwards full of the gas in question. The
weights of the gas and of the air are obtained by subtracting the weight of
the exhausted globe from the weight of the globes filled, respectively, with

X 2

Fig. 307,

3o8 On Heat. [335-

air and gas. The quotient, obtained by dividing the latter by the former,
gives the specific gravity of the gas. It is difficult to make these determina-
tions at the same temperature and pressure, and therefore all the weights
are reduced to zero and the normal pressure of 760 millimetres.

The gases are dried by causing them to pass through drying tubes before
they enter the globe, and air must also be passed over potash to free it from
carlDonic acid. And as even the best air-pumps never produce a perfect
vacuum, it is necessary to exhaust the globe until the manometer in each
case marks the same pressure.

The globe having been exhausted, dried air is allowed to enter, and the
process is repeated several times until the globe is perfectly dried. It is then
finally exhausted until the residual pressure in millimetres is e. The weight
of the exhausted globe is/. Air, which has been dried and purified by passing
through potash and chloride of calcium tubes, is then allowed to enter
slowly. The weight of the globe full of air is P. If H is the barometric
height in millimetres, and f the temperature at the time of weighing, P -p is
the weight of the air in the globe at the temperature /, and the pressure H - ^.

To reduce this weight to the pressure 760 millimetres and the tempera-
ture zero, let a be the coefficient of the expansion of air, and 8 the coefficient
of the cubical expansion of glass. From Boyle's law the weight, which is

P -p at f and a pressure of H - ^, would be ^ —~'flj^^ under the pressure

H — ^

760 millimetres and at the same temperature f. If the temperature is 0°,

the capacity of the globe will diminish in the ratio i + S/ to i, while the

weight of the gas increases in the ratio 1:1+ «/, as follows from the problems

in Art. 332. Consequently, the weight of the air in the globe ato"^ and at the

pressure 760 millimetres will be

76o(i^«0

^ ^^(H ~c){i+bt) ^ '

Further, let a' be the coefficient of expansion of the gas in question ; let
P' be the weight of the globe full of gas at the temperature /' and the pres-
sure H', and let/' be the weight of the globe when it is exhausted to the
pressure e ; the weight of the gas in the globe at the pressure 760 and the
temperature zero will be

iV'-p') 76oii+aY)^ .... (2)

Dividing the latter formula by the former we obtain the density

n-(P^-/')(H-^)(i+ar)(i+a/)

(F-p) (H'-e) (i+o/)(n SO
If the temperature and the pressure do not vary during the experiment,

H = H' and / = /' ; whence D = (-^-:i^lil±«_'^_), and if n = a', D = ^'~J'.
(P-/)(i+a/j' P-p

336. Reg-nault's xnetbod of deterxniningr the density of gases. —

Regnault so modified the above method that many of the corrections may
be dispensed with. The globe in which the gas is weighed is suspended

336]

Density of Gases.

309

from one pan of a balance, and is counterpoised by means of a second globe
of the same dimensions, and hermetically sealed, suspended from the other.
These two globes, expanding at the same time, always displace the same
cjuantity of air, and consec^uently variations in the temperature and pressure
of the atmosphere do not influence the weighing. The globe too, is filled
with the air or with the gas, at the temperature of zero. This is effected by
placing it in a vessel full of ice, as shown in fig. 308. It is then connected
with a three-way cock, A, by which it may be connected either with an air-
pump, or with the tubes M and N, which are connected with the reservoir
of gas. The tubes M and N contain substances which by their action on
the gas dry and also purify it.

The stopcock A being so turned that the globe is only connected with
the air-pump, a vacuum is produced ; by means of the same cock, the con-
nection with the pump being cut off, but established with M and N, the

Fig. 308.

gas soon fills the globe. But, as the exhaustion could not have been com-
plete, and some air must have been left, the globe is again exhausted and
the gas allowed to enter, and the process is repeated until it is thought all
air is removed. The vacuum being once more produced, a differential
barometer (fig. 152), connected with the apparatus by the tube E, indicates
the pressure of the residual rarefied gas e. Closing the cock B and de-
taching A, the globe is removed from the ice, and after being cleaned is
weighed.

This gives the weight of the empty globe/ ; it is again replaced m the
ice, the stopcock A adjusted, and the gas allowed to enter, care being taken
to leave the stopcocks open long enough to allow the gas in the globe to ac-
quire the pressure of the atmosphere, H, which is marked by the barometer.
The stopcock A is then closed, A removed, and the globe weighed with the
same precautions as before. This gives the weight P' of the gas.

310

On Heat.

[336-

The same operations are then repeated on this globe with air, and two
corresponding weights j^J and P are obtained. The only correction necessary
is to reduce the weights in the two cases to the standard pressure by the
method described in the preceding paragraph. The correction for temperature
is not needed, as the gas is at the temperature of melting ice. The ratio of
the weight of the gas to that of the air is thus obtained by the formula

v-p-

337. Density of grases which attack metals. — For gases which attack
the ordinary metals, such as chlorine, a metal stopcock cannot be used, and
vessels with ground-glass stoppers are substituted. The gas is introduced
by a bent glass tube, the vessel being held either upright or inverted, accord-
ing as the gas is heavier or lighter than air ; when the vessel is supposed to
be full, the tube is withdrawn, the stopper inserted, and the weight taken.
This gives the weight of the vessel and gas. If the capacity of the vessel
be measured by means of water, the weight of the air which it contains is
deduced, for the density of air at 0° C. and 760 millimetres pressure is ^i^
that of distilled water under the same circumstances. The weight of the
vessel full of air, less the weight of the contained air, gives the weight of the
vessel itself. From these three data — the weight of the vessel full of the gas,
the weight of the air which it contains, and the weight of the vessel alone —
the specific gravity of the gas is readily deduced, the necessary corrections
being made for temperature and pressure.

Density of gases at zero and at a pressure of -bo niillimetres, that of
air being taken as ttnity .

Air .

I -oooo

Sulphuretted hydrogen

1-1912

Hydrogen .

0-0693

Hydrochloric acid

1-2540

Ammoniacal gas .

0-5367

Protoxide of nitrogen .

1-5270

Marsh gas .

0-5590

Carbonic acid

1-5291

Carbonic oxide .

0-9670

Cyanogen .

I -8600

Nitrogen .

0-9714

Sulphurous acid .

2-2474

Binoxide of nitrogen

I -0360

Chlorine

3-4400

Oxygen

I-I057

Hydriodic acid .

4-4430

Regnault made the following determinations of the weight of a litre of
the most important gases at 0° C. and 760 mm. : —

Air. . . 1-293187 grms. Nitrogen . 1-256157 grms.

Oxygen . . 1-429802 ,, Carbonic acid 1-977414 „

Hydrogen . 0-089578 „

-338]

Fusion. Its Laivs.

311

CHAPTER V.

CHANGES OF CONDITION. VAPOUR.

338. Fusion. Its laws. — The only phenomena of heat with which we
have hitherto been engaged have been those of expansion. In the case of
solids it is easy to see that this expansion is limited. For in proportion as
a body absorbs a larger quantity of heat, the vis viva of the molecules is
increased, and ultimately a point is reached at which the molecular attraction
is not sufificient to retain the body in the solid state. A new phenomenon is
then produced; melting ox fusion takes place; that is, the body passes from
the solid into the liquid state.

Some substances, however, such as paper, wood, wool, and certain salts,
do not fuse at a high temperature, but are decomposed. Many bodies have
long been considered refractory — that is, incapable of fusion ; but, in pro-
portion as it has been possible to produce higher temperatures, their number
has diminished. Gaudin succeeded in fusing rock crystal by means of a
lamp fed by a jet of oxygen ; and Despretz, by combining the effects of the
sun, the voltaic battery, and the oxy-hydrogen blowpipe, melted alumina
and magnesia, and softened carbon so as to be flexible, which is a condition
near that of fusion.

It has been found experimentally that the fusion of bodies is governed
by the two following laws : —

I. E'i'e7y substa?tce begins to fuse at a certain temperature, which is
invai'iable for each substance, if the pressure be coftstant.

II. Whatever be the intensity of the source of heat, from the moment
fusion begins, the temperature of the body ceases to rise, and remains constant
tin til the fusioji is complete.

Melting points of certain substances.

Mercury .

-38-8°

Potassium

55'

Oil of turpentine

-27

Margaric acid .

Bromine .

- 12

Stearine .

Ice .

White wax

Nitrobenzene

+ 3-0

Wood's fusible metal

Formic acid

8-5

Stearic acid .

Acetic acid

Sodium .

Butter

T:)

Rose's fusible metal .

Rubidium .

Sulphur .

114

Phosphorus

Benzoic acid .

120

Spermaceti

Indium .

176

Heat.

Tin

228°

Aluminium

Bismuth .

246

Silver

Cadmium .

321

Gold

Lead

335

Copper .

Zinc ....

422

Iron.

Antimony

450

Platinum .

Arsenic

. 500

Iridium .

Magnesium

• 750

[338-

850°
954
1035
1054
1500

1775
1950

Some substances pass from the solid to the liquid state without showing
any definite melting point ; for example, glass and iron become gradually
softer and softer when heated, and pass by imperceptible stages from the
solid to the liquid condition. This inter-
mediate condition is spoken of as the state
oi vitreous fusion. Such substances may be
said to melt at the lowest temperature at
which perceptible softening occurs, and to be
fully melted when the further elevation of
temperature does not make them more fluid ;
but no precise temperature can be given as
their melting points.

The determination of the melting point
of a body is a matter of considerable im-
portance in fixing the identity of many che-
mical compounds, and is moreover a point
of frequent practical application in deter-
mining the commercial value of tallow and
other fats.

It is done as follows : — A portion of the
substance is melted in a watch-glass, and a
small quantity of it sucked into a fine capil-
laiy tube, which is then placed in a bath
T of clear water (fig. 309) attached to a ther-

==^- ^^^^^Z=^ mometer, and the temperature of the bath

Fig 30Q is gradually raised until the substance is

completely melted, which from its small mass
is very easily observed. The bath is then allowed to cool, and the solidi-
fying point noted ; and the mean of the two is taken as the true melting
point.

339. Influence of pressure on the melting- point. — Thomson and
Clausius have deduced from the principles of the mechanical theory of heat
that, with an increase of pressure, the melting point of a body must be raised.
All bodies which expand on passing from the solid to the liquid state have
to perform external work — namely, tc raise the pressure of the atmosphere
by the amount of this expansion. Under ordinary circumstances, the
amount of external work which solids and liquids thus perfoi"m is so small
that it may be neglected. But, if the external pressure be increased, the
power of overcoming it can only be obtained by an increase of vis viva of
the molecules. The increase can do more work ; the temperature of fusion

-339] lufiiiciicc of Pressjire on the Melting Point. 3 1 3

and the heat of fusion are both increased. Bunsen examined the influence
of pressure on the melting point by means of the apparatus represented in
fig. 310, in which act is a thick tube about the thickness of a straw in the
clear, in the parts ca and the bent part b. The whole tube having been filled
with mercury, it was sealed at «, and then a small quantity was driven out
at b and some of the substance introduced ; the end b was then w

sealed and a opened, and the whole tube gently warmed so as
to expel some mercury, upon which a was again hermetically
sealed.

When the tube was placed in a bath of warm water a little
above the melting point of the body, the mercury expanded and
a pressure resulted which could be accurately measured from
the diminution in volume of the air in ca., which was carefully
calibrated for this purpose. By carefully raising or lowering
the instrument in the water, the pressure could be increased
or diminished at will. It only then remained to observe the
temperature at which the substance solidified, and the corre-
sponding pressure at that moment. In this way Bunsen found
that spermaceti, which melts at 48° under a pressure of i atmo-
sphere, melts at 51" under a pressure of 156 atmospheres.
Hopkins found that spermaceti melted at 60° under a pressure
of 519 atmospheres, and at 80° under 792 atmospheres; the
meltmg point of sulphur under these pressures was respectively
135° and 141°.

But with regard to those bodies which contract on passing
from the solid to the liquid state, and of which water is the best
example, the reverse is the case. Melting ice has no external p.^ ^^^
work to perform, since it has no external pressure to raise ; on
the contrary, in melting, it absorbs external w^ork, which, transformed into
heat, renders a smaller quantity of heat necessary ; the external work acts in
the same direction as the internal heat — namely, in breaking up the crystal-
line aggregates. Yet these differences of temperature must be but small, for
the molecular forces in solids preponderate far over the external pressure ;
the internal work is far greater than the external.

Sir W. Thomson found that increase of pressure lowered the melting-
point of ice. The apparatus consisted of a piezometer (fig. 311) ; a thick
leaden ring divided the vessel into two compartments, the upper one of which
contained water and the lower one crushed ice, which was thus prevented
from rising, This also served to support a thermometer enclosed in a very
stout tube, and a manometer with compressed air. The pressures were
exerted by means of a screw piston V.

Sir W. Thomson thus found that pressures of St and 16 "8 atmospheres
lowered the melting point of ice by 0-059'^ and 0-126° respectively. These
results justify the theoretical previsions of Prof. J. Thomson, according to
which an increase of pressure of n atmospheres lowers the melting point of
ice by 0-0074;;° C., so that a pressure of 135 atmospheres, or about 2,000
pounds to the square inch, would lower the melting point 1° C.

This lowering of the melting point is also shown by the experiment of
Mousson (fig. 312). The apparatus consists of a stout steel tube closed

314 On Heat. [339-

at one end by a screw and with a screw piston at the other (fig. 312). The
tube is filled with water and a metal bullet introduced. When the apparatus
is closed it is inverted so that the bullet rests on the piston, and placed thus

in a freezing mixture ;
the water freezes and
presses the ball against
the piston. This is then
turned again, and pressure
is gradually applied by
turning the handle of the
screw. When the lower
screw is opened the
copper ball falls out, and
is followed by a thick
cylinder of ice which must

Fig. 311. Fig. 312.

have been formed at the moment of opening. Hence the ice must, by a
pressure estimated at 13,000 atmospheres, have been converted into water

at about -18° C.

This influence is likewise readily
demonstrated by an experiment of
Von Helmholtz (fig. 313). Water
is boiled in a flask until all air is
expelled, and it is then closed. It
is afterwards placed in a freezing
mixture so that some ice forms
inside. This is then allowed to
melt again in great part, and the
flask is placed in a vessel of water
containing lumps of ice. It is then
found that the still unfrozen water
inside the flask freezes while that
of the outside is melting.

340. Alloys. Fluxes. — Alloys

are generally more fusible than

any of the metals of which they

'°' ^^■'' are composed ; for instance, an

alloy of 5 parts of tin and i of lead fuses at 194°. The alloy known as

Rose's fusible inctal^ which consists of 4 parts of bismuth, i part of lead.

-342]

Solution. 3 1 5

and I of tin, melts at 94°, and an alloy of i or 2 parts of cadmium with 2
parts of tin, 4 parts of lead, and 7 or 8 parts of bismuth, known as Wood's
fusible Jlieial, melts between 66° and 71° C. An alloy of potassium and
sodium in equivalent proportions is liquid at the ordinary temperature.
F'usible alloys are of extended use in soldering and in taking casts. Steel
melts at a lower temperature than iron, though it contains carbon, which
is almost completely infusible.

Mixtures of the fatty acids melt at lower temperatures than the pure acids.
A mixture of the chlorides of potassium and of sodium fuses at a lower tem-
perature than either of its constituents ; the same is the case with a mixture
of the carbonates of potassium and sodium, especially when they are mixed
in the proportion of their chemical equivalents.

An application of this property is met with in the case o{ fluxes, which are
much used in metallurgical operations. They consist of substances which,
when added to an ore, partly by their chemical action, help the reduction of
the substance to the metallic state, and, partly, by presenting a readily
fusible medium, promote the agglomeration of the individual particles with
the formation of a mass of metal or regulus.

341. Xiatent heat. — Since, during the passage of a body from the solid
to the liquid state, the temperature remains constant until the fusion is com-
plete, whatever be the intensity of the source of heat, it must be concluded
that, in changing their condition, bodies absorb a considerable amount of
heat, the only effect of which is to maintain them in the liquid state. This
heat, which is not indicated by the thermometer, is called latent heat or
latent heat of fusion, an expression which, though not in strict accordance
with modern ideas, is convenient from the fact of its universal recognition
and employment (461).

An idea of what is meant by latent heat maybe obtained from the follow-
ing experiment :— If a pound of water at 80° is mixed with a pound of water
at zero, the temperature of the mixture is 40°. But if a pound of pounded ice
at zero is mixed with a pound of water at 80°, the ice melts and two pounds
of water at zero are obtained. Consequently the mere change of a pound of
ice to a pound of water at the same temperature requires as m.uch heat as
will raise a pound of water through 80°. This quantity of heat represents
the latent heat of the fusion of ice, or the latent heat of water.

Every liquid has its own latent heat, and in the chapter on Calorimetiy
we shall show how this is determined.

342. Solution. — A body is said to dissolve when it becomes liquid in con-
sequence of an attraction between its molecules and those of a liquid. Gum
arabic, sugar, and most salts dissolve in water. The weight dissolved gene-
rally increases with the temperature. When a Hquid has dissolved as much
as it can at a particular temperature, it is said to be saturated.

During solution, as well as during fusion, a certain quantity of heat always
becomes latent, and hence it is that the solution of a substance usually
produces a diminution of temperature. In certain cases however, instead
of the temperature being lowered, it actually rises, as when caustic potash is
dissolved in water. This depends upon the fact that two simultaneous
and contrar)' phenomena are produced. The first is the passage from the
solid to the liquid condition, which always lowers the temperature. The

3i6 On Heat. [342-

second is the chemical combination of the body dissolved with the hquid,
and which, as in the case of all chemical combinations, produces an increase
of temperature. Consequently, as the one or the other of these effects pre-
dominates, or as they are equal, the temperature either rises or sinks, or
remains constant.

343. Solidification — Solidification or congelation is the passage of a
body from the liquid to the solid state. This phenomenon is regulated by
the two following laws : —

I. Every body, under the same pressure, solidifies at a fixed temperature,
which is the same as that of ficsio7i.

II. Frojn the commencement to the end of the solidification, the tempera-
ture of a liquid remains constant.

Certain bodies, more especially some of the fats, present an exception to
the first law, in so far that by repeated fusions they seem to undergo a
molecular change which alters their melting point.

The second law is the consequence of the fact that the latent heat ab-
sorbed during fusion becomes free at the moment of solidification.

The application of the very low temperature which can now be so readily
procured has lessened the number of those liquids which it was formerly
thought could not be solidified. By allowing liquid ethylene (382) to boil in
a vacuum, Wroblewski and Olszewski obtained a temperature of — 136°.
They observed that carbon disulphide solidified at - 116° and fused again at
about —110°. Absolute alcohol became viscid at — 129° and solidified at
— 130-5°. Pure ether solidifies at 129°.

Water containing a salt dissolved always solidifies below zero; the de-
pression of the freezing point is proportional to the weight of salt dissolved,
at any rate for weak solutions. This is known as Blagden^s law.

If several salts which have no chemical action on each other be dis-
solved in a given weight of water the loweinng of the freezing point is the
sum of the depressions which each of them, would produce separately if dis-
solved in the same quantity of water.

When the numbers observed in any experiment of this kind do not agree
with those calculated, this points to the occurrence of some chemical action
between the substances dissolved, and the observation of such deviations
has been of use in questions of chemical statics.

The elaborate researches of Raoult on the temperature of solidification
of solutions of bodies in water and other solvents have led to important con-
clusions. The temperature at which a solution solidifies, or its freezing point,
is always lov/er than that of the pure solvent. If P be the weight in grammes
of any substance dissolved in 100 grammes of a solvent, and C be the depres-

C ■

sion in the freezing point observed, then = A is the depression which would

be produced by dissolving 07ie gramme of the substance in 100 grammes,
and is known as the coefficient of depression.

A comparison of the values for A for various substances and the same
solvent shows that they differ considerably ; this is not so if we compare the
depressions produced by molecular weights of the substances. That is, if we
multiply the value of A in the above equation by M, the molecular weight of
the substance dissolved, we obtain the depression which would be produced

-345] Retardation of the Point of Solidification. 317

by dissolving one molecule of a body in 100 grammes of the solvent, or the
coefficient of inotecular dep7'ession ; this is called T, and we have T = -5—.

Now it is found that in a very large number of cases the value of T, for
one and the same solvent, is a constant number ; it has the value 19 for
water, 39 for glacial acetic acid, and 49 for benzene.

This relation makes it possible to calculate the molecular weight of a
solid in solution by means of a simple determina-
tion of the freezing point of a solution, which is
effected by means of the apparatus represented in
fig. 314, due to Prof Ramsay. A wide test-tube is
closed by an indiarubber stopper A perforated with
two holes. In one of these is a sensitive thermo-
meter D, specially graduated, and by which the
looth of a degree may be read off. In the other is
a piece of wide glass tubing B, through which a
stirrer C moves freely up and down. The beaker
E contains hot or cold water, as required, in order
to raise the temperature above, or depress it below,
the melting point of the solvent.

Since C and P are known, M is determined
from the formula

^ {

where T is the constant for the particular solvent
employed, which is ordinary glacial acetic acid in
the majority of cases.

344. Crystallisation, — Generally speaking. Fig 31^
bodies which pass slowly from the liquid to the

solid state assume regular geometrical forms, such as the cube prisms,
rhombohedra, &c. ; these are called crystals. If the crystals are formed
from a body in fusion, such as sulphur or bismuth, the crystallisation is
said to take place by the dry way. The crystallisation is said to be by the
moist way when it takes place owing to the slow evaporation of a solution of
a salt, or when a solution saturated at a higher temperature is allowed to
cool slowly. Snow, ice, and many salts present examples of crystallisation.

345. Retardation of the point of solidification. — The freezing point of
pure water can be diminished by several degrees, if the water be previously
freed from air by boiling and be then kept in a perfectly still place. In
fact, it may be cooled to — 15° C, and even lower, without freezing. But
when it is slightly agitated, the liquid at once solidifies. This may be con-
veniently shown by means of the apparatus represented in fig. 315, which
consists of a delicate thermometer, round the bulb of which is a wider one
containing some water. Before sealing at a the whole outside bulb was
filled with water, which was then boiled out and sealed so that over the
water the space is quite empty. This is clamped in a retort stand, and
ether is dropped on it, that which has dropped off, and become colder,
being used over and over again. In this way the temperature may soon

3i8

On Heat.

[345-

be reduced to — 6°, and if then the bulb be shaken part of the water freezes
and the temperature rises to zero. The smaller the quantity of liquid, the
lower is the temperature to which it can be cooled, and the greater the
mechanical disturbance it supports without fi-eezing. Fournet has observed
the frequent occurrence of mists formed of particles of liquid
matter suspended in an atmosphere whose temperature was io°
or even 15° below zero.

A very rapid agitation also prevents the formation of ice.
The same is the case with all actions which, hindering the
molecules in their movements, do not permit them to arrange
themselves in the conditions necessary for the solid state.
Despretz was able to lower the temperature of water contained in
ly fine capillary tubes to — 20° without their solidifying. This
experiment shows how it is that plants in many cases do not
become frozen even during severe cold, as the sap is contained
in very fine capillary vessels.

If water contains salts, or other foreign bodies, its freezing point
is lowered. Sea water freezes at -2'5°to — 3°C. ; the ice which
forms is quite pure, and a saturated solution remains. In Finland
advantage is taken of this property to concentrate sea-water for
the purpose of extracting salt from it. If water contains alcohol,
precisely analogous phenomena are observed ; the ice formed is
pure, and practically all the alcohol is contained in the residue.

Dufour has observed some very curious cases of liquids cooled
out of contact with solid bodies. His mode of experimenting was
to place the liquid in another of the same specific gravity but of
lower melting point, and in which it is insoluble. Drops of water,
for instance, suspended in a mixture of chloroform and oil, usually
solidified between - 4° and - 12°, while still smaller globules cooled
down to —18° or -20°. Contact with a fragment of ice immedi-
ately set up congelation. Globules of sulphur (which solidifies
p;„ at 115°) remained liquid at 40°; and globules of phosphorus

(solidifying point 42°) at 20°.
The superfusion of phosphorus may be illustrated by the experiment repre-
sented by fig. 316. A long test tube containing phosphorus, A, and covered
with a layer of water, is fixed along with a thermometer T in a large flask con-
taining water. This flask is raised to a temperature of about 44° at which the
phosphorus fuses, and is then withdrawn from the source of heat ; as its mass
is considerable, it cools very slowly and the phosphorus remains liquid even at
ordinary temperature. A glass rod may even be dipped into it without change ;
but if the rod be rubbed along solid phosphorus so as to detach a small par-
ticle, it at once brings about solidification if dipped in the melted mass.

When a liquid solidifies after being cooled below its normal freezing pointy
the solidification takes place very rapidly, and is accompanied by a disen-
gagement of heat, which is sufficient to raise its temperature from the point
at which solidification begins up to its ordinary freezing point. This is
well seen in the case of hyposulphite of sodium, which melts in its own
water of crystallisation at 45°, and when carefully cooled will remain liquid
at the ordinary temperature of the atmosphere. If it then be made to

-346] Change of Volume on Solidification. 319

solidify by agitation, or by adding a small fragment of the solid salt, the
rise of temperature is distinctly felt by the hand. In this case the heat,
which had become latent in the process of liquefaction, again l^ecomes free,,
and a portion of the sub-
stance remains melted ; for
it is kept liquid by the heat
of solidification of that which
has solidified.

346. Change of volume
on solidification and lique-
faction.— The rate of ex-
pansion of bodies generally
increases as they approach
their melting points, and is
in most cases followed by a
further expansion at the
moment of liquefaction, so
that the liquid occupies a
greater volume than the solid
from which it is formed. The
apparatus represented in fig.
317 is well adapted for ex-
hibiting this phenomenon.
It consists of a glass tube,
ab, containing water or some
other suitable liquid, to which
is carefully fitted a cork with

a graduated glass tube c. This forms, in fact, a thermometer, and the
values of the degrees on the tube c are determined in terms of the
capacity of the whole apparatus. A known volume of the substance is.
placed in the tube aa and the cork inserted ; the apparatus is then
placed in a space at a temperature very little below the melting point
of the body in question, until it has acquired its temperature, and the
position of the liquid in c is noted. The temperature is then allowed
to rise slowly, and the position noted when the melting is complete.
Knowing then the difference in the two readings and the volume of the
substance under experiment, and making a correction for the expansion of
the liquid and of the glass, it is easy to deduce the increase due to the
melting alone. Phosphorus, for instance, increases about 3-4 per cent, on
liquefaction ; that is, 100 volumes of solid phosphorus at 44° (the melting
point) become 103-4 at the same temperature when melted. Sulphur expands
about 5 per cent, on liquefying, and stearic acid about 1 1 per cent.

Water presents a remarkable exception ; it expands at the moment of
solidifying, or contracts on melting, by about 10 per cent. One volume of
ice at 0° gives 0-9 178 of water at 0°, or i volume of water at 0° gives i'io2
of ice at the same temperature. In consequence of this expansion, ice floats
on the surface of water. According to Dufour, the specific gravity of ice is
0-9178 ; Bunsen found for ice which had been freed from water by boiling
the somewhat smaller number 0-91674.

Fig.

Fig. 317.

320 On Heat. [346-

The iiicrease of volume in the formation of ice is accompanied by an
expansive force whicii sometimes produces powerful mechanical effects, of
which the bursting of water-pipes and the breaking of jugs containing water
are familiar examples. The splitting of stones, rocks, and the swelling up
of moist ground during frost, are caused by the fact that water penetrates
into the pores and there becomes frozen ; in short, the great expansion of
water on freezing is the most active and powerful agent of disintegration on
the earth's surface.

The expansive force of ice was strikingly shown by some experiments of
Major Williams, in Canada. Having cjuite filled a 13-inch iron bomb-shell
with water, he firmly closed the touch-hole with an iron plug weighing three
pounds and exposed it in this state to the frost. After some time the iron
plug was forced out with a loud explosion, and thrown to a distance of 415
feet, and a cylinder of ice 8 inches long issued from the opening (fig. 318).
In another case the shell burst before the plug was driven out, and in this
case a sheet of ice spread out all round the crack. It is probable that under
the great pressure some of the water still remained licjuid up to the time
at which the resistance was overcome ; that it then issued from the shell in
a liquid state, but at a temperature below 0°, and therefore instantly began
to solidify when the pressure was removed, and thus retained the shape of
the orifice whence it issued.

Cast-iron, bismuth, and antuBony expand on solidifying, like water, and
can thus be used for casting ; but gold, silver, and copper contract, and
hence coins of these metals cannot be cast, but must be stamped with a die.
This increase of volume when liquids solidify, and the correlated decrease
on melting again, in the case of water and some other
crystalline substances such as bismuth, are probably due to
the fact that such bodies are aggregates of small crys-
talline masses, which are grouped in such a way that
small interstices are formed. When the liquid melts
these interstices fill up owing to the mobility of the mole-
Fig. 31S. cules, and, notwithstanding the greater space which each
individual group takes up, owing to expansion, there is a decrease of volume.
347. rreezing- mixtures. — The absorption of heat in the passage of
bodies from the solid to the liquid state has been used to produce artificial
cold. This is effected by mixing together bodies which have an affinity for
each other, and of which one at least is solid, such as water and a salt, ice
and a salt, or an acid and a salt. Chemical affinity accelerates the fusion :
the portion which melts robs the rest of the mixture of a large quantity of
sensible heat, which thus becomes latent. In many cases a very consider-
able diminution of temperature is produced.

The following table gives the names of the substances mixed, their pro-
portions, and the corresponding diminutions of temperature : —

Parts Reduction of

Substances by weight temperature

Sulphate of sodium . . . 8 ) o 0

Hydrochloric acid . . . . 5, +10 to -17

Pounded ice or snow . . . 21

Common salt

-I- lo^to-ii

+ lo'to-

-348] Guth'ie's Researches. 321

. Parts Reduction of

Substances by weight temperature

Sulphate of sodium . . . . 3) +10° to -19°

Dilute nitric acid . . . . 2 )

Sulphate of sodium . . . . 6 j

Nitrate of ammonium . . . 5- +10° to -26°

Dilute nitric acid . . . . 4'

Phosphate of sodium . . . 9 )

Dilute nitric acid . . . . 4 j

If the substances taken be themselves previously cooled down, a still
more considerable diminution of temperature is occasioned.

Freezing mixtures are frequently used in chemistry, in physics, and in
domestic economy. One form of the portable ice-making machines which
have come into use during the last few years consists of a cylindrical
metallic vessel divided into four concentric compartments. In the central
one is placed the water to be frozen ; in the next there is the freezing
mixture, which usually consists of sulphate of sodium and hydrochloric acid ;
6 pounds of the former and 5 of the latter will make 5 to 6 pounds of ice in
an hour. The third compartment also contains water, and the outside one
contains some badly conducting substance, such as cotton, to cut off the
influence of the external temperature. The best effect is obtained when
pretty large quantities (2 or 3 pounds) of the mixture are used, and when
the ingredients are intimately mixed. It is also advantageous to use the
machines for a succession of operations.

348. Guthrie'.s researclies.— It appears from the experiments of the late
Dr. Guthrie that what are called freezing mixtures may be divided into two
classes, namely those in which one of the constituents is liquid and those
in which both are soHd. The temperature indicated by the thermometer
placed in a freezing mixture is, of course, due to the loss of heat by the
thermometer to the liquefying freezing mixture, and is measured by the rate
of such loss. The quantity of heat absorbed by the freezing mixture is
obviously the heat required to melt the constituents, together with ( ± ) the
heat of combination of the constituents. When one constituent is Hquid,
as when hydrochloric acid is added to ice, then a lower temperature is got
by previously cooling the hydrochloric acid. There is no advantage in
cooling the ice. But when both constituents are solid, as in the case of the
ice-salt freezing mixture, there is no advantage to be gained by cooling one
or both constituents. Within very wide limits it is also in the latter case a
matter of indifference as to the ratio between the constituents. Nor does it
matter whether the ice is finely powdered as snow or in pieces as large as a pea.

The different powers of various salts when used in conjunction with ice
as freezing mixtures appear to have remained unexplained until Guthrie
showed that, with each salt, there is always a minimum temperature below
which it is impossible for an aqueous solution of any strength of that salt to
exist in the liquid form ; that there is a certain strength of solution for each
salt which resists solidification the longest, that is, to the lowest temperature.
Weaker solutions give up ice on being cooled, stronger solutions give up the
salt either in the anhydrous state or in combination with water. That
particular strength of a particular salt, which resists solidification to the

322 On Heat. [348-

lowest temperature, is called by Guthrie a cryohydrate. It is of such a
strength that when cooled below o° C. it solidifies as a whole ; that is, the
ice and the salt solidify together and form crystals of constant composition
and constant melting and the same solidifying temperatures. The liquid
portion of a freezing mixture, as long as the temperature is at its lowest, is,
indeed, a melted cryohydrate. The slightest depression of temperature below
this causes solidification of the cryohydrate, and hence the temperature can
never sink below the solidifying temperature of the cryohydrate.

Guthrie has also shown that colloid bodies, such as gum and gelatine,
neither raise the boiling point of water nor depress the solidifying point, nor
can they act as elements in freezing mixtures.

VAPOURS. MEASUREMENT OF THEIR TENSION.

349. Vapours. — We have already seen (146) that vapours are the aeriform
fluids into which volatile substances, such as ether, alcohol, water, and
mercury, are changed by the absorption of heat. Volatile liquids are those
which thus possess the property of passing into the aeriform state, and fixed
liquids are those which do not form vapour at any temperature without
undergoing chemical decomposition, such as the fatty oils. Ice and snow
volatilise in closed spaces, forming crystals on the cooled parts. The forma-
tion of vapour is thus not restricted to the liquid state, and in some bodies^
such as arsenic, the boiling point is below the freezing point. As the boiling
point is raised by pressure it is possible to liquefy such bodies also, by apply-
ing sufficient pressure.

Iodine melts at 104° and boils at 175° under ordinary pressure. It there-
fore evaporates after melting ; but at a pressure of 250 mm. its boiling point
is below its melting point, and it then evaporates without melting. Even at
ordinary temperatures a considerable quantity volatilises without melting.

Vapours are transparent, like gases, and generally colourless ; there are
only a few coloured liquids 'which also give coloured vapours.

350. Vaporisation — The passage of a liquid into the gaseous state is
designated by the general term vaporisation ; the term evaporation espe-
cially refers to the slow production of vapour at the free surface of a liquid,,
and boiling to its rapid production in the mass of the liquid itself We shall
presently see (356) that at the ordinary atmospheric pressure, ebullition,
like fusion, takes place at a definite temperature. This is not the case
with evaporation, which occurs even with the same liquid at very different
temperatures, although the formation of a vapour seems to cease below a
certain point. Mercury, for example, gives no vapour below - 10°, nor sul-
phuric acid below 30°.

351. Elastic force of vapour. — Like gases, vapours have a certain
elastic force, in virtue of which they exert pressures on the sides of vessels in
which they are contained. The elastic force of vapour may be demonstrated
by the following experiment :— A quantity of mercury is placed in a bent
glass tube (fig. 319), the shorter leg of which is closed ; a few drops of ether
are then passed into the closed leg and the tube is immersed in a water bath
at a temperature of about 45°. The mercury then sinks slowly in the short
branch, and the space ab is filled with a gas which has all the appearance of

-352J

Formation of Vapour in a Vacuum.

323

air, and whose elastic force counterbalances the pressure of the coknnn of
mercury cd., and the atmospheric pressure on d. This gas is the vapour of
ether. If the water be cooled, or if the tube be removed from the bath, the
vapour which fills the space ab disappears, and the drop of ether is reproduced.
If, on the contraiy,
the bath be heated still
higher, the level of the
mercury descends be-
low b, indicating an
increase in the elastic
force of the vapour.

352. rormation of
vapour In a vacuum.
— In the previous ex-
periment the liquid
changed very slowly
into the vaporous con-
dition ; this occurs
also when a liquid is
freely exposed to the
air. In both cases the
atmosphere is an ob-
stacle to the vapori-
sation. In a vacuum
there is no resistance,
and the formation of
vapour is instanta-
neous, as is seen in
the following experi-
ment : — Four baro-
meter tubes, filled with

mercury, are immersed in the same trough, fig. 320. One of them. A,
serves as a barometer, and a few drops of water, alcohol, and ether are re-
spectively introduced into the tubes B, C, D. When the liquids reach the
vacuum, a depression of the mercury is at once produced. And as this
depression cannot be caused by the weight of the liquid, which is an ex-
tremely small fraction of the weight of the displaced mercury, it must be
due to the formation of some vapour whose elastic force has depressed the
column of mercury.

The experiment also shows that the depression is not the same in all the
tubes ; it is greater in the case of alcohol than of water, and greater with
ether than wfth alcohol. We consequently obtain the two following laws of
the formation of vapours : —

I. In a vacuum all volatile liquids qrc instantaneously co freer ted into
vapour.

II. At the same temperature the vapours of different liquids have different
elastic forces.

For example, at 20° the tension of ether vapour is 25 times as great as
that of aqueous vapour.

Y 2

F.g.

Fig. 320.

324 On Heat. [353-

353. Saturated vapour. Maximum of tension. — When a very small
quantity of a volatile liquid, such as ether, is introduced into a barometer
tube, it is at once completely vaporised, and the mercurial column is not
depressed to its full extent ; for if some more ether be introduced the
depression increases. By continuing the addition of ether, it finally ceases
to vaporise, and remains in the liquid state. There is, therefore, for a cer-

tam temperature, a limit to the quantity of vapour
which can be formed in a given space. This space
is accordingly said to be saturated. Further, when
the vaporisation of the ether ceases, the depression
of the mercurial column stops. And hence there
is a limit to the tension of the vapour, a limit
which, as we shall presently see (354), varies with
the temperature.

To show that, in a closed space, saturated with
vapour and containing liquid /// excess^ the tempera-
ture remaining constant, there is a maximian of
teiision which the vapour cannot exceed, a baro-
metric tube is used which dips in a deep bath
(fig. 321). This tube is filled with mercury, and
then so much ether is added as to be in excess
after the Torricellian vacuum is saturated. The
height of the mercurial column is next noted by
means of the scale graduated on the tube itself
Now, whether the tube be depressed, which tends
to compress the vapour, or whether it be raised,
which tends to expand it, the height of the mercurial
column is constant. The tension of the vapour
remains constant in the two cases, for the depres-
sion neither increases nor diminishes it. Hence it
is concluded that when the saturated vapour is
compressed, a portion returns to the liquid state ;
that when, on the other hand, the pressure is
diminishedj a portion of the excess of liquid vapor-
ises, and the space occupied by the vapour is again
saturated ; but in both cases the tension and the
density of the vapour remain constant.

354. Unsaturated vapours. — From what has been said, vapours pre-
sent two vei-y different states, according as they are saturated or not. In
the first case, where they are saturated and in contact with the liquid, they
differ completely from gases, since for a given temperature they can neither
be compressed nor expanded ; their elastic force and their density remain
constant.

In the second case, on the contrary, where they are not saturated, they
exactly resemble gases. For if the' experiments (fig. 321) be repeated, only a
small quantity of ether being introduced, so that the vapour is not saturated,
and if the tube be then slightly raised, the level of the mercury is seen to rise,
which shows that the elastic force of the vapour has diminished. Similarly,
by immersing the tube still more, the level of the mercury sinks. The vapour

Fig. 321

-356 J Tension of Aqueous Vapour beloiv Zero. 325

consequently behaves just as a gas would do, its tension diminishes when the
volume increases, and vice 7'ef-sd ; and as in both cases the volume of the
vapour is inversely as the pressure, it is concluded that icnsaturated vapours
obey Boyle's law.

When an unsaturated vapour is heated, its volume increases like that of
a gas ; and the number 0"oo366, which is the coefficient of the expansion of
air, may be taken for that of vapours.

Hence we see that the physical properties of unsaturated vapours are
comparable with those of gases, and that the formulae for the compressibility
and expansibility of gases (182 and 332) also apply to unsaturated vapours.

355. Tension of aqueous vapour belowr zero. — In order to measure
the elastic force of aqueous vapour below zero, Gay-Lussac used two baro-
meter tubes filled with mercury, and placed in
the same bath (fig. 322). The straight tube, A,
serves as a barometer ; the other, C, is bent, so
that part of the Torricellian vacuum can be sur-
rounded by a freezing mixture, B (347). When
a little water is admitted into the bent tube, the
level of the mercury sinks below that in the
tube A, to an extent which varies with the tem-
perature of the freezing mixture.

At o*^ the depression is . 4'54 millimetres

„ - 1° ,,
„ - 3° „

• 4-25
■ 3-63

• 3-II
. 2-67
. 2 -08
. 0-84

• 0-36

These depressions, which must be due to
the pressure of aqueous vapour in the space BC,
show that even at very low temperatures there
is always some aciueous vapour in the atmo-
sphere.

Although in the above experiment the part B
and the part C are not both immersed in the
freezing mixture, we shall presently see that
when two communicating vessels are at different
temperatures, the tension of the vapour is the
same in both, and always corresponds to that of the lower temperature.

That water evaporates even below zero follows from the fact that wet linen
exposed to the air during frost becomes first stiff and then dry, showing that the
particles of water evaporate even after the latter has been converted into ice.

356. Tension of aqueous vapour between zero and one hundred
degrees. — i. Daltoiis method. Dalton measured the elastic force of aqueous
\apour between 0° and 100° by means of the apparatus represented in
fig. 323. Two barometer tubes, A and B, are filled with mercur}', and inverted
in an iron bath full of mercury, which is placed on a furnace. The tube A

Fig. 322.

326

On Heat.

[356-

contains a small quantity of water. The tubes are supported in a cylindrical
vessel full of water, the temperature of which is indicated by the thermometer.
The bath being gradually heated, the water in the cylinder becomes heated
too ; the water which is in the tube A vaporises, and in proportion as the
tension of its vapour increases, the mercury sinks. The depressions of the
mercury corresponding to each degree of the thermometer are indicated on
the scale E, and in this manner a table of the elastic forces between zero and
1 00° has been constructed.

ii. Regnaidfs method.— Dalton's method is wanting in precision, for the
liquid in the cylinder has not everywhere the same temperature, and con-

Fig. 323. r 1 -4

sequently the exact temperature of the aqueous vapour is not shown.
Regnault's apparatus is a modification of that of Dalton. The cylindrical
vessel is replaced by a large cylindrical zinc drum, MN (fig. 324), in the
bottom of which are two tubulures. The .tubes A and B pass through these
tubulures, and are fixed by caoutchouc collars. The tube containing vapour,
B, is connected with a flask, a., by means of a brass three-way tube, O. The
third limb of this tube is connected with a drying tube, D, containing
pumice charged with sulphuric acid, which is connected with the air-pump.

-357] Tension of Aqueous Vapour above lOO degrees. 327

When the flask a contains some water, a small portion is distilled into B
by gently heating the flask. Exhausting, then, by means of the air-pump,
the water distils continuously from the flask and from the barometric tube
towards D, which condenses the vapour. After having vaporised some
quantity of water, and when it is thought that the air in the tube is with-
drawn, the capillary tube which connects B with the three-way tube is sealed.
The tube B being thus closed, it is experimented with as in Dalton's method.

The drum, MN, being filled with water, is gently heated by a spirit lamp,
which is screened from the tubes by a wooden board. By means of a
stirrer, K, all parts of the liquid are kept at the same temperature. In the
side of the drum is a glass window, through which the height of the mercury
in the tubes can be read off by means of a cathetometer ; from the difference
in these heights, reduced to zero, the tension of vapour is deduced. By
means of this apparatus, the elastic force of vapour between 0° and 50° has
been determined with accuracy.

F.s S25

357. Tension of aqueous vapour above one hundred degrees. — Two

methods have been employed for determining the tension of aqueous vapour
at temperatures above 100°; the one by Dulong and Arago, in 1830, and the
other by Regnault, in 1844.

Fig. 325 represents a vertical section of the apparatus used by Dulong
and Arago. It consisted of a copper boiler, k, with very thick sides, and of
about 20 gallons' capacity. Two gun-barrels, a, of which only one is seen in
the drawing, were firmly fixed in the sides of the boiler, and plunged in the
water. The gun-barrels were closed below, and contained mercury, in which
were placed thermometers, /, indicating the temperature of the water and of
the vapour. The tension of the vapour was measured by means of a mano-
meter with compressed air, ;//, previously graduated (184) and fitted into
an iron vessel, d^ filled with mercury. In order to see the height of the

328

On Heat.

[357-

mercury in the vessel, it was connected above and below with a glass tube, ;?,
in which the level was always the same as in the bath. A copper tube, i,
connected the upper part of the vessel, d, with a vertical tube, c, fitted in the
boiler. The tube / and the upper part of the bath d were filled with water,
which was kept cool by means of a current of cold water flowing from a
reservoir, and circulating through the tube b.

The vapour which was disengaged from the tube c e.xerted a pressure
on the water of the tube / ; this pressure was transmitted to the water and
to the mercury in the bath d^ and the mercury rose in the manometer. By
noting on the manometer the pressures corresponding to each degree of the
thermometer, Dulong and Arago were able to make a direct measurement
of the tension up to 24 atmospheres, and the tension from this pressure to
50 atmospheres was determined by calculation.

358. Tension of vapour below and above one hundred degrees. —
Regnault devised a method by which the tension of vapour may be measured

Fig. 326.

at temperatures either below or above 100°. It depends on the principle
that when a liquid boils, the tension of the vapour is equal to the pressure
it supports (363). If, therefore, the temperature and the correspondmg
pressure are known, the question is solved, and the method merely consists
in causing water to boil in a vessel under a given pressure, and measuring
the corresponding temperature.

The apparatus consists of a copper retort, C (fig. 326), hermetically sealed
and about two-thirds full of water. In the cover there are four thermometers,

358]

Table of Tensions of Aqueous Vapour.

two of which just dip into the water, and two descend ahiiost to the bottom.
By means of a tube, AB, the retort C is connected with a glass globe, M, of
about 6 gallons' capacity, and full of air. The tube AB passes through a
metal cylinder, D, through which a, current of cold water is constantly
tlowing from the reservoir E. To the upper part of the globe a tube with
two branches is attached, one of which is connected with a manometer, O ;
the other tube, HH', which is of lead, can be attached either to an exhaust-
ing or a condensing air-pump, according as the air in the globe is to be rare-
fied or condensed. The reservoir K, in which is the globe, contains water
at the temperature of the surrounding air.

If the elastic force of aqueous vapour below ioo° is to be measured, the
end H' of the lead pipe is connected with the plate of the air-pump, and
the air in the globe M, and consequently that in the retort C, is rarefied.
The retort being gently heated, the water begins to boil at a temperature
below ioo°, in consequence of the diminished pressure. And since the vapour
is condensed in the tube AB, which is always cool, the pressure originally
indicated by the manometer does not increase, and therefore the tension of
the vapour during ebullition remains equal to the pressure on the liquid.

A little air is then allowed to enter ; this alters the pressure, and the
liquid boils at a new temperature ; both these are read off, and the experi-
ment repeated as often as desired up to ioo°.

In order to measure the tension above ioo°, the tube H' is connected
with a condensing pump, by means of which the air in the globe M and that
in the vessel C are exposed to successive pressures, higher than the atmo-
sphere. The ebullition is retarded (367), and it is only necessary to observe
the difference in the height of the mercury in the two tubes of the mano-
meter O, and the corresponding temperature, in order to obtain the tension
for a given temperature. The following tables by Regnault give the tension
of acjueous vapour from — 10° to 104° : —

Tensiojis of aqueous vapour from

- 10° to 104° C.

Tempe-

Tensions in

Tempe-

Tensions in

Tempe-

Tensions in

Tempe-

Tensions in

ratures

millimetres

ratures

millimetres

ratures

millimetres

ratures

millimetres

-10°

2-078

1 12°

10-457

29°

29-782

90°

525-45

2-456

1 1 -062

31-548 I

545-78

2-890

1 1 -906

33-405 1

566-76

3-387

i 15

12-699

35-359

588-41

3'955

13-635

37-410

610-74

4-600

i 17

14-421

39-565

633-78

H- I

4-940

1 ^8

15-357

41-827

657-54

5-302

1 19

16-346

54-906

682-03

5-687

j 20

17-391

71-391

707-26

6-097

.. 21

18-495

91-982

98-5

720-15

6-534

19-659

117-479

99-0

733-91

6-998

-3

20-888

148-791

99-5

746-50

7-492

; -4

22-184

186-945

loo-o

760-00

S-ot7

23-550

233-093

100-5

773-71

8-574

' 26

24-998

288-517

loi-o

787-63

9-165

I, 27

26-505

354-643

I02-0

816-17

9-792

: 28

28-101

433-41

104-0

875-69

330

On Heat.

[358-

Tensions in atmospheres from loo

' to 230-9°.

Number

Temperatures

of atmo-

Temperatures

of atmo-

Temperatures

of atmo-

Temperatures

of atmo-

spheres

ioo-o°

170-8°

198-8°

217-9°

I 12-2

i '-'

175-8

201-9

220-3

I20-6

180-3

204-9

222-5

133-9

184-5

207-7

224-7

I44-0

188-4

210-4

226-8

152-2

192-1

213-0

228-9

156-2

1 6

195-5

215-5

230-9

165-3

In the second table the numbers were obtained by direct observation
up to 24 atmospheres ; the others were calculated by the aid of a formula of
interpolation.

This table and the one next following show that the elastic force increases
much more rapidly than the temperature. It has been attempted to express
the relation between them by formukt, but none of the formula; seems to have
the simplicity which characterises a true law.

359. Tension of the vapours of different liquids. — Regnault deter-
mined the elastic force, at various temperatures, of a certain number of
liquids which are given in the following table : —

Liquids

Tempe-
ratures

Tensions in
millimetres

Liquids

Tempe-
ratures

millimetres

(

0°

0-02

-20°

Mercury .

o-ii

Ether

182

(

100

0-74

1728

100

4950

Alcohol. .

100

-20

220

1695

Sulphurous
acid

-20

479
1165
8124

Bisulphide ]

132

{

-30

876

of carbon 1

1 164

Ammonia .

3163

100

3329

8832

360. Tension of the vapours of mixed liquids. — Regnault's experiments
on the tension of the vapour of mixed liquids prove that (i.) when two liquids
exert no solvent action on each other — such as water and bisulphide of carbon,
or water and benzole — the tension of the vapour which rises from them is
nearly equal to the sum of the tensions of the two separate 'liquids at the
same temperature ; (ii.) with water and ether., which partially dissolve each
other, the tension of the mixture is much less than the sum of the tensions
of the separate liquids, being scarcely equal to that of the ether alone ;
(iii.) when two liquids dissolve in all proportions, as ether and bisulphide of
carbon, or water and alcohol, the tension of the vapour of the mixed liquids
is intermediate between the tensions of the separate liquids.

362J

Evaporation. Causes luliich Accelerate it.

331

Wiillner has shown that for weak sokitions the tension of aqueous vapour
emitted from a sahne solution, as compared with that of pure water, is
diminished by an amount proportional to the quantity of anhydrous salt dis-
solved, when the salt crystallises without water or yields efflorescent crystals :
when the salt is deliquescent, or has a powerful attraction for water, the re-
duction of tension is proportional to the quantity of crystallised salt.

361. Tension in two communicatingr vessels at different tempera-
tures.— When two vessels containing the same liquid, but at different tem-
peratures, are
connected with
each other, the
elastic force is
not that corre-
sponding to the
mean of the two
temperatures, as
would naturally
be supposed.
Thus, if there
are two globes
(fig. 327), one, A,
containing water
kept at zero by
means of melting
ice, the other, B,

containing water at 100°, the tension, as long as the globes are not con-
nected, is 4 to 6 millimetres in the first, and 760 millimetres in the second.
But when they are connected by opening the stopcock C, the vapour in the
globe B, from its greater tension, passes into the other globe, and is there
condensed, so that the vapour in B can never reach a higher pressure than
that in the globe A. The liquid simply distils from B towards A without
any increase of tension.

From this experiment the general principle may be deduced that luhen
two vessels containing the same liquid, but at different temperatures, are con-
nected, tlie pressure is identical in both vessels, atzd is the same as that corre-
sponding to the lower temperature. An application of this principle has been
made by Watt in the condenser of the steam-engine.

362. evaporation. Causes which accelerate it. — Evaporation, as has
been already stated (349), is the slow production of vapour at the surface of
a liquid. It is in consequence of this evaporation that wet clothes dry when
exposed to the air, and that open vessels containing water become empty.
The vapours which, rising in the atmosphere, condense, and, becoming clouds,
fall as rain, are due to the evaporation from seas, lakes, rivers, and the earth.

Four causes influence the rapidity of the evaporation of a liquid : i. the
temperature ; ii. the quantity of the same vapour in the surrounding atmo-
sphere ; iii. the renewal of this atmosphere ; iv. the extent of the surface of
evaporation.

Increase of temperature accelerates the evaporation by increasing the
elastic force of the vapours.

33:

On Heat.

[362-

In order to understand the intluence of the second cause, it is to be ob-
served that no evaporation could take place in a space already saturated
with vapour of the same licpid, and that it would reach its maximum in
air completely freed from this vapour. It therefore follows that between
these two extremes, the rapidity of evaporation varies according as the
surrounding atmosphere is already more or less charged with the same
vapour.

The effect of the renewal of this atmosphere is similarly explained ; for
if the air or gas, which surrounds the liquid, is not renewed, it soon becomes
saturated, and evaporation ceases. Dalton found that the ratios of the
evaporation in a feeble, medium, and strong draught were respectively as
270 : 347 : 424. He also observed that the quantity evaporated in perfectly
dry, almost still air, at a temperature of 20°, was equivalent to o-i of a gramme
on a square decimetre of surface in a minute.
The effect of the fourth cause is self-evident.

Vegetation exercises a great influence on evaporation. Schiibler found
that the evaporation from a space covered with meadow grass, in the most
vigorous stage of its growth, was thrice as rapid as that from an adjacent
surface of water. As the plants ripened the evaporation diminished.

363. Xiaws of ebullition — Ebullition.,
or boiling, is the rapid production of
elastic bubbles of vapour in the mass of a
liquid itself.

When a liquid, water for example, is
heated at the lower part of a vessel, the
first bubbles are due to the disengagement
of air which had previously been absorbed.
Small bubbles of vapour then begin to
rise from the heated parts of the sides,
but as they pass through the upper layers,
the temperature of which is lower, they
condense before reaching the surface. The
formation and successive condensation of
these first bubbles occasion the singitig
noticed in liquids before they begin to
boil. Lastly, large bubbles rise and burst
on the surface, and this constitutes the
phenomenon of ebullition (fig. 328).

The laws of ebullition have been
determined experimentally, and are as
follows : —

I. Tlic tcmpe7'atiire of ebullition or the boiling point increases with the
pressure.

II. For a given pressure ebullition begins at a certain te7nperature, which
varies in differ e7tt liquids., but which, for equal pressures, is always the same
in the same liquid.

III. Whatever be the intensity of the source of heat, as soon as ebullition
begins the temperature of the liquid remains statiottary.

Fig 328

*J 1 UeorcticaL HxpU
Boiling points

ination c
aide?- the

]/ iLvaporation and h mil
pressure ofj6o niillinietres.

Lition.

Nitrous oxide

■ -93°

Butyric acid

156°

Carbonic acid

. -80

Turpentine

157

Ammonia

• -39

Aniline

182

Chloride of methyle

• -23

Iodine

200

Cyanogen

-20

Naphthaline

217

Sulphurous acid .

- 10

Benzoic acid .

261

Chloride of ethyle

. + ir

Phosphorus

290

Aldehyde

Diphenylamine

310

Ether .

Strong sulphuric acid

318

Bisulphide of carbon

Phenanthrene .

340

Acetone

• 56

Mercury .

-358

Bromine

■ 58

Phosphate of phenyl

407

Methylic alcohol .

Arsenic

437

Alcohol

• 78

Sulphur .

448

Benzole

Phosphorus pentasulphide

530

Distilled water

100

Selenium .

665

Acetic acid .

117

Cadmium .

746

Amylic alcohol

131

Zinc ....

940

Propionic acid

• 137

Kopp has pointed out that in homologous chemical compounds the same
difference in chemical composition frequently involves the same difference
of boiling points ; and he has shown that in a very extensive series of com-
pounds, the fatty acids for instance, the difference of CH'- is attended by
a difference of 19° C. in the boiling poini. In other series of homologous
compounds, the corresponding difference in the boiling point is 30°, and in
others again 24°.

364. Theoretical explanation of evaporation and ebullition. — From
what has been said about the nature of the motion of the molecules in liquids
(292), it may readily be conceived that in the great variety of these motions,
the case occurs in which, by a fortuitous concurrence of the progressive,
vibratory, and rotatory motions, a molecule is projected from the surface of
the liquid with such force that it overleaps the sphere of the action of its cir-
cumjacent molecules, before, by their attraction, it has lost its initial velocity ;
and that it then flies into the space above the liquid.

Let us first suppose this place limited and originally vacuous ; it gradu-
ally fills with the propelled molecules, which act like a gas and in their
motion are driven against the sides of the envelope. One of these sides,
however, is the surface of the liquid itself, and a molecule when it strikes
against this surface will not in general be repelled, but will be retained by the
attraction which the adjacent ones exert. Equilibrium will be established
when as many molecules are dispersed in the surrounding space as, on the
average, impinge against the surface and are retained by it in the unit of
time. This state of equilibrium is not, however, one of rest, in which eva-
poration has ceased, but a condition in which evaporation and condensation,
which are equally strong, continually compensate each other.

The density of a vapour depends on the number of molecules which are

334 On Heat. [364-

repelled in a given time, and this manifestly depends on the motion of the
molecules in the liquid, and therefore on the temperature.

What has been said respecting the surface of the liquid clearly applies to
the other sides of the vessel within which the vapour is formed : some vapour
is condensed, this is subject to evaporation, and a condition ultimately occurs
in which evaporation and condensation are equal. The quantity of vapour
necessary for this depends on the density of vapour in the closed space, on
the temperature of the vapour and of the sides of the vessel, and on the force
with which this attracts the molecules. The maximum will be reached \\'hen
the sides are covered v^nth a layer of liquid, which then acts like the free
surface of a liquid.

In the interior of a liquid it may happen that the molecules repel each
other with such force as to momentarily destroy the coherence of the mass.
The small vacuous space which is thereby formed is entirely surrounded by
a medium which does not allow of the passage of the repelled molecules.
Hence it cannot increase and maintain itself as a bubble of vapour, unless so
many molecules are projected from the inner sides that the internal pressure
which thereby results can balance the external pressure which tends to
condense the bubble. The expansive force of the enclosed vapour must
therefore be so much the greater, the higher the external pressure on the
liquid, and thus we see the influence of pressure on the temperature of
boiling.

365. Influence of substances in solution on the boiling point. — The
ebullition of a liquid is the more retarded the greater the quantity of any
substance it may contain in solution, provided that the substance be not
volatile, or, at all events, be less volatile than the liquid itself Water, which
boils at 100° when pure, boils at the following temperatures when saturated
with different salts : —

Water saturated with common salt . . boils at 102°

„ ,, nitrate of potassium ., 116

„ „ carbonate of potassium „ 135

„ „ chloride of calcium „ 179

Acids in solution present analogous results ; but substances merely
mechanically suspended, such as earthy matters, bran, wooden shavings, &c.,
do not affect the boiling point.

Absorbed air exerts a very marked influence on the boiling point of
water. Deluc first observed that water freed from air by ebullition, and
placed in a flask with a long neck, could be raised to 112° without boiling.
M. Donny examined this phenomenon by means of the apparatus depicted in

figure 329. It consists of a glass tube CAB, bent at one end and closed at
C, while the other is blown into a pear-shaped bulb, B, drawn out to a

-366] Influence of Nature of Vessel on the Boiling Point. 335

point. The tube contains water which is boiled until all air is expelled, and
the open end is hermetically sealed. By inclining the tube the water passes
into the bent end CA ; this end being placed in a bath of chloride of calcium,
the temperature maybe raised to 130° without any signs of boiling. At 138°
the liquid is suddenly converted into steam and the water is thrown over
into the bulb, which is smashed if not sufficiently strong.

Boiled-out water, covered with a layer of oil, may be raised to 120° with-
out boiling, but above this temperature it suddenly begins to boil, and with
almost explosive violence.

When a liquid is suspended in another of the same specific gravity, but
of higher boiling point, with which it does not mix, it may be raised far be-
yond its boiling point without the formation of a trace of vapour. Dufour
has made a number of valuable experiments on this subject ; he used in the
case of water a mixture of oil of cloves and linseed oil, and placed in it
globules of water, and then gradually heated the oil ; in this way ebullition
rarely set in below 110° or 115° ; very commonly globules of 10 millimetres'
diameter reached a temperature of 120° or 130°, while very small globules of
I to 3 millimetres reach the temperature of 175°, a temperature at which
the tension of vapour on a free surface is 8 or 9 atmospheres.

At these high temperatures the contact of a solid body, or the production
of gas bubbles in the liquid, occasioned a sudden vaporisation of the globule,
accompanied by a sound like the hissing of a hot iron in water.

Saturated aqueous solutions of sulphate of copper, chloride of sodium,,
&c., remain liquid at a temperature far beyond their boiling point, when
immersed in melted stearic acid. In like manner, globules of chloroform
(which boils at 61°), suspended in a solution of chloride of zinc, could be
heated to 97° or 98° without boiling.

It is a disputed question as to what is the temperature of the vapour
from boiling saturated saline solutions. It has been stated by Rudberg to
be that of pure water boiling under the same pressure. The most recent
experiments of Magnus seem to show, however, that this is not the case, but
that the vapour of boiling solutions is hotter than that of pure water ; and
that the temperature rises as the solutions become more concentrated, and
therefore boil at higher temperatures. Nevertheless, the vapour was always
found somewhat cooler than the mass of the boiling solution, and the differ-
ence was greater at high than at low temperatures.

The boiling point of a liquid is usually lowered when it is mixed with a
more volatile liquid than itself, but raised when it contains one which is less
volatile. Thus a mixture of two parts alcohol and one of water boils at 83°,
a mixture of two parts of bisulphide of carbon and one part of ether boils
at 38°. In some cases the boiling point of a mixture is lower than that of
either of its constituents. A mixture of water and bisulphide boils at 43°,
the boiling point of the latter being 46°. On this depends the following
curious experiment. If water and bisulphide of carbon, both at the tempe-
rature 45°, are mixed together, the mixture at once begins to boil briskly.

366. Influence of the nature of the vessel on the boiling' point.—
Gay-Lussac observed that water in a glass vessel required a higher tempera-
ture for ebullition than in a metal one. Taking the temperature of boiling
water in a copper vessel at 100°, its boiling point in a glass vessel was.

^^6 On Heat, [366-

found to be loi'^ ; and if the glass vessel had been previously cleaned by
means of sulphuric acid and of potass, the temperature would rise to 105°,

or even to 106°, before ebullition com-
menced. A piece of metal placed in
the bottom of the vessel was always
sufficient to lower the temperature to
100°, and at the same time to prevent
the violent concussions which accom-
pany the ebullition of saline or acid
solutions in glass vessels. Whatever
be the boiling point of water, the tem-
perature of its vapour is uninfluenced
by the substance of the vessels.

367. Influence of pressure en
the boiling- point. — We see from the
table of tensions (35S) that at 100^,
the temperature at which water boils
under a pressure of 760 millimetres,
which is that of the atmosphere, aque-
ous vapour has a tension exactly equal
to this pressure. This principle is
general, and may be thus enunciated :
A liquid boils zvhen the tensio?! of its
vapour is equal to tJie pressure it sup-
ports. Consequently, as the pressure
increases or diminishes, the tension of the vapour, and therefore the tempe-
rature necessary for ebullition, must increase or diminish. Hence a liquid
has, strictly speaking, an indefinite number of boiling points.

In order to show that the boiling point is lower under diminished pres-
sure, a small dish containing water at 30° is placed under the receiver of an
air-pump, which is then exhausted. The liquid soon begins to boil, the
vapour formed being pumped out as rapidly as it is generated.

A paradoxical but very simple experiment also well illustrates the de-
pendence of the boiling point on the pressure. In a glass flask, water is
boiled for some time, and when all air has been expelled by the steam, the
flask is closed by a cork and inverted, as shown in fig. 330. If the bottom
is then cooled by a stream of cold water from a sponge, the water begins to
boil again. This arises from the condensation of the steam above the sur-
face of the water, by which a partial vacuum is produced.

It is in consequence of this diminution of pressure that liquids boil on
high mountains at lower temperatures. On Mont Blanc, for example, water
boils at 84°, and at Quito at 90°.

On the more rapid evaporation of water under feeble pressures is based
the use of the air-pump in concentrating those solutions which either cannot
bear a high degree of heat, or which can be more cheaply evaporated in an
exhausted space. Howard made a most important and useful application of
this principle in the manufacture of sugar. The syrup, in his method, is
enclosed in an air-tight vessel, which is exhausted by a steam-engine. The
evaporation consequently goes on at a lower temperature, which secures the

Fig. 330.

Fig. 3^

-369] Measurement of Heights by the Boiling Point. 337

syrup from injury. The same plan is adopted in evaporating the juice of
certain plants used in preparing medicinal extracts.

On the other hand, boiling is retarded by increasing the pressure :
under the pressure of two atmospheres, for example, water only boils at 1 20°-6.

368. Franklin's experiment. — The influence of pressure on boiling may
further be illustrated by means of an experiment originally made by Frank-
lin. The apparatus consists of a bulb, cc, and a tube, (5, joined by a tube of
smaller dimensions (fig. 331). The

tube b is drawn out, and the appa-
ratus filled with water, which is
then in part boiled away by means
of a spirit lamp. When it has
been boiled sufficiently long to
expel all the air, the tube b is sealed.
There is then a vacuum in the
apparatus, or rather there is a pres-
sure due to the tension of acjueous
vapour, which at ordinary tempe-
ratures is very small. Consequently, if the bulb, a, be placed in the hand, the
heat is sufficient to produce a pressure which drives the water into the tube,
b, and causes a brisk ebullition.

369. measurement of heights by the boil- ^ -. '
Ingr point.— From the connection between the
boiling point of water and the pressure, the
heights of mountains may be measured by the
thermometer instead of by the barometer. Sup-
pose, for example, it is found that water boils
on the summit of a mountain at 90°, and at its
base at 98°; at these temperatures the elastic
force or tension of the vapour is equal to that of
the pressure on the liquid ; that is, to the pres-
sure of the atmosphere at the two places re-
spectively. Now, the tensions of aqueous vapour
for various temperatures have been determined,
and accordingly the tensions corresponding to
the above temperatures are sought in the tables.
These numbers represent the atmospheric pres-
sures at the two places ; in other words, they
give the barometric heights, and from these the
height of the mountain may be calculated by
the method already given (178). An ascent of
about 1,080 feet produces a diminution of 1° C.
in the boilmg point.

The instruments used for this purpose are
called thermo-barometers or hypsometers, and
were first applied by Wollaston. They consist es-
sentially of a small metallic vessel for boiling water
(fig. 332), fitted with very delicate thermometers,
which are only graduated from 80° to 100^ ; so that, as each degree occupies

33^

On Heat.

[369-

a considerable space on the scale, the loths, and even the looths, of a
degree may be estimated, and thus it is possible to determine the height of
a place by means of the boiling point to within about lo feet.

370. Formation of vapour in closed tubes. — We have hitherto con-
sidered vapours as being produced in an indefinite space, or where they
could expand freely, and it is only under this condition that boiling can
take place. In a closed vessel the vapours produced finding no issue, their
tension and their density increase with the temperature, but that rapid disen-
gagement of vapour which constitutes boiling is impossible. Hence, while
the temperature of a liquid in an open vessel can never exceed that of boil-
ing, in a closed vessel it may be much higher. The liquid state has,
nevertheless, a limit ; for, according to experiments by Cagniard-
Latour, if either water, alcohol, or ether be placed in strong glass
tubes, which are hermetically sealed after the air has been ex-
pelled by boiling, and if then these tubes are exposed to a
sufficient degree of heat, a moment is reached at which the
liquid suddenly disappears, and is converted into vapour at
200°, occupying a space less than double its volume in the liquid
state, its tension being then 38 atmospheres.

Alcohol which half fills a tube is converted into vapour at
207° C. If a glass tube about half filled with water, in which
some carbonate of soda has been dissolved, to diminish the
action of the water on the glass, be heated, it is completely
vaporised at about the temperature of melting zinc.

When chloride of ethyle is heated in a very stout sealed

tube, the upper surface ceases to be distinct at 170°, and is

replaced by an ill-defined nebulous zone. As the temperature

rises this zone increases in width in both directions, becoming

m at the same time more transparent ; after a time the liquid is

^ I completely vaporised, and the tube becomes transparent and

H seemingly empty. On cooling, the phenomena are reproduced in

opposite order. Similar appearances are observed on heating

ether in a sealed tube at 190°.

Andrews made a series of observations on the behaviour
of condensed gases at different temperatures, by means of an
apparatus, the principal features of which are represented in

fig- 333-

The pure and dry gas is contained in a tube g, which is
sealed at one end, and the gas is shut in by a thread of mer-
cury. The tube is inserted in a brass end-piece, E, which is
firmly screwed on a strong copper tube, R. At the other end is
a similar piece, in which a steel screw works, perfect tightness
Fig. 333. being ensured by good packing. The tube is full of water, so
that by turning this screw the pressure on the enclosed gas
can be increased up to 500 atmospheres. In some cases the projecting
capillary tube is bent downwards, so that it can be placed in a freezing
mixture.

Andrews found on raising liquid carbonic acid in such a tube to a tempe-
rature of 31° C. that the surface of demarcation between the liquid and the

-370]

Formation of Vapour in Closed Tubes.

339

gas became fainter, lost its curvature, and gradually disappeared. The
space was then occupied by a homogeneous fluid, which, when the pressure
was suddenly diminished, or the temperature slightly lowered,
exhibited a peculiar appearance of moving or flickering stride
throughout its whole mass. Above 30° no apparent liquefac-
tion of carbonic anhydride, or separation into two distinct
forms of matter, could be effected, not even when the pressure
of 400 atmospheres was applied.

From similar observations made with other substances it
seems that there exists for eveiy liquid a temperature, the
critical poittt or critical temperature. While below this critical
point a sudden transition from gas to liquid is accompanied
by a sudden diminution of volume, and liquid and gas are
separated by a sharp line of demarcation, above this critical
point the change is connected with a gradual diminution of
volume, and is quite imperceptible. The condensation can,
indeed, only be recognised by a sudden ebullition when the
pressure is lessened. Hence, ordinary condensation is only
possible at a temperature below the critical point, and it is not
surprising, therefore, that mere pressure, however great, should
have failed to liquefy many of the gases.

The phenomenon of the critical temperature may also be
conveniently illustrated by the following arrangement (fig. 334),
which is also well adapted for projection on a screen by
means of a magic-lantern for lecture purposes. A stout glass "^llilSili^
tube about 2-5""" wide and 40*"'" long, contains liquid sulphurous pig. 334.
acid, and is supported, with the drawn-out end downwards, in
a test-tube by means of a wire frame. Pure melted paraffin is added to
about lo''™ above the inner tube. The whole arrangement is suspended in
a retort-holder, and heat applied with a spirit lamp. With careful manipula-
tion there is no danger, and the course of the phenomenon is readily seen
through the clear paraffin.

The boiling point of a body may be defined as the temperature above
which a body passes into the state of gas, not only on the surface but in the
body of the liquid ; this temperature is therefore different for different
pressures, and is accordingl}'- a relative magnitude. The absolute boilino-
point is the temperature at which a body is converted into gas, whatever
be the pressure ; it is identical with the critical temperature. Mendelejeff
found that a relation existed between the absolute temperature and the
capillarity of liquids. Increase of temperature diminishes the cohesion, and
therefore the capillarity of liquids. The capillarity ultimately vanishes
and the temperature at which this takes place is the absolute boiling
point. Some of them are very low ; that of air, for instance, is - 158^.

The critical pressure is that at which condensation takes place at the
critical temperature, and the volume of the saturated vapour at the critical
temperature, and under the critical pressure, is called the critical volume.

A vapour may be defined as being a gas at any temperature below its
critical point. Hence a vapour can be converted into a liquid by pressure
alone, and can therefore exist in the pressure of its own liquid, while a o-as

340

On Heat.

[370-

requires cooling as well as pressure to convert it into a liquid ; that is, to alter
its arrangement in such a manner that a liquid can be seen to be separated
from a gas by a distinctly bounded surface.

371. Papin's dig-ester. — Papin appears to have been the first to investi-
gate the effects of the production of vapour in closed vessels. The apparatus
which bears his name consists of a cylin-
drical iron vessel (fig. 335), provided with
a cover, which is firmly fastened down
by the screw B. In order to close the
vessel hermetically, sheet lead is placed
between the edges of the cover and the
vessel. At the bottom of a cylindrical
cavity, which traverses the cylinder S,
and the tubulure ^, the cover is perforated
by a small orifice in which there is a rod
71. This rod presses against a lever A,
movable at a., and the pressure may be
regulated by means of a weight movable
on this lever. The lever is so weighted
that when the pressure in the interior is
equal to six atmospheres, for example, the
valve rises and the vapour escapes. The
destruction of the apparatus is thus
avoided, and this mechanism has hence
received the name of safety-valve. The
digester is filled about two-thirds with
water, and is heated on a furnace. The
water may thus be raised to a temperature
far .above 100°, and the pressure of the vapour increased to several atmo-
spheres, according to the weight on the lever.

We have seen that water boils at much lower temperatures on high
mountains (367) ; the temperature of water boiling in open vessels in such
localities is not sufficient to soften animal fibre completely and extract
the nutriment, and hence Papin's digester is used in the preparation of
food.

Papin's digester is used in extracting gelatine. When bones are digested
in this apparatus they are softened, so that the gelatine which they contain
is dissolved : the part through which the screw B passes is made of such
elasticity that it yields, and the lid opens when the pressure of the vapour
becomes dangerous.

372. Iiatent lieat of vapour. — As the temperature of a liquid remains
constant during boiling, whatever be the source of heat (363), it follows
that a considerable quantity of heat becomes absorbed in boiling, the only
effect of which is to transform the body from the liquid to the gaseous con-
dition. And, conversely, when a saturated vapour passes into the state of
liquid, it gives out a definite amount of heat.

These phenomena were first observed by Black, and he described them
by saying that during vaporisation a quantity of sensible heat became latent,
and that the latent heat again became free during condensation. The quan-

Fig. 335-

-372] Latent Heat of Evaporation. 341

tity of heat which a liquid must absorb in passing from the liquid to the
gaseous state, and which it gives out in passing from the state of vapour to
that of liquid, is spoken of as the latent heat of evaporation.

The analogy of these phenomena to those of fusion will be at once seen ;
the modes of determining them will be described in the chapter on Calori-
metry ; but the following results, which have been obtained for the latent
heats of evaporation at 0°, may be here given : —

Water .

. 607

Bisulphide of carbon .

. 90

Alcohol .

. . 236

Turpentine

• 74

Acetic acid

. 102

Bromine

■ 49

Ether .

• 94

Iodine

. 24

The meaning of these numbers is, in the case of water, for instance, that
it requires as much heat to convert a pound of water from the state of liquid
at boiling point, to that of vapour at the same temperature, as would raise
a pound of water through 607 degrees, or 607 pounds of water through one
degree ; or that the conversion of one pound of vapour of alcohol at 0°
into liquid alcohol of the same temperature would heat 208 pounds of water
through one degree.

Watt, who investigated the subject, held that the whole quantity of heat
necessary to raise a given weight of water from zero to any temperature,
and then to evaporate it entirely, or what is called the heat of evaporation.,
is a constant quantity. His experiments showed that this quantity is 640.
Hence the lower the temperature the greater the latent heat, and, on the other
hand, the higher the temperature the less the latent heat. The latent heat of
the vapour of water evaporated at 100° would be 540, while at 50 degrees it
would be 590. At higher temperatures the latent heat of aqueous vapour
would go on diminishing. Water evaporated under a pressure of 1 5 atmo-
spheres at a temperature of 200° would have a latent heat of 440, and if it
could be evaporated at 640° it would have no latent heat at all.

Regnault, who examined this question with great care, found that the
total quantity of heat necessary for the evaporation of water increases with
the temperature, and is not constant, as Watt had supposed. It is repre-
sented by the formula

Q = 606-5 +o'3o5^)

in which Q is the total quantity of heat, and / the temperature of the water
during evaporation, while the numbers are constant quantities. The total
quantity of heat necessary to evaporate water at 100° is 606-5 -t- (0-305 ■•< 100)
= 637 ; at 120° it is 643 ; at 150° it is 651 ; and at 180° it is 661.

Thus the heat required to raise a pound of water from zero and convert
it into steam at 100° represents a mechanical work of 885430 units, which
would be sufficient to raise a ton weight through a height of nearly 400 feet.

The total heat of the evaporation of ether is expressed by a formula
similar to that of water, namely, Q = 64 + 0-045/; and that for chloroform
Q = 67 + 0-1375/.

The heat which is expended simply in evaporating a liquid, and which is
spoken of as the latent heat, produces no rise of temperature, and only
appears as doing the work of a change of state. One portion of this work

342 On Heat. [372-

is expended in overcoming the cohesion of the particles in the liquid state,
and enabling them to assume the gaseous form — this is the internal work.,
and is by much the greater ; the other, the external work, is expended in
overcoming the external pressure on the vapour formed, and which is much
larger than in the original liquid state, for the volume is greatly increased.

Knowing the increase of volume, and the pressure, the external work may
readily be calculated ; for if the volumes of unit weight of the substance in the
state of lic]uid and of vapour are respectively s and cr, and the pressure for
unit surface is^, then the external work is \p {(t — s), A being the mechanical
equivalent of heat. So that, if r is tjie total heat of evaporation,

r = p + Kp {(T-s)
in which p is the internal work. From the values of r and of A/ {^~^)i it is
easy to deduce that of p, and it is found that this value decreases as the tem-
perature increases.

Thus for the temperatures o, 50, 100, and 150° the values are 576, 536,
496, and 457° respectively ; that is, that when water at 0° is converted into
vapour, a greater internal work is required to overcome the cohesion, than
at 100° for instance.

373. Cold due to evaporation. Mercury frozen. — Whatever be the
temperature at which a vapour is produced, an absorption of heat always
takes place. If, therefore, a liquid evaporates, and does not receive from
without a quantity of heat equal to that which is expended in producing the
vapour, its temperature sinks, and the cooling is greater in proportion as the
evaporation is more rapid.

Leslie succeeded in freezing water by means of rapid evaporation. Under
the receiver of the air-pump is placed a vessel containing strong sulphuric
acid, and above it a thin metal capsule, A (fig. 336), containing a small

quantity of water. By
exhausting the receiver
the water begins to
boil (360), and since
the vapour is absorbed
by the sulphuric acid
as fast as it is formed,
a rapid evaporation
is produced, which
quickly effects the
freezing of the water.

This experiment is
best performed by
using, instead of a thin
metal dish, a watch-
glass coated with lamp-
black and resting on a cork. The advantage of this is twofold : firstly, the
lampblack is a very bad conductor ; and, secondly, it is not moistened by the
liquid, which remains in the form of a globule not in contact with the glass.
A small porous dish may also advantageously be used. '

The same result is obtained by means of Wollaston's cryophorus (fig.
'iyj), which consists of a bent glass tube provided with a bulb at each end.

-373] Cold due to Evaporation. 343

The apparatus is prepared by infroducing a small quantity of water, which
is then boiled so as to expel all air. It is then hermetically sealed, so that
on cooling it contains only water and the vapour of water. The water being
introduced into the bulb A, the other bulb is immersed in a freezing
mixture. The vapour in the tube is thus condensed ; the water in A rapidly
yields more. But this rapid production of vapour requires a large amount
of heat, which is abstracted from the water in A, and its temperature is so
much reduced that it freezes.

By using liquids more volatile than water, more particularly liquid sul-
phurous acid, which boils at - 10°, or still better, chloride of methyle, which
is now prepared industrially in large quantities, a degree of cold is obtained
sufficiently low to freeze mercury. This experiment may be made on a
small scale by covering the bulb of a thermometer with cotton wool, and,
after having moistened it with the liquid in question, placing it under the
receiver of the air-pump. When a vacuum is produced the mercury is
quickly frozen.

By passing a current of air, previously cooled, through liquid chloride of
methyle, temperatures of from —23° to —70° C. may be maintained with
great constancy for several hours. Thilorier, by directing a jet of liquid
carbonic acid on the bulb of an alcohol thermometer, obtained a tempera-
ture of — 100° without freezing the alcohol (343).

By means of the evaporation of bisulphide of carbon the formation of ice
may be illustrated without the aid of an air-pump. A little water is dropped
on a board, and a capsule of thin copper foil, containing bisulphide of carbon,
is placed on the water. The evaporation of the bisulphide is accelerated by
means of a pair of bellows, and after a i&w minutes the water freezes round
the capsule so that the latter adheres to the wood.

In like manner, if some water be placed in a test-tube, which is then
dipped in a glass containing some ether, and a current of air be blown
through the ether by means of a glass tube fitted to the nozzle of a pair of
bellows, the rapid evaporation of the ether very soon freezes the water in
the tube. Richardson's apparatus for producing local aneesthesia also de-
pends on the cold produced by the evaporation of ether.

The cold produced by evaporation is used in hot climates to cool water
by means of alcarrazas. These are porous earthen vessels, through which
water percolates, so that on the outside there is a continual evaporation,
which is accelerated when the vessels are placed in a current of air. For
the same reason wine is cooled by wrapping the bottles in wet cloths and
placing them in a draught.

In Harrison's method of making ice artificially, a steam-engine is used
to work an air-pump which produces a rapid evaporation of some ether, in
which is immersed the vessel containing the water to be frozen. The apparatus
is so constructed that the vaporised ether can be condensed and used again.

The cooling effect produced by a wind or draught does not necessarily
arise from the wind being cooler, for it may, as shown by the thermometer,
be actually warmer, but arises from the rapid evaporation it causes from the
surface of the skin. We have the feeling of oppression even at moderate
temperatures, when we are in an atmosphere saturated by moisture, in which
no evaporation takes place.

344

On Heat.

[374-

374. Carre's apparatus for freezing- water.- — We have already seen
that when any Hquid is converted into vapour it absorbs a considerable
quantity of sensible heat ; this furnishes a source of cold which is more
abundant the more volatile the liquid, and the greater its heat of vaporisation.

This property of liquids has been utilised by M. Carre, in freezing water
by the distillation of ammonia. The apparatus consists of a cylindrical
boiler C (figs. 338, 339), and of a slightly conical vessel A, which is the
freezer. These two vessels are connected by a tube, in, and a brace, «, binds
them firmly. They are made of strong galvanised iron plate, and can resist
a pressure of seven atmospheres.

The boiler C, which holds about two gallons, is three parts filled with a
strong solution of ammonia. In a tubulure in the upper part of the boiler
some oil is placed, and in this a thermometer t. The freezer A consists of
two concentric envelopes, in such a manner that, its centre being hollow, a

1.^

F 'g- 33S.

Fiy;. 330.

metal vessel, G, containing the water to be frozen, can be placed in this space.
Hence only the annular space between the sides of the freezer is in commu-
nication with the boiler by means of the tube m. In the upper part of the
freezer there is a small tubulure, which can be closed by a metal stopper, and
by which the solution of ammonia is introduced.

The formation of ice comprises two distinct operations. In the first,
the boiler is placed in a furnace F, and the freezer in a bath of cold water of
about 12°. The boiler being heated to 130°, the ammoniacal gas dissolved
in the water of the boiler is disengaged, and, in virtue of its own pressure, is
liquefied in the freezer A, along with about a tenth of its weight of water. This
distillation of C towards A lasts about an hour and a quarter, and when it is
finished the second operation commences ; this consists in placing the boiler
in the cold-water bath (fig. 339), and the freezer A outside, care being taken
to surround it with dry flannel. The vessel G, about three-quarters full of

-374] Carre's Apparatus for Freezing Water. 345

water, is placed in the freezer. As the boiler cools, the ammoniacal gas with
which it is filled is again dissolved ; the pressure thus being diminished, the
ammonia which has been liquefied in the freezer is converted into the gaseous
form, and now distils from A towards C, to redissolve in the water which
has remained in the boiler. During this distillation the ammonia which is
gasified absorbs a great quantity of heat, which is withdrawn from the vessel
G and the water it contains. Hence it is that this water freezes. In order
to have better contact between the sides of the vessel G and the freezer,
alcohol is poured between them. In about an hour and a quarter a perfectly
compact cylindrical block of ice can be taken from the vessel G.

This apparatus gives about four pounds of ice in an hour, at a price of
about a farthing per pound ; large continuously working apparatus have, how-
ever, been constructed, which produce as much as 800 pounds of ice in an hour.
Carre has constructed an ice-making machine which is an industrial
application of Leslie's experiment {yri)^ and by which considerable quantities
of water may be frozen in a short time. It consists of a cylinder R, about 15
niches long by 4 in diameter, made of an alloy of lead and antimony
(fig. 340). At one end is a funnel E, by which strong sulphuric acid can be
introduced ; at the other is a tubulure w, to which is screwed a dome d that
supports a series of obstacles intended to prevent any sulphuric acid from
spirting into m and b. There are, moreover, on the receiver a wide tube u,
closed by a thick glass disc O, and a long tube /^, to the top of which is fitted
the bottle C con-
taining water to be
frozen. The dome
c/, the disc O, and
the stopper i of the
funnel E are all
sealed with wax.

On the side of
the receiver is an
air-pump P, con-
nected with it by a
tube <^, and worked
by a handle M. To
this handle is at-
tached a rod /,
which, by the
mechanism repre-
sented on the left
of the figure, works
a stirrer A in the
sulphuric acid. A
lever x connected
with a horizontal
axis which tra-
verses a small stuff"- Fig. 340.
ing-box n, trans-
mits its backward and forward motion to the rod e and to the stirrer. This

346

071 Heat.

[374-

and the stuffing-box ;/ are fitted in a tubulure on the side of the tubu-
kire VI.

The smallest size which Carre makes contains 2-5 kilogrammes of sul-
phuric acid, and the water-bottle about 400 grammes, when it is one-third full.
After about 70 strokes of the piston the water begins to boil ; the acid being
in continued agitation, the vapour is rapidly absorbed by it, and the pump is
worked until freezing begins. For this purpose it is merely necessary to
give a few strokes every five minutes. The rate of freezing depends on the
strength of the acid ; when this gets very dilute it requires renewal ; but 12
water-bottles can be frozen with the same quantity of acid.

LIQUEFACTION OF VAPOUR AND GASES.

375. lilquefaetion of vapours. — The liquefactioji or condensatiotj of
vapours is their passage from the aeriform to the liquid state. Condensa-
tion may be due to three causes — cooling, compression, or chemical action.
For the first two causes the vapours must be saturated (353), while the
latter produces the liquefaction of the most rarefied vapours. Thus, a large
number of salts absorb and condense the aqueous vapour in the atmosphere,
however small its quantity.

When vapours are condensed, their latent heat becomes free ; that is, it
affects the thermometer. This is readily seen when a current of steam at
100° is passed into a vessel of water at the ordinary temperature. The liquid
becomes rapidly heated, and soon reaches 100°. The quantity of heat given
up in liciuefaction is equal to the quantity absorbed in producing the vapour.

376. aistillation. Stills. — Distillation is an operation by which a

Fig. 341-

volatile liquid may be separated from substances which it holds in solution
or by which two licpids of different volatilities may be separated. The

-377j

Liebi^'s Condenser,

347

operation depends on the transformation of liquids into vapour by the action
of heat, and on the condensation of this vapour by cooHng.

The apparatus used in distillation is called a still. Its form may vary
greatly, but it consists essentially of three parts ; ist, the body A (fig. 341),
a copper vessel containing the liquid, the lower part of which fits in the
furnace ; 2nd, the /lead, B, which fits on the body, and from which a lateral
tube, C, leads to ; 3rd, the worm, S, a long spiral tin or copper tube placed
in a cistern kept constantly full of cold water. The object of the worm is to
condense the vapour by exposing a greater extent of cold surface.

To free ordinary water from the many impurities which it contains, it is
placed in a still and heated. The vapours disengaged are condensed in the
worm, and the distilled water arising from the condensation is collected in
the receiver D. The vapours in condensing rapidly heat the water in the
cistern, which must, therefore, be constantly renewed. For this purpose a
continual supply of cold water passes into the bottom of the cistern, while
the lighter heated water rises to the surface and escapes by a tube in the top
of the cistern.

■yj']. Iilebig-'s Condenser. — In distilling small quantities of liquids, or in
taking the boiling point of a liquid, so as not to lose any of it, the apparatus
known as Liebig's Condenser is extremely useful. It consists of a glass
tube, // (fig. 342), about thirty inches long, fitted in a copper or tin tube
by means of perforated corks. A constant supply of cold water from the
vessel a passes into the space between the two tubes, being conveyed to the

Fig. 342-

lower part of the condenser by a funnel and tube g, flowing out from the
upper part of the tube/ The liquid to be distilled is contained in a retort,
the neck of which is placed in the tube ; the condensed liquid drops quite
cold into a vessel placed to receive it at the other extremity of the con-
densing tube.

348

On Heat.

[378-

Fig. 343.

glass is filled with the -wine up to a

378. j^pparatus for determining^ the alcoholic value of wines. — One

of the forms of this apparatus consists of a glass flask resting on a tripod,
and heated by a spirit lamp (fig. 343). By means of a caoutchouc tube

this is connected

^Bii»' '^1 " „|, with a worm

^''* placed in a cop-

per vessel filled
with cold water,
and below which
is a test glass
for collecting the
distillate. On
this are three
divisions, one a,
which measures
the quantity of
wine taken ; the
two others indi-
J^ eating one-half
l^^gflsiigHE=^ and one-third of

" this volume.

The test-
this is then poured into the flask,
which having been connected with the worm, the distillation is commenced.
The liquid which distils over is a mixture of alcohol and water ; for ordinary
wines, such as clarets and hocks, about one-third is distilled over, and
for wines richer in spirit, such as sherries and ports, one-half must be
distilled ; experiment has shown that under these circumstances practically all
the alcohol passes over in the distillate. The measure is then filled up with
distilled water to a ; this gives the mixture of alcohol and water of the same
volume as the wine taken, free from all solid matters, such as sugar, colour-
ing matter, and acid, but containing all the alcohol. The specific gravity
of this distillate is then taken by means of an alcoholometer (128), and the
number thus obtained corresponds to a certain strength of alcohol as indi-
cated by the tables.

379. Safety-tube. — In preparing gases and collecting them over mercury
or water, it occasionally happens that these liquids rush back into the

generating vessel, and destroy the operation.
This arises from an excess of atmospheric pressure
over the elastic force in the vessel. If a gas —
sulphurous acid for example — be generated in the
^^1 -^-^5— - J^. flask in (fig. 344), and be passed into water in the

|l| t^ %^^^^^' vessel A, as long as the gas is given off freely,
its elastic force exceeds the atmospheric pressure,
and the weight of the column of water, o;i, so that
the water in the vessel cannot rise in the tube,
and absorption is impossible. But if the tension
decreases, either through the flask becoming
disengaged too slowly, the external pressure pre-

cooled or the gas beinc

-380]

Liquefaction of Gases.

349

vails, and when it exceeds the internal tension by more than the weight of
the cokimn of water £•<?, the water rises into the flask, and the operation is
spoiled. This accident is prevented by means of safety-tubes.

These are tubes which prevent absorption by allowing the air to enter in
proportion as the internal tension decreases. The simplest is a tube C
(fig. 345), passing through the cork which
closes the flask M, in which the gas is
generated, and dipping in the liquid.
When the tension of the gas diminishes in
M, the atmospheric pressure on the water
in the bath E causes it to rise to a certain
height in the tube DA ; but this pressure,
acting also on the liquid in the tube C,
depresses it to the same depth, assuming
that the liquid has the same density as
the water in E. Now, as this depth is
less than the height DH, air enters by the
aperture, before the water in the bath can
inse to A, and no absorption takes place.

■},%o. I.iquefaction of gases. — We have already seen that a saturated
vapour, the temperature of which is constant, is liquefied by increasing the
pressure, and that, the pressure remaining constant, it is brought into the
liquid state by diminishing the temperature.

Unsaturated vapours behave in all respects like gases. For the gaseous
form is accidental, and is not inherent in the nature of the substance. At
ordinary temperatures sulphurous anhydride is a gas, while in countries near
the poles it is a liquid ; in temperate climates ether is a liquid, at a tropical
heat it is a gas. And just as unsaturated vapours may be brought to the
state of saturation, and then liquefied, by suitably diminishing the tempe-
rature or increasing the pressure, so by the same means gases may be
liquefied. But as they are mostly very far removed from this state of satura-
tion, great cold and pressure are i^equired. Some of them may indeed be
liquefied either by cold or by pressure ; for the majority, however, both
agencies must be simultaneously employed. The
recent researches of Cailletet and of Pictet (382)
have shown that the distinction permanent gas
no longer exists, now that all are liquefied.

We have seen that there is for each gas a
critical temperature (370), so that no pressure
however great can liquefy a gas which is above this
temperature. If a gas is below this point, then
the nearer it is to it the greater is the pressure
required ; conversely, if the temperature is very
low, the pressure required to liquefy it may be
low too.

Faraday was the first to liquefy some of the gases. His method con-
sists in enclosing in a bent glass tube (fig. 346) substances by whose
chemical action the gas to be liquefied is produced, and then sealing the
shorter leg. In proportion as the gas is disengaged its pressure increases,

Fig. 346.

350 On Heat. [380-

and it ultimately liquefies and collects in the shorter leg, more especially if its
condensation is assisted by placing the shorter leg in a freezing mixture. A
small manometer may be placed in the apparatus to indicate the pressure.

Cyanogen gas is readily liquefied by heating cyanide of mercury in a bent
tube of this description ; other gases have been condensed by taking advan-
tage of special reactions, the consideration of which belongs rather to
chemistry than to physics. For example, chloride of silver absorbs about
200 times its volume of ammoniacal gas ; when the compound thus formed
is placed in the long leg of a bent tube and gently heated, while the shorter
leg is immersed in a freezing mixture, a quantity of liquid ammoniacal
gas speedily collects in the shorter leg.

381. Apparatus to liquefy and solidify gases. — Thilorier first con-
structed an apparatus by which considerable quantities of carbonic acid
could be liquefied. Its principle is the same as that used by Faraday in
working with glass tubes ; the gas is generated- in an iron cylinder, and
passes through a metal tube into another similar cylinder, where it con-
denses. The use of this apparatus is not free from danger; many accidents
have already happened with it, and it has been superseded by an apparatus
constructed by Natterer, of Vienna, which is both convenient and safe.

A perspective view of the apparatus, as modified by Bianchi, is repre-
sented in fig. 348, and a section on a larger scale in fig. 347. It consists of
a wrought-iron reservoir A, of something less than a quart capacity, which
can resist a pressure of more than 600 atmospheres. A small force-pump is
screwed on the lower part of this reservoir. The piston rod / is mo\'ed by
the crank-rod E, which is worked by the handle M. As the compression of
the gas and the friction of the piston produce a considerable disengagement
of heat, the reservoir A is surrounded by a copper vessel, in which ice or a
freezing mixture is placed. The water arising from the melting of the ice
passes by a tube m into a cylindrical copper case C, which surrounds the
force-pump, from whence it escapes through the tube n and the stopcock o.
The whole arrangement rests on an iron frame, PQ.

The gas to be liquefied is previously collected in airtight bags R, from
whence it passes into a bottle V, containing some suitable drying substance ;
it then passes into the condensing pump through the vulcanised india-rubber
tube H. After the apparatus has been worked for some time the reservoir
A can be unscrewed from the pump without any escape of the liquid, for it is
closed below by a valve S (fig. 347). In order to collect some of the liquid
gas, the reservoir is inverted, and on turning the stopcock r the liquid escapes
by a small tubulure x.

When carbonic acid has been liquefied and is allowed to escape into the
air, a portion only of the liquid volatilises ; in consequence of the heat ab-
sorbed by this evaporation, the rest is so much cooled as to solidify in white
flakes like snow or anhydrous phosphoric acid. This may be collected by plac-
ing a stout woollen bag like a tobacco pouch over a pipe attached to the tube x: ;
if the porous mass is compressed or hammered in stout wooden cj^linders,
sticks of solid carbonic acid are obtained, very like chalk in appearance.

Solid carbonic acid evaporates very slowly. By means of an alcohol
thermometer its temperature has been found to be about —90°. A small
quantity placed on the hand does not produce the sensation of such great

-381]

Apparatus to Liquefy and Solidify Gases.

351

cold as might be expected. This arises from the imperfect contact. But if
the soHd be mixed with ether the cold produced is so intense that when a
little is placed on the skin all the effects of a severe burn are produced. A
mixture of these two substances solidifies four times its weight of mercury
in a few minutes. When a tube containing liquid carbonic acid is placed in
thismixture, the liquid becomes solid and looksjike a transparent piece of ice.

Fig. 34S.

The most remarkable liquefaction obtained by this apparatus is that of
nitrous oxide. The gas once liquefied only evaporates slowly, and produces
a temperature of 88° below zero. Mercury placed in it in small quantities
instantly solidifies. The same is the case with water ; it must be added
drop by drop, otherwise, its latent heat being much greater than that ot
mercury, the heat given up by the water in solidifying'would be sufficient to
cause an explosion of the nitrous oxide.

Nitrous oxide is readily decomposed by heat, and has the property of
supporting the combustion of bodies with almost as much brilliancy as

352 On Heat. [381-

oxygen ; and even at low temperatures it preserves this property. When a
piece of incandescent charcoal is thrown on liquid nitrous oxide, it continues
to burn with a brilliant light.

The cold produced by the evaporation of ether (373) has been used by
Loir and Drion in the liquefaction of gases. By passing a current of air
from a blowpipe bellows through several tubes into a few ounces of ether, a
temperature of — 34° C. can be reached in five or six minutes, and may be
kept up for fifteen or twenty minutes. By evaporating liquid sulphurous
acid in the same manner a great degree of cold, —50° C, is obtained. At
this temperature ammoniacal gas may be liquefied. By rapidly evaporating
liquid ammonia under the air-pump, in the presence of sulphuric acid, a
temperature of —87° is attained, which is found sufficient to liquefy carbonic
acid under the ordinary pressure of the atmosphere.

2,^1.. Cailletet's and Pictet's researches. — Cailletet and Pictet, working
independently, but simultaneously, have effaced the old distinction between
permanent and non-permanent gases, by effecting
the liquefaction of oxygen and hydrogen, and other
gases which it was supposed could not be condensed.
This has been accomplished by means of powerful
material appliances directed with great skill and
ingenuity. The critical temperature of these gases
is mostly below — 100°, while their critical pressure
is somewhat less than that of carbonic acid, ex-
cepting hydrogen, which is over 100 atmospheres.
The essential parts of Cailletet's apparatus are

represented in fig. 349. The gas to be condensed

is contained in the tube TP, which is fitted, by

means of a bronze screw A, into a strong wrought-

iron mercury bath B. By means of a screw RE,
and a tube U, this is connected with a hydraulic

or a screw press not represented in the figure. The

capillary part P of the tube T is placed in a vessel

M, in which it can be surrounded by a freezing

mixture, and this again is surrounded by a stout

safety bell-jar C.

When a pressure of 250 to 300 atmospheres is

applied by meaijs of the hydraulic press, after

waiting until the heat due to the compression has

disappeared, if a screw arranged in the press is

suddenly opened, the pressure being diminished,

the cold produced by the sudden expansion of the

gas in the tube TP is so great as to liquefy a portion of the rest, as is shown

by the production of a mist.

This observation was first made with nitric oxide, but similar results

have been obtained with marsh gas, carbonic acid, and oxygen.

The principle of Pictet's method is that of liberating the gas under great

pressure, combined with the application of great degrees of cold. The

essential parts of the apparatus are the following : — Two double-acting

pumps, A and B (fig. 350), are so coupled together that they cause the

382]

CailleteVs and Pictefs Researches.

353

evaporation of liquid sulphurous acid contained in the annular receiver C.
By the play of the pumps the gas thus evaporated is forced into the re-
ceiver D, where it is cooled by a current of water, and again liquefied under
a pressure of three atmospheres. Thence it passes again by the narrow tube
d to the receiver C, to replace that which is evaporated.

In this way the temperature of the liquid sulphurous acid is reduced to
— 65°. Its function is to produce a sufficient quantity of liquid carbonic acid,
which is then submitted to a perfectly analogous process of rarefaction and
condensation. This is effected by means of two similar pumps E and F.
The carbonic acid gas, perfectly pure and dry, is drawn from a reservoir
through a tube not represented in the figure, and is forced into the condenser
K, which is cooled by the liquid sulphurous acid to a temperature of —65°,
and is there liquefied.

H is a tube of stout copper in connection with the condenser K by a
narrow tube k. When a sufficient quantity of carbonic acid has been liquefied,
the connection with the gasholder is cut off, and by working the pumps E
and F a vacuum is created over the liquid carbonic acid in H, which pro-
duces so great a cold as to solidify it.

L is a stout wrought-iron retort capable of standing a pressure of 1,500
atmospheres. In it are placed the substances by whose chemical actions
the gas is produced :
potassium chlorate
in the case of
oxygen. This re-
tort is closed by a
strong copper tube
in which the actual
condensation is ef-
fected, near the end
of which is a spe-
cially constructed
manometer R, and
which is closed by
a stopcock N.

When the four
pumps are set in
action, for which a
steam-engine of 1 5
horse-power is re-
quired, heat is ap-
plied to the retort.
Oxygen is liberated
in a calculated
quantity, the tem-
perature of the retort being about 485°. Towards the close of the de-
composition the manometer indicates a pressure of 500 atmospheres, and
then sinks to 320. This diminution is due to the condensation of gas,
and at this stage the tube contains liquefied oxygen. If the cock N is
opened, the gas issues with violence, having the appearance of a dazzling

A A

354 On Heat. [382-

white pencil. This lasts three or four seconds. On closing the stopcock
the pressure, which had diminished to 400 atmospheres, now rises, and
again becomes stationary, proving that the gas is once more being con-
densed. The density of liquid oxygen has been found to be 0-9.

The phenomena presented by the jet of oxygen when viewed by the
electric light showed that the light it emits was partially polarised, indicating
a probable transient crystallisation of the gas.

For hydrogen the gas was disengaged by heating a mixture of potassic
formate and hydrate, and liquid protoxide of nitrogen was used instead of
carbonic acid, by which the temperature could be reduced to — 140° C.
When the pressure had reached 650 atmospheres, and the cock was opened,
a steel-blue jet issued from the aperture with a brisk noise. This suddenly
became intermittent, and resembled a shower of hailstones. As the separate
granules struck the ground they produced a loud noise, and Pictet considers
that in all probability the hydrogen in the interior was frozen.

In some later experiments, the details of which are too complicated to
give here, Cailletet has produced very low temperatures by the use of liquid
ethylene gas. This gas can be liquefied by a pressure of 45 atmospheres at
a temperature of 1°. By promoting the evaporation of this liquid, by passing
through it a current of air or of hydrogen which has been previously cooled by
the rapid evaporation of chloride of methyle, the temperature is easily reduced
to - 120°. When oxygen gas is cooled to this temperature the application of
pressure is sufficient to resolve it into a colourless, transparent liquid, sharply
separated from the gas by a meniscus.

By surrounding the gas under experiment by concentric tubes containing
lic|uid oxygen that boils under the atmospheric pressure at — 181°, which in
turn is surrounded by liquid ethylene, Olszewski obtained temperatures low
enough to solidify nitrogen, carbonic oxide, marsh gas, and nitric oxide. The
evaporation of solid nitrogen under a pressure of 4""" produces a tempe-
rature of —225°.

:\IIXTURE OF GASES AND VAPOURS.

383. ]baws of the mixture of grases and vapours. — Every mixture of a
gas and a vapour obeys the two following laws : —

I. The pressure, and, co7iseqiiently, the quantity, of vapour which saturates
a given space are the same for the same temperature, whether this space con-
tains a gas or is a vacuum.

I I . TJie pressure of the mixture of a gas and a vapour is equal to the sum
of the pressures which each would possess if it occupied the same space a/ofie.

These are known as Daltoifs laws, from their discoverer, and are de-
monstrated by the following apparatus, which was invented by Gay-Lussac :—
It consists of a glass tube A (fig. 351), to which two stopcocks, b and d, are
cemented. The lower stopcock is provided with a tubulure which connects
the tube A with a tube B of smaller diameter. A scale between the two
tubes serves to measure the heights of the mercurial columns in these tubes.

The tube A is filled with mercury, and the stopcocks b and d are closed.
A glass globe M, filled with dry air or any other gas, is screwed on by means
of a stopcock in the place of the funnel C. All three stopcocks are then
opened, and a little mercury is allowed to escape, which is replaced by the

384]

Mixture of Gases and Vapours.

355

li^

dry air of the globe. The stopcocks are then closed, and as the air in the

tube expands on leaving the globe, the pressure on it is less than that of

the atmosphere. Mercury is accordingly poured into the tube B until it is

at the same level in both tubes. The globe is then removed, and replaced

by the funnel C, provided with a stopcock a of a peculiar construction. It is

not perforated, but has a small cavity, as represented in «, on the left of the

figure. Some of the liquid to be vaporised is

poured into C, and the height of the mercury

k having been noted, the stopcock b is opened,

and a turned so that its cavity becomes filled

with liquid ; being again turned, the liquid

enters the space A and vaporises. The liquid

is allowed to fall drop by drop until the air in

the tube is saturated, which is the case when

the level k of the mercury ceases to sink (353).

As the pressure of the vapour produced in
the space A is added to that of the air already
present, the total volume of gas is increased.
It may easily be restored to its original volume
by pouring mercury into B. When the mercury
in the large tube has been raised to the level k,
there is a difference B<9 in the level of the
mercury in the two tubes, which obviously re-
presents the pressure of the vapour ; for as the
air has resumed its original volume, its pressure
has not changed. Now, if a few drops of the
same liquid be passed into the vacuum of a
barometric tube, a depression exactly equal to
B<? is produced, which proves that, for the
same temperature, the pressure of a saturated
vapour is the same in a gas as in a vacuum :
from which it is concluded that at the same
temperature the quantity of vapour is also the
same.

The second law is likewise proved by this
experiment, for, when the mercury has regained its level, the mixture sup-
ports the atmospheric pressure on the top of the column B, in addition to
the weight of the column of mercury B<7. But of these two pressures, one
represents that of the dry air, and the other that of the vapour. The second
law is, moreover, a necessary consequence of the first.

Experiments can only be made with this apparatus at ordinary tempera-
tures ; but Regnault, by means of an apparatus which can be used at different
temperatures, investigated the tensions of the vapours of water, ether, bisul-
phide of carbon, and benzole, both in a vacuum and in air. He found that the
tension in air is less than it is in a vacuum, but the differences are so small
as not to invalidate Dalton's law. Regnault was even inclined to consider
this law as theoretically true, attributing the differences which he observed
to the hygroscopic properties of the sides of the tubes.

384. Problems on mixtures of gases and vapours.- — i. A volume of

A A 2

356 On Heat. [384-

dry air V, at the pressure H, being given, what will be its volume V, when

it is saturated with vapour, the temperature and the pressure remaining the

same ?

If F be the elastic force of the vapour which saturates the air, the latter,

in the mixture, only supports a pressure equal to H - F (381). But by Boyle's

law the volumes V and V are inversely as their pressures, consequently

V H , .,, VH

whence V'=

V H-F' H-F

ii. Let V be a given volume of saturated air at the pressure H, and the
temperature t ; what will be its volume V, also saturated, at the pressure H'
and the temperature /' ?

If/be the maximum tension of aqueous vapour at /°, and/' its maximum
tension at /'°, the air alone in each of the mixtures V and V will be respec-
tively under the pressures H — / and H'— _/'; consequently, assuming first
that the temperature is constant, we obtain
V^_H-/
V W-f
But as the volumes V and V of air, at the temperatures t' and /, are in the
ratio of i + at' to i + a/, a being the coefficient of the expansion of air, the
equation becomes

V H'-/'' \^ai

iii. What is the weight P of a volume of air V, saturated with aqueous
vapour at the temperature t and pressure H ?

If F be the maximum pressure of the vapour at /°, the pressure of
the air alone will be H-F, and the problem reduces itself to finding : ist,
the weight of V cubic inches of dry air at /, and under the pressure H - F ;
and 2nd, the weight of V cubic inches of saturated vapour at t° under the
pressure F.

To solve the first part of the problem, we know that a cubic inch of dry
air at 0° and the pressure 760 millimetres weighs 0-31 gram, and that at /°,

and the pressure H - F, it weighs -j^ — \~ t, {'hTfl) \ consequently V cubic

inches of dry air weigh

o-3i(H-F)V

(i+«/) 760 ■ ■ ■ ■ • ^ ^

To obtain the weight of the vapour, the weight of the same volume of

dry air at the same temperature and pressure must be sought, and this is to

be multiplied by the relative density of the vapour. Now as V cubic inches

of dry air at t°. and the pressure F, weigh —^ — ^-- — V cubic inches of

aqueous vapour, whose density is f that of air (385), weigh

0-31 xVF ^ 5 ,

(i+a/) 760 8 ■ ^"^

and as the weight P is equal to the sum of the weights (i) and (2) we have
p_o-3JxV(H-F)_^ 0-3IXVF ^5 _ 0-31 xV .^-^ p^
(i+a/)76o (I + a/) 760 8 (i+rt/)76o^ '^ ''

-385] Spheroidal Conditiojz. 357

SPHEROIDAL CONDITION.

385. Iieidenfrost's phenomena. Boutig'ny's experiments. — When
liquids are thrown upon incandescent metal surfaces they present remark-
able phenomena, which were first observed by Leidenfrost a century ago,
and have been named after their discoverer. They have since then been
studied by other physicists, and more especially by Boutigny.

Figure 352 represents an interesting method of illustrating this. F is a
small copper flask which is heated to dull redness over a spirit lamp, and
a small quantity of boil-
ing hot water is carefully
introduced ; a cork C
having been loosely fitted,
the lamp is removed, and
in a short time steam is
formed rapidly with such
explosive violence as to
drive out the cork.

When a tolerably
thick silver or platinum
dish is heated to redness,
and a little water, pre-

, J . Fig. 352.

viously warmed, is
dropped into the dish by means of a pipette, the liquid does not spread itself
out on the dish, and does not moisten it, as it would at the ordinaiy tempera-
ture, but assumes the form of a flattened globule, which fact Boutigny ex-
presses by saying that it has passed into the spheroidal state. It rotates
rapidly round on the bottom of the dish, taking sometimes the form of a star,
and not only does it not boil, but its evaporation is only about one-fiftieth
as rapid as if it boiled. As the dish cools, a point is reached at which it is
not hot enough to keep the water in the spheroidal state ; it is accordingly
moistened by the Hquid, and a violent ebullition suddenly ensues.

All volatile Hquids can assume the spheroidal condition ; the lowest
temperature at which it can be produced varies with each liquid, and is
more elevated the higher the boiling point of the liquid. For water, the
dish must have at least a temperature of 200° ; for alcohol, 134° ; and for
ether, 61°.

The temperature of a liquid in the spheroidal state is always below its
boiling point. This temperature has been measured by Boutigny by means
of a very dehcate thermometer ; but his method is not free from objections,
and it is probable that the temperatures he obtained were too high. He
found that of water to be 95° ; alcohol, 75° ; ether, 34°; and liquid sulphu-
rous acid, -11°. But the temperature of the vapour which is disengaged
appears to be as high as that of the vessel itself.

This property of liquids in the spheroidal state remaining below their
boiling point was applied by Boutigny in a remarkable experiment, that
of freezing water in a red-hot crucible. He heated a platinum dish to
bright redness, and placed a small quantity of liquid sulphurous acid in it.
It immediately assumed the spheroidal condition, and its evaporation was

358

On Heat.

[385-

remarkably slow. Its temperature, as has been stated, was about - 1 1°, and
when a small quantity of water was added, it immediately solidified, and a
small piece of ice could be thrown out of the red-hot crucible. In a similar
manner Faraday, by means of a mixture of solid carbonic acid and ether,
succeeded in freezing mercury in a red-hot crucible.

In the spheroidal state the liquid is not in contact with the vessel.
Boutigny proved this by heating a silver plate placed in a horizontal position
and dropping on it a little dark-coloured water. The liquid assumed the
spheroidal condition, and the flame of a candle placed at some distance

perforated by several fine holes be heated, a liquid will assume the spheroidal

state when pro-
jected upon it.
This is also the
case with a flat
helix of plati-
n u m w i r e

pressed into a
slightly concave
shape. An ex-
periment of an-
other class, due
to Prof Church,
also illustrates

the same fact. A polished silver dish is made red-hot, and a few drops
of a solution of sulphide of sodium are projected on it. The liquid passes
into the spheroidal condition, and the silver undergoes no alteration. But
if the dish is allowed to cool, the liquid instantly moistens it, producing a
dark spot, due to the formation of sulphide of silver. In like manner nitric
acid assumes the spheroidal state when projected on a heated silver plate,
and does not attack the metal so long as the plate remains hot.

An analogous phenomenon is observed when potassium is placed on
water. Hydrogen is liberated, and burns with a yellow flame ; hydrate of
potassium, which is formed at the same time, floats on the surface without
touching it, owing to its high temperature. In a short time it cools down,
and the globule, coming in contact with water, bursts with an explosion.

Similarly, liquids may be made to roll upon liquids, and solid bodies
which vaporise without becoming liquid also assume a condition analogous
to the spheroidal state of liquids when they are placed on a surface whose
temperature is sufficiently high to vaporise them rapidly. This is seen when
a piece of carbonate of ammonium is placed in a red-hot platinum crucible.
The phenomena of the spheroidal state seem to prove that the liquid
globule rests upon a sort of cushion of its own vapour, produced by the heat
radiated from the hot surface against its under side. As fast as this vapour
escapes from under the globule, its place is supplied by a fresh quantity
formed in the same way, so that the globule is constantly buoyed up by it,
and does not come in actual contact with the heated surface. When, how-
ever, the temperature of the latter falls, the formation of vapour at the under
surface becomes less and less rapid, until at length it is not sufficient to pre-

-386]

Gay-Lussacs Method.

359

vent the globule touching the hot metal or liquid on which it rests. As soon
as contact occurs, heat is rapidly imparted to the globule, it enters into
ebullition and quickly boils away.

This explanation is confirmed by the experiments of Budde, who found
that in an exhausted receiver water passes into the spheroidal state, even when
the temperature of the support is not more than 80° or 90°; for then the
vapour has only to support the drop, and not the atmospheric pressure also.

These experiments on the spheroidal state explain the fact that the hand
may be dipped into melted lead, or even melted iron, without injury. It is
necessary that the liquid metal be heated greatly above its solidifying point.
Usually the natural moisture of the hand is sufficient, but it is better to wipe
it with a damp cloth. In consequence of the great heat the hand becomes
covered with a layer of spheroidal fluid, which prevents the contact of the
metal with the hand. Radiant heat alone operates, and this is principally
expended in forming aqueous vapour on the surface of the hand. If the
hand is immersed in boiling water, the water adheres to the flesh, and con-
sequently a scald is produced.

The tales of ordeals by fire during the middle ages, of men who could
run barefooted over red-hot iron without being injured, are possibly true in
some cases, and would find an explanation in the preceding phenomena.

DENSITY OF VAPOURS.

386. Gay-Xussac's method. — The deftsity of a vapour is the relation
between the weight of a given volume of this vapour and that of the same
volume of air at the same temperature and
pressure.

The older methods used in determining the
density of vapours are : Gay-Lussac's, which
serves for liquids that boil at about 100°, and
Dumas', which can be used up to 350°.

Fig. 354 represents the apparatus used by
Gay-Lussac. It consists of an iron vessel con-
taining mercury, in which there is a glass
cylinder M. This is filled with water or oil,
and the temperature is indicated by the ther-
mometer T. In the interior of the cylinder is
a graduated gas jar C, which at first is filled
with mercury.

The liquid whose vapour-density is to be
determined is placed in a small glass bulb A,
represented on the left of the figure. The bulb
is then sealed and weighed ; the weight of the
liquid taken is obviously the weight of the bulb
when filled, minus its weight while empty. The
bulb is then introduced into the jar C, and the
liquid in M gradually heated somewhat higher
than the boiling point of the liquid in the bulb.
In consequence of the expansion of this liquid the bulb breaks, and the

36o On Heat. [386-

liquid becoming converted into vapour, the mercury is depressed, as repre-
sented in the figure. The bulb must be so small that all the liquid in it is
vaporised. The volume of the vapour is given by the graduation on the jar.
Its temperature is indicated by the thermometer T, and the pressure is
shown by the diiTerence between the height of the barometer at the time of
the observation and the height of the column of mercury in the gas jar. It
is only necessary then to calculate the weight of a volume of air equal to that
of the vapour under the same conditions of temperature and pressure. The
quotient, obtained by dividing the weight of the vapour by that of the air,
gives the required density of the vapour.

Let^ be the weight of the vapour in grains, v its volume in cubic inches,
and t its temperature ; if H be the height of the barometer, and h that of
the mercury in the gas jar, the pressure on the vapour will be H —h.

It is required to find the weight p' of a volume of air ?', at the tempera-
ture /, and under a pressure H -h. At zero, under a pressure of 760 milli-
metres, a cubic inch of air weighs 0-31 grain ; consequently, under the
same conditions, v cubic inches will weigh 0-317/ grains. And therefore
the weight of v cubic inches of air, at t° and the pressure 760 millimetres, is

-^ — gram [332, prob. n. ].
\\ at

As the weight of a volume of air is
proportional to the pressure, the above
weight may be reduced to the pressure

TT J

Vl—Ji by multiplying by — - — , which

0-317/ (H-//)

gives —^ -^- — — ^

* (i+rt/)76o

for the weight p' of the volume of air v,
under the pressure W — Ji and at /". Con-
sequently, for the desired density we have

T\-P -P (^ -^ (it) 760

~ P'~ 0-317/ (H-/^)"

387. Hofmann's metliod. — Hofmann
has materially improved the method
of Gay-Lussac by having the mercury
tube //5, in which the vapour is pro-
duced, about a metre in length (fig. 355) ;
it is, in fact, a barometer, and the vapour
is formed in the Torricellian vacuum.
This tube is surrounded by another glass
tube a, which is connected, by a bent tube
6", with a canister e, so that water, amylic
alcohol, or aniline, or, indeed, any sub-
stance with a constant boiling point, may
be distilled through the tube a, and the
vapour issues by the tube d, which is
arrangement not represented in the figure. In

connected with a condensing

-388]

Dumas' Method.

361

this way more constancy in the temperatures is ensured than with the use of
a mercury bath. The hquid is contained in very minute stoppered tubes, h,
holding from 20 to 100 miUigrammes of water ; the stoppers come out in the
vacuum, and the tubes can be used over again.

As, under the above conditions, the Hquid vaporises into a vacuum, the
vapour is formed under a very much lower pressure than that of the atmo-
sphere, and therefore at a temperature much below its ordinary boiling point.
Thus, the vapour-density of a body which only boils at a temperature of
1 50° can be determined at the temperature of boiling water. This is of great
use in the case of those bodies which decompose at their boiling point
under the ordinary atmospheric pressure.

388. Dumas' method. — The original method of Gay-Lussac cannot be
applied to liquids whose boiling point exceeds 150° or 160°. In order to raise
the oil in the cylinder to this temperature it would be necessary to heat the
mercuiy to such a degree that its vapour would be dangerous to the operator.
And, moreover, the pressure of the mercurial vapour in the graduated jar
would add itself to that of the vapour of the liquid, and so far vitiate the result.

The following method, devised by Dumas, can be used up to the tem-
perature at which glass begins to soften ; that is, about 400^ A glass
globe is used with the neck drawn out to a fine point (fig. 356). The globe,
having been dried externally and internally, is weighed, the temperature i
and barometric height h being noted. This weight, W, is the weight of the
glass G in addition to p, the weight of the air it contains. The globe is
then gently warmed and its point immersed in the liquid whose vapour-
density is to be determined : on cooling, the air contracts, and a quantity
of liquid enters the globe. The globe is then immersed in a bath, either
of oil or fusible metal, according to the tempera-
ture to which it is to be raised. In order to keep
the globe in a vertical position a metal support,
on which a movable rod slides, is fixed on the
side of the vessel. This rod has two rings, be-
tween which the globe is placed, as shown in the
figure. There is another rod, to which a weight
thermometer, D (324), is attached.

The globe and thermometer having been im-
mersed in the bath, the latter is heated until
slightly above the boiling point of the liquid in
the globe. The vapour which passes out by the
point expels all the air in the interior. When
the jet of vapour ceases, which is the case when
all the liquid has been converted into vapour, the
point of the globe is hermetically sealed, the
temperature of the bath t\ and the barometric
height h', being noted. When the globe is cooled
it is carefully cleaned and again weighed. This
weight, W', is that of the glass G, plus p', the weight of the vapour which fills
the globe at the temperature t\ and pressure h'; or W' = G +p'. To obtain
the weight of the glass alone, the weight^ of air must be known, which is
determined in the following manner : — The point of the globe is placed under

Fig. 356.

362

On Heat.

[388

mercury and the extremity broken off' with a small pair of pincers : the
vapour being condensed, a vacuum is produced, and mercury rushes up,
completely filling the globe, if, in the experiment, all the air has been com-
pletely expelled. The mercury is then poured into a carefully graduated
measure, which gives the volume of the globe. From this result, the volume
of the globe at the temperature /' may be easily calculated, and consequently
the volume of the vapour. From this determination of the volume of the
globe, the weight/ of the air at the temperature / and pressure h is readily
calculated, and this result subtracted from W gives G, the weight of the
glass. Now the weight of the vapour/' is W — G. We now know the
weight/' of a given volume of vapour at the temperature f and pressure h\
and it is only necessary to calculate the weight /" of the same volume of
air under the same conditions, which is easily accomplished. The quotient

-?— is the required density of the vapour.
P"

Deville and Troost modified Dumas' method so that it can be used for

determining the vapour-density of liquids with very high boiling points.
The globe is heated in an iron cylinder in the vapour of mercury or of
sulphur, the temperatures of which are constantrespectively at 35o°and440°.
In other respects the determination is the same as in Dumas' method.

For determinations at higher temperatures, Deville and Troost em-
ployed the vapour of zinc, the temperature of which is 1040°. As glass
vessels are softened by this heat, they used porcelain globes with finely-
drawn-out necks, which are sealed by means of
the oxyhydrogen flame.

In the case of substances having a high boiling
point, Victor Meyer has advantageously used a
non-volatile substance. Wood's fusible alloy, which
melts at 70°, instead of mercury. Habermann has
y ^\ zj introduced into Dumas' method Hofmann's modi-

'^^ \ = fication of Gay-Lussac's, by connecting the open

^''- ^ " end of the vessel B (fig. 356) with a space in which

a partial vacuum is made. Thus the vapour-
density can be determined for temperatures far
below the boiling point.

A method of determining vapour-density, much
in use, is that devised by Victor Meyer. The
vessel b (fig. 357), of about 100 cub. cent, capacity,
is fused to a narrow glass tube about 60 cm. in
length, provided with a caoutchouc stopper </,
which is always pushed in to the same depth, and
with a narrow delivery tube a.

This apparatus is hung in the glass flask Cy
the bulb of which holds about 80 cm., and con-
tains a liquid of constant boiling point, such as aniline or diphenyl.
This is heated until it boils constantly, which is seen when no air-bubbles
issue from the delivery tube. When this is attained a graduated tube full
of water is pushed over the end of the tube a ; the stopper d is removed
and quickly replaced after dropping in the weighed substance contained

-389] Dissociation. 363

in a small glass tube ; in order to prevent a possible breakage some
asbestos is placed in the bottom of b. As soon as the substance vaporises
a corresponding volume of air issues and is collected in the tube. When
no more issues the tube is placed in a cylinder of water and is depressed
until the level inside and outside is the same. The volume v is read
off, and also the temperature of the water /, which is also that of the room,
and the barometric height H. These data, together with the weight of the
substance^, and h, the pi^essure of aqueous vapour at ^°, enable us to calcu-
late the density from the formula

D = ^ = P X 760 (273 + t) _;g^ (273+/) 2152

p' V (0-001293) (H-//) 273 V (H-/«)

Thus neither the capacity of the vessel b nor the temperature of the vapour
need be known, unless it be desired to investigate in what respect the density
varies with the temperature ; the volume of the vapour is obtained in the
form of an equal volume of air measured at the temperature of the room.

389. Kelation of vapour-density to molecular weigrht. Dissocia-
tion.— The densities of \apours, determined at temperatures a few degrees
above their boiling points, and when they may be considered as perfect
gases, are governed by a simple but very important law, that the densities
of vapoitrs are proportiottal to their molecular weights. If both densities
and molecular weights are ret'erred to the same standard, that of hydrogen
being taken as 2 for instance, the vapour-densities are equal to the mole-
cular weights. If the density of air is taken at i, that of hydrogen is
0-0693 = ^, and hence for all other gases and superheated vapours the
density is 5^^^ of the molecular weight.

This law is of great importance in chemistry and in fixing the molecular
weights of bodies, more especially in organic chemistry. In some cases
exceptions are met with ; these, when small, may be ascribed to imperfection
of the gaseous state. A more important cause is the following : — When sal-
ammoniac, NH^Cl, for instance, is strongly heated, it is resolved into
ammonia, NH^, and hydrochloric acid, HCl, and it then occupies a volume
double that required by the law. But there is a partial decomposition
even at lower temperatures, so that the vapour- consists of molecules of
sal-ammoniac, mixed with molecules of free hydrochloric acid and of free
ammonia. In such cases the vapour-density is said to be abnormal ; and
this partial decomposition, in which there is a mixture of undecomposed
and of decomposed molecules, is spoken of as dissociation. Thus, sulphuric
acid, SO |H.,, at 325°, consists of about one half undecomposed molecules, while
the other moiety decomposes into sulphuric anhydride, SO,, and water, H.,0.
The dissociation of water begins at 1200° C, and is complete at 2500°.

Dissociation does not take place suddenly, but gradually ; it increases
with the temperature, and is limited by the tendency of the components to
recombine ; for each temperature the quantity dissociated is in a constant
ratio to the whole. As the temperature sinks, the bodies again recombine,
and at the initial temperature the body is in its original state. In this
respect dissociation differs from decomposition. The temperature at which
the decomposition is half complete is taken as that of dissociation.

Dissociation is also met with in elementary bodies ; thus at a tempera-

364

On Heat.

[389-

ture of 500° C. sulphur has the vapour density 96 (H = i), representing a
molecular weight of 192 ; as the temperature increases this becomes less,
and from 1000° it is constant, being then 32, which is normal, corresponding
to a molecular weight of 64. At the lower temperature the molecule is con-
sidered to be an aggregate consisting of six atoms or three molecules, while
at higher temperatures this complex splits up, and at 1000° consists of the
normal diatomic molecule. In like manner the density of iodine vapour,
which up to 600° is 8716, is only 4-5, or about half as much, at 1500°, but
this remains constant. This represents a dissociation of the iodine molecule,
I.,, into two atoms.

Densities of vapours.

Air ....

. I -0000 Vapo

ur of carbon bisul

abide 2-4476

Vapour of water .

. 0-6225

, phosphorus

• 4-3256

„ alcohol

. 1-6138

, turpentine

• 5'oi3o

„ acetic acid .

. 2-0800

, sulphur

. 6-6542

„ ether .

. 2-5860

, mercury

. 6-9760

„ benzole

. 2-7290

„ iodine .

. 8-7160

The density of aqueous vapour, when a space is saturated with it, is at
all temperatures |, or, more accurately, 0-6225, of the density of air at the
same temperature and pressure.

390. Relation between the volume of a liquid and tbat of its
vapour. — The density of vapour being known, we can readily calculate the
ratio between the volume of a vapour in the saturated state at a given tem-
perature and that of its liquid at zero. We may take as an example the
relation between water at zero and steam at 100°.

The ratio between the weights of equal volumes of air at zero, and the
normal barometric pressure, and of water under the same circumstances, is
as I : ii})- But from what has been already said (332), the density of air
at zero is to its density at 100° as i ■\- at : i. Hence the ratio between the
weights of equal volumes of air at 100° and water at 0° is
I

: 773, or 0-73178 : -jTi

I +0-003665 X 100

Now from the above table the density of steam at 100° C, and the
normal pressure, compared with that of air under the same circumstances,
is as 0-62225 • I- Hence the ratio between the weights of equal volumes of
steam at 100° and water at o'^ is

0-73178 X 0-6225 : 113, or 0-4555 : 773, or i : 1698.

Therefore, as the volumes of bodies are inversely as their densities, one
volume of water at zero expands into 1-698 volumes of steam at loo*^ C.
The practical rule, that a cubic inch of water yields a cubic foot of steam,
though not quite accurate, expresses the relation in a convenient form.

-392] 365

CHAPTER VI.

HYGROMETRY.

391. Province of hygrometry. — The province oi hygrometry\% to deter-
mine the quantity of aqueous vapour contained in a given volume of air.
This quantity is very variable ; but the atmosphere is seldom or never
completely saturated with vapour, even m our climate. Nor is it ever com-
pletely dry ; for if hygrometric substances — that is to say, substances with a
great affinity for water, such as chloride of calcium, sulphuric acid, &c. — be
at any time exposed to the air, they absorb aqueous vapour.

392. Kyg-rometrlc state. — As, in general, the air is never saturated, the
ratio of the quantity of aqueous vapour actually present in the atmosphere
to that which it would contain if it were saturated, the temperature remain-
ing the same, is called the hygrometric state, or degree of sattcratio7i.

The absolute inoistiire is measured by the weight of water actually present
in the form of vapour in the unit of volume.

We say the ' air is dry ' when water evaporates and moist objects dry
rapidly; and the 'air is moist' when they do not dry rapidly, and when
the least lowering in temperature brings about deposits of moisture. The
air is dry or moist according as it is more or less distant from its point
of saturation. Our judgment is, in this respect, independent of the absolute
quantity of moisture in the air. Thus, if in summer, at a temperature of
25° C, we find that each cubic metre of air contains 13 grammes of vapour,
we say it is very dry, for at this temperature it could contain 22-5 grammes.
If, on the other hand, in winter we find that the same volume contains
6 grammes, we call it moist, for it is nearly saturated with vapour, and the
slightest diminution of temperature produces a deposit. When a room is
warmed, the quantity of moisture is not diminished, but the humidity of
the air is lessened, because its point of saturation is raised. The air
may thus become so dry as to be injurious to the health, and hence it is
usual to place vessels of water on the stoves used for heating in France and
Germany.

As Sonde's law applies to non-saturated vapours as well as to gases (354),
it follows that, with the same temperature and volume, the weight of vapour
in an unsaturated space increases with the pressure, and therefore with
the pressure of the vapour itself. Instead, therefore, of the ratio of the
quantities of vapour, that of the corresponding pressures may be substituted,
and it may be said that the hygrometric state is the ratio of the elastic
force of the aqueous vapour •which the air actually contains, to the elastic
force of the vapour which it would contain at the same temperature if it
were saturated.

If/ is the actual pressure of aqueous vapour in the air, and F that of satu-

366

On Heat.

[392-

rateci vapour at the same temperature, and E the hygrometric state, we have

E = -1^ ; whence /= F x E.
F

As a consequence of this second definition, it is important to notice that,
the temperature having varied, the air may contain the same quantity of
vapour and yet not have the same hygrometric state. For, when the tem-
perature rises, the tension of the vapour which the air would contain, if satu-
rated, increases more rapidly than the tension of the vapour actually present
in the atmosphere, and hence the ratio between the two forces — that is to
say, the hygrometric state — becomes smaller.

Jamin proposes to replace this

ratio -(-,-, which expresses the relative
r

moisture, by the ratio ^f-/—^, in which H is the barometric height ; he calls

this the hygrometric richness, and contends that it brings out changes in the
quantity of moisture present in the air with greater distinctness.

It will presently be explained (401) how the weight of the vapour contained
in a given \olume of air may be deduced from the hygrometric state.

393. Different kinds of hygrometers. — Hygrometers are instruments for
measuring the hygrometric state of the air. There are numerous varieties of
them — chemical hygrometers, condensing hygrometers, and psychrometers.

394. Chemical hygrometer. — The method of the chemical hygrometer
consists in passing a known volume of air over a substance which readily

Fig. 3S8.

absorbs moisture — chloride of calcium, for instance. The substance having
been weighed before the passage of air, and then afterwards, the increase
in weight represents the amount of aqueous vapour present in the air. By
means of the apparatus represented in fig. 358 it is possible to examine any

-396] Danicirs Hygrometer. 367

given volume of air. Two brass reservoirs, A and B, of the same size and
construction, act alternately as aspirators, by being fixed to the same axis,
about which they can turn. They are connected by a central tubulure, and
by means of two tubulures in the axis the lower reservoir is always in con-
nection with the atmosphere, while the upper one, by means of a caoutchouc
tube, is connected with two tubes M and N, filled either with chloride of
calcium, or with pumice-stone impregnated with sulphuric acid. The first
absorbs the vapours in the air drawn through, while the other, M, stops any
vapour which might diffuse from the reservoirs into the tube N.

The lower reservoir being full of water, and the upper one of air, the
apparatus is inverted so that the liquid flows slowly from A to B. A partial
vacuum being formed in A, air enters by the tubes N M, in the first of which
all the vapour is absorbed. When all the water is run into B it is inverted ;
the same flow recommences, and the same volume of air is drawn through
the tube N. Thus, if each reservoir holds a gallon, for example, and the
apparatus has been turned five times, 6 gallons of air have traversed the
tube N, and have been dried. If then, before the experiment, the tube with
its contents has been weighed, the increase of weight gives the weight of
aqueous vapour present in 6 gallons of air at the time of the experiment.

Edelmann has devised a new form of hygrometer, the principle of which
is to enclose a given volume of air, and then to absorb the aqueous vapour
present by means of strong sulphuric acid ; in this way a diminution in the
pressure is produced which is determined, and which is a direct measure of
the tension y of the aqueous vapour previously present.

Similar apparatus have been devised by Rudorff and by Neesen.

395. Condensing- hygrometers. — When a body gradually cools in a
moist atmosphere — as, for instance, when a lump of ice is placed in water
contained in a polished metal vessel — the layer of air in immediate contact
with it cools also, and a point is ultimately reached at which the vapour
present is just sufficient to saturate the air ; the least diminution of tempera-
ture then causes a precipitation of moisture on the vessel in form of dew^
When the temperature rises again, the dew disappears. The mean of these
two temperatures is taken as the dew-poi?it, and the object of condensing
hygrometers is to observe this point. Daniell's and Regnault's hygrometers
belong to this class.

396. Baniell's hygrrometer. — This consists of two glass bulbs at the
extremities of a glass tube bent twice (fig. 359). The bulb A is two-thirds
full of ether, and a very delicate thermometer plunged in it ; the rest of the
space contains nothing but the vapour of ether, the ether having been boiled
before the bulb B was sealed. The bulb B is covered with muslin, and
ether is dropped upon it. The ether in evaporating cools the bulb, and the
vapour contained in it is condensed. The internal pressure being thus dimi-
nished, the ether in A forms vapour which condenses in the other bulb B. In
proportion as the liquid distils from the lower to the upper bulb, the ether in
A becomes cooler, and ultimately the temperature of the air in immediate
contact with A sinks to that point at which its vapour is more than sufficient
to saturate it, and it is, accordingly, deposited on the outside as a ring of
dew corresponding to the surface of the ether. The temperature of this point
is noted by means of the thermometer in the inside. The addition of ether to

368

On Heat.

[396-

the bulb B is then discontinued, the temperature of A rises, and the tempera-
ture at which the dew disappears is noted. In order to render the deposition
of dew more perceptible, the bulb A is
made of black glass.

These two points having been deter-
mined, their mean is taken as that of the
dew-point. The temperature of the air
at the time of the experiment is indicated
by the thermometer on the stem. The
pressure^ corresponding to the tempera-
ture of the dew-point, is then found in the
table of pressures (358). This pressure is
exactly that of the vapour present in the
air at the time of the experiment. The
pressure F of vapour saturated at the
temperature of the atmosphere is found
by means of the same table ; the quotient
obtained by dividing _/" by F represents
the hygrometric state of the air (392).
For instance, the temperature of the air
being 15°, suppose the dew-point is 5°.
From the table the corresponding pres-
sures are /= 6-534 millimetres, and
F = I2"699 millimetres, which gives 0-514
for the ratio of f to F, or the hygro-
metric state.
There are many sources of error in Daniell's hygrometer. The principal
are : ist, that as the evaporation in the bulb A only cools the liquid on the
surface, the thermometer dipping on it does not exactly give the dew-point ;
2nd, that the observer standing near the instrument modifies the hygro-
metric state of the surrounding air, as well as its temperature ; the cold
ether vapour also flowing from the upper bulb may cause inaccuracy.

397. Regrnault's hygrometer. — Regnault's hygrometer is free from the
sources of error incidental to the use of Daniell's. It consists of two very
thin polished silver thimbles 1-75 inch in height, and 0-75 inch in diameter
(fig. 360). In these are fixed two glass tubes, D and E, in each of which is
a thermometer. A bent tube. A, open at both ends, passes through the cork
of the tube D, and reaches nearly to the bottom of the thimble. There is a
tubulure on the side of D, fitting in a brass tube which forms a support for
the apparatus. The end of this tube is connected with an aspirator G. The
tube E is not connected with the aspirator ; its thermometer simply indicates
the temperature of the atmosphere.

The tube D is then half filled with ether, and the stopcock of the aspirator
opened. The water contained in it runs out, and just as much air enters
through the tube A, bubbling through the ether, and causing it to evaporate.
This evaporation produces a diminution of temperature, so that dew is de-
posited on the silver just as on the bulb in Daniell's hygrometer ; the ther-
mometer T is then instantly to be read, and the stream from the aspirator
stopped. The dew will soon disappear again, and the thermometer T is

Fig. 359-

398]

PsycJu'oineter. Wet-Bulb HygrometcT.

369

again to be read ; the mean of the two readings is taken ; the thermometer
/ gives the corresponding temperature of the air, and hence there are all the
elements necessary for
calculating the hygro-
metric state.

As all the ether
in this instrument is
at the same tempera-
ture in consequence of
the agitation, and the
temperatures may be
read off at a distance by
means of a telescope,
the sources of error in
Daniell's hygrometer
are avoided.

A much simpler
form of the apparatus
may be constructed
out of a common test-
tube containing a
depth of \\ inch of
ether. The tube is
provided with a loosely
fitting cork in which are
a delicate thermometer
and a narrow bent tube dipping
through a caoutchouc tube of considerable length, a diminution of tempera-
ture is caused, and dew is ultimately deposited on the glass ; after a little
practice the whole process can be conducted almost as well as with
Regnault's more complete instrument. The temperature of the air is
indicated by a detached thermometer.

y^"a. Sines' hyg-rometer. — Dines has constructed a hygrometer which
is also one of condensation, but which dispenses with the use of such volatile
liquids as ether. The principle of this instrument is to have a thin flat
metal box, through which a small stream of cooled water is allowed to flow
for a few seconds. The dew is deposited on the top of the box, which is of
thin dark polished metal. By alternately stopping the flow and allowing it
to continue, the disappearance and formation of the dew may be very accu-
rately observed, and the corresponding temperatures read off by a delicate
thermometer placed inside.

398. Psychrometer. "Wet-bulb hygrrometer. — A moist body evaporates
in the air more rapidly in proportion as the air is drier, and the temperature
of the body sinks in consequence of this evaporation. The psychrometer,
or wet-bidb hygrotfteter, is based on this principle, the application of which
to this purpose was first suggested by Leslie. The form usually adopted in
this country is due to Mason. It consists of two delicate thermometers
placed on a wooden stand (fig. 361 ). One of the bulbs is covered with muslin,
and is kept continually moist by being connected with a reservoir of water

P. R

Fig 360

in the ether. On blowing' into the ether

370

On Heat.

[398-

by means of a string. Unless the air is saturated with moisture the wet-bulb
thermometer always indicates a lower temperature than the other, and the
difference between the indications of the two thermometers is greater in pro-
portion as the air can take up more moisture. The tension e of the aqueous
vapour in the atmosphere may be calculated from the indications of the two
thermometers by means of the following empirical formula : —

t' = ^' — o'ooo77 (/-/')//,
in which e' is the maximum tension corresponding to the temperature of the
wet-bulb thermometer, 0-00077 is a constant, // is the barometric height, and
/ and /' the respective temperatures of the dry and wet bulb thermometers.
If, for example, // = 750 millimetres, /= 15° C, /'= 10° C. ; ac-
cording to the table of pressures (358), e' = 9"i65, and we have

£? = 9-165 -0-00077 X 5 X 750 = 6-278.

This pressure corresponds to a dew-point of about 4-5° C.
If the air had been saturated, the pressure would have been
12-699, <i"d the air is therefore about half saturated with
moisture.

This formula expresses the result with tolerable accuracy,
but the above constant 0-00077 requires to be controlled for
different positions of the instrument ; in small closed rooms
it is 0-00128, in large rooms it is o-ooioo, and in the open
air without wind it is 0-00090 : the number 0-00077 is its
value in a large room with open windows. Regnault found
that the difference in temperature of the two bulbs depends
on the rapidity of the current of air ; he also found that at
a low temperature, and in very moist air, the results ob-
tained with the psychrometer differed from those yielded by
his hygrometer. It is probable that the indications of the
psychrometer are only true for mean and high temperatures,
and when the atmosphere is not too moist.

A formula frequently used in this country is that given
by Dr. Apjohn. It is

d h ^ ^ , d h

F=/-

— , or F = /- -
88 30' ■' 96 30

in which d is the difference of the wet and dry bulb thermometers in
Fahrenheit degrees ; h the barometric height in i?zches ; / the pressure of
vapour for the temperature of the wet bulb, and F the pressure of vapour
at the dew-point, from which the dew-point may, if necessary, be found from
the tables. The constant coefficient 88, for the specific heats of air and
aqueous vapour, is to be used when the reading of the wet bulb is above 32°
F., and 96 when it is below. •

According to Glaisher the temperature of the dew-point may be obtained
by multiplying the difference between the temperatures of the wet and dry
bulb by a constant depending on the temperature of the air at the time of
observation, and subtracting the product thus obtained from this last-named
temperature.

-399] Absorption Hygrometers. 371

The following table gives the numbers, which are known as ClaisJier's
factois.

Dry bulb
Temperature F.°

Factor

Dry bulb
Temperature F.°

Factor

Below 24°

8-5

34 to 35

2-8

24 to 25

6-9

35-40

2-5

25-26

6-5

40—45

2'2

26 — 27

6-1

45-50

2-1

27—28

5-6

50-55

2-0

28—29

5-1

55—60

1-9

29—30

4-6

60—65

1-8

30—31

4-1

65—70

1-8

31—32

70-75

32-33

y}>

75-80

33-34

3-0

80-85

1-6

399. Absorption hygrometers. — These hygrometers are based on the
property which organic substances have of elongating when moist, and of
again contracting as they become dry. The most common form is the hair
or Saiissure's Jiygrometer.

It consists of a brass frame (fig. 362), on which is fixed a hair, f, fastened
at the top in a clamp, cz, provided with a screw, d. This clamp is moved by
a screw, b. The lower part of the hair passes round a
pulley, 0, and supports a small weight, /. On the
pulley there is a needle, which moves along a graduated
scale. When the hair becomes shorter the needle rises,
when it becomes longer the weight j?^. makes it sink.

The scale is graduated by calling that point zero at
which the needle would stand if the air were completely
dry, and 100 the point at which it stands in air completely
saturated with moisture. The distance between these
points is divided into 100 equal degrees.

Regnault devoted much study in order to render the
hair hygrometer scientifically useful, but without much
success. The utmost that can be claimed for it is that it
can be used as a hygroscope ; that is, an instrument which
shows approximately whether the air is more or less
moist, without giving any indication as to the quantity of
moisture present. To this class of hygroscopes belong
the chimney ornaments, one of the most common forms
of which is that of a small male and female figure, so
arranged in reference to a little house, with two doors, that
when it is moist the man goes out and the woman goes
in, and vice versa when it is fine. They are founded on the property which
twisted strings or pieces of catgut possess of untwisting when moist, and of
twisting when dry. As these hygroscopes only change slowly, their indi-
cations are always behindhand with the state of the weather ; nor are they,
moreover, very exact.

372 On Heat. [399-

A strip of drawing-paper, coated on one side with gelatine and varnished
on the other, readily absorbs moisture, so that the strip curves outwards on
the gelatine side, like the compensating strips in (320), when heated. If such
a strip be coiled as a spiral, then, according to the greater or less quantity of
moisture it absorbs, this twists and untwists like a Breguet's thermometer
(309), and thus serves as a sensitive hygroscope.

400. IMCoisture of the atmosphere. — The absolute moisture varies with
the temperature in the course both of the year and of the day. In summer
there is a maximum at eight in the morning and evening, and a minimum at
3 P.M. and 3 A.M, because the ascending current of air carries the moisture
upwards. The absolute moisture is greatest in the tropics, where it represents
a pressure of 25 mm., while in our latitudes it does not exceed 10 mm. The
relative moisture, on the other hand, is on the average greater in high than
in low latitudes ; it is at the minimum in the hottest and at its maximum in
the coolest part of the day. It varies also in different regions. It is greater
in the centre of continents than it is on the sea or the sea-coast. Thus in
summer the relative moisture at Greenwich is "j"]^ at Venice 64, Lugano
58, and Uralsk 42*^. That the dryness increases with the distance from
the sea is shown by the clearer skies of continental regions. In Platowskya
in Siberia the air, at a temperature of 24°, was found to contain a quantity of
moisture only sufficient to saturate it at —3°; the air might therefore have
been cooled through 27° without any deposit of moisture. On the ground
the absolute moisture is greatest, and diminishes rapidly as we ascend ; the
relative moisture however increases, so that at a certain height the air is
saturated with moisture. From this zone upwards the relative moisture de-
creases, for the aqueous vapour is confined to the lower regions. In some
parts of East Africa the springs of powder-flasks exposed to the damp snap
like twisted quills ; on the contrary, paper becomes soft and sloppy by the
loss of its glaze ; and gunpowder, if not kept hermetically sealed, refuses
to ignite. On the other hand in North America, where the south-west winds
blow over large tracts of land, the relative moisture is less and the evapo-
ration is far more rapid than in Europe ; clothes dry quickly, bread soon
becomes hard, newly built houses can be at once inhabited, European pianos
soon give way there, while American ones are very durable on this side of
the ocean. As regards the animal economy, liquids e\'aporate more rapidly,
by which the circulation and the assimilation are accelerated, and the whole
character is more nervous. For evaporation is quicker the drier the air, and
the more frequently it is renewed ; it is, moreover, more rapid the higher
the temperature, and the less the pressure. This is not in disaccord with the
statement that the quantity of vapour which saturates a given space is the
same however this be filled with air ; a certain space takes up the same
weight of vapour whether it is vacuous, or filled with rarefied or dense air ;
the saturation with vapour takes place the more rapidly the smaller the
pressure of the air.

401. Problem on hygrometry. — To calculate the weight P of a volume
of moist air \", the hygrometric state of which is E, the temperature /, and
the pressure H, the density of the vapour being | that of air.

From the second law of the mixture of gases and vapours, it will be seen
that the moist air is nothing more than a mixture of V cubic inches of dry

-402] Correction for Loss of Weight in Air. 2)7?)

air at /°, under the pressure H minus that of the vapour, and of V cubic
inches of vapour at t° and the pressure given by the hygrometric state ;
these two values must, therefore, be found separately.

The formula /= F x E (392) gives the pressure /of the vapour in the air,
for E has been determined, and F is found from the tables. The pressure /
being known, if/' is the pressure of the air,/+/' = H, from which
/' = H -/= H - FE.

The question consequently resolves itself into calculating the weight of

V cubic inches of dry air at /", and the pressure H - FE, and then that of

V cubic inches of aqueous vapour also at /"", but under the pressure FE.

Now V cubic inches of dry air under the given conditions weigh

° 1 ^-x— "^ ) ^"d we readily see from problem iii. art. 384, that V cubic

(i +at) 760 ^ -^ ^'

inches of vapour at t°, and the pressure FE, weigh < x -2-=2 . Adding

^ "^ ' "^ 8 (I + a/) 760 ^

these two weights, and reducing, we get

p_o-3i V(H-|FE)
(i +0^760
If the air were saturated we should have E = i, and the formula would thus
be changed into that already found for the mixture of gases and saturated
vapours (384).

This formula contains, besides the weight P, many variable quantities, V,
E, H, and /, and consequently, by taking successively each of these quanti-
ties as unknown, as many different problems might be proposed.

402. Correction for the loss of \(reigrht experienced by bodies
weighed in the air. — It has been seen in speaking of the balance that the
weight which it indicates is only an apparent weight, and is less than the
real weight. The latter may be deduced from the former when it is remem-
bered that every body weighed in the air loses a weight equal to that of the
displaced air (195). This problem is, however, very complicated, for not
only does the weight of the displaced air vary with the temperature, the
pressure, and the hygrometric state, but the volume of the body to be
weighed, and that of the weights, vary also with the temperature ; so that a
double correction has to be made ; one relative to the iceights., the other to
the body weighed.

Correction relative to tJie weights. — In order to make this correction let
P be their weight in air, and n their weight ifi vacuo ; further, let V be the
volume of these weights at 0°, D the density of the substance of which they
are made, and K its coefficient of linear expansion.

The volume V becomes V (i + 2,^s.t) at t° ; hence this is the volume of air
displaced by the weights. If /x be the weight of a cubic inch of air at /,and
the pressure H at the time of weighing, we have
P = n-MV (i + 3l^0-

From the formula P = VD (125) V may be replaced by _^, and the
formula becomes

TV • • • • • \ J

x.n[

374 On Heat. [402-

which gives the value, in air, of a weight n, when ix is replaced by its value.
But since /x is the weight of a cubic inch of air more or less moist, at the
temperature / and the pressure H, its value may be calculated by means of
the formula in the foregoing paragraph.

Correction relative to the body weighed. — Let p be the apparent weight
of the body to be weighed, tt its real weight in vacuo., d its density, t: its
coefficient of expansion, and / its temperature ; by the same reasoning as
above we have

/-[.-"(-i^] w

By using the method of double weighing, and of a counterpoise whose
apparent weight is^', the real weight tt', the density d\ and the coefficient
/('', and assuming that the pressure does not change, which is usually the
case, we have again

M(i3 + i-r)l

P' = l.'\^

(3)

If a and b are the two arms of the beam, we have in the first weighing ap =pb :
and in the second aV = bp, whence p = V. Replacing P and p by their values
deduced from the above equations, we have

L d

whence
which solves the problem.

M(i + 3^vn ^r^ _Ki + 3K/)-|

-404] 375

CHAPTER VII.

CONDUCTIVITY OF SOLIDS, LIQUIDS, AND GASES.

403. Transmission of beat. — When we stand at a little distance from a
■fire or other source of heat we experience the sensation of warmth. The
heat is not transmitted by the intervening air ; it passes through it without
raising its temperature, for if we place a screen before the fire the sensation
ceases to be felt. The heat from the sun reaches us in the same manner.
The heat, which, as in this case, is transmitted to a body from the source of
heat without affecting the temperature of the intervening medium, is said to
be radiated.

That heat can Ije transmitted through a medium without raising its tem-
perature is proved by a remarkable experiment of Prevost in 18 11. Water
from a spring was allowed to fall in a thin sheet ; on one side of this was held
a red-hot iron ball, and on the other a delicate thermometer. The tempera-
ture of the latter was observed to rise steadily, a result which could not have
been due to any heating effect of the water itself, as this was cold, and was
being continually renewed. It could only have been due to heat which
traversed the water without raising its temperature. A similar experiment
has been made by a hollow glass lens through which cold water flowed in a
constant stream. The sun's rays concentrated by this arrangement ignited
a piece of wood placed in the focus.

Heat is transmitted in another way. When the end of a metal bar is
heated, a certain increase of temperature is presently observed along the
bar. Where the heat is transmitted in the mass of the body itself, as in this
case, it is said to be conducted. We shall first consider the transmission of
heat by conduction.

404. Conductivity of solids. — Bodies conduct heat with different de-
grees of facility. Good condtwtofs are those

which readily transmit heat, such as are the
metals ; while bad cofidiictors, to which class
belong the resins, glass, wood, and more espe-
cially liquids and gases, offer a greater or less
resistance to the transmission of heat.

In order to compare roughly the conducting
power or conductivity of different solids, Ingen-
haus constructed the apparatus which bears his
name and which is represented in fig. 363. It
is a metal trough, in which, by means of tubu- ' *"' " -"

lures and corks, are fixed rods of the same dimensions, but of different
materials ; for instance, iron, copper, wood, glass. These rods extend to
a slight distance ip the trough, and the parts outside are coated with wax
which melts at 61'^. The box being filled with boiling water, it is observed
that the wax melts to a certain distance on the metal rods, while on the

376

On Heat.

[404-

others there is no trace of fusion. The conducting power is evidently greater
in proportion as the wax has fused to a greater distance. The experiment is
sometimes modified by attaching glass balls or marbles to the ends of the
rods by means of wax. As the wax melts, the balls drop off, and this in the
order of their respective conductivities. The quickness with which melting
takes place is, however, only a measure of the conducting power, in case the
metals have the same or nearly the same specific heat.

Despretz compared the conducting powers of solids by forming them into
bars (fig. 364), in which small cavities are made at short intervals : these
cavities contain mercury, and a delicate thermometer is placed in each of
them. Such a bar, AB, is exposed at one end to a constant source of heat,

such as that of a bath of paraffin or of fusible metal heated by a Bunsen's
burner ; the thermometers gradually rise until they indicate fixed tempera-
tures, which are less according as the thermometers are farther from the
source of heat By this method Despretz verified the following law : — If the
distances «, a, a^ .... «vi from the source of heat mcrease in arithnetical
progression, the excess of temperature over that of the surrounding air,
t,t-^,t^:^ .... /v 5 decreases in geometrical progression.

This law, however, only prevails in the case of very good conductors,
such as gold, platinum, silver, and copper ; it is only approximately true for
iron, zinc, lead, and tin, and does not apply at all to non-metallic bodies,
such as marble, porcelain, &c.

Taking the conducting power of gold at 1000, Despretz constructed the
following table of conductivities : —

Platinum .

Silver

Copper

Iron ....

Zinc ....

By making cavities in the bars, as in Despretz's metho'

981

Tin .

97.3

Lead

897

Marble .

,374

Porcelain

363

Brick earth

• 304

• 179

• 23

1, their form is

altered, and the continuity partially destroyed. Wiedemann and Franz

;oo-o

Iron

73-6

Steel .

S3'~

Lead .

23-1

Platinum

19-0

Rose's alloy

14-5

Bismuth

-405] Coefficient of Conductivity. 377

avoided this source of error by measuring the temperature of the bars in
different places by applying to them the junction of a thermo-electric couple
(412). The metal bars were made as regular as possible, one of the ends
was heated to 100°, the rest of the bar being surrounded by air at a constant
temperature. The thermo-electric couple was of small dimensions, in order
not to abstract too much heat.

By this method Wiedemann and Franz obtained results which differ con-
siderably from those of Despretz. Representing the conductivity of silver
by 100°, they found the following numbers for. the other metals : —

Silver .... igq-o Iron . . . .11-9

Copper .... 73-6 Steel . . . . ii-6

Gold ...

Brass

Zinc . ' .

Tin ...

These experimenters found that the conducting power of the pure metals
for heat and electricity is the same.

Organic substances conduct heat badly. De la Rive and De Candolle
showed that woods conduct better in the direction of their fibres than in a
transverse direction, and this difference is greater with the soft than with the
hard woods ; they remarked upon the influence which this feeble conduct-
ing power, in a transverse direction, exerts in preserving a tree from sudden
changes of temperature, enabling it to resist alike a sudden abstraction of
heat from within, and the sudden accession of heat from without. Tyndall
has also shown that this tendency is aided by the low conducting power of
the bark, which in all cases is less than that of the wood. Cotton, wool,
straw, bran. &c., are all bad conductors.

Rocks and the earth are the worse conductors, the less dense and homo-
geneous is the mass. Hence the length of time required for the sun's heat to
penetrate into the earth. The mean highest temperature of the air near the
ground in Central Europe is in the month of July, but at a depth of 25 to 28
feet in the earth it is in the month of December.

405. Coefficient of conductivity.— The numbers given in the foregoing
article only express the relative conducting powers of the respective sub-
stances. Numerous experiments have been made to determine the quantity
of heat, W, which passes, for instance, through a plate the two sides of which
are kept at a constant difference of temperature. This will clearly be pro-
portional to the area of the plate A and to the time /. It is further propor-
tional to the excess of the temperature of the one face B^ over that of the
other 6 — that is, to ^j — ^ ; and as the flow of heat is different in different
substances, it will be proportional to a constant k.

On the other hand it will be inversely proportional to the thickness of the
plate d. These results are expressed by the formula

W = ^J^i)_A^from which ^^ ,,— ^v". ..•
d {01 - 6) Atd

On the CGS system of units, the coefficient of thermal or calorimetrical
conductivity^ k, is the quantity of heat which passes in a second of time,

3/8 On Heat. [405-

betvveen the two opposite faces of a cube of the substance one centimetre in
thickness, and which are kept at a constant difference of one degree. The
mean values, as found by Neumann, are as follows: — copper, i-io8; zinc,
0-307 ; iron, 0-163 ; argentan, 0-109 ; ice, 0-0057.

Thus if the two opposite faces of a cube of iron one centimetre in thick-
ness, that is to say, a cubic centimetre of iron, are kept at a constant differ-
ence of 1° C, the quantity of heat which passes in each second of time will
be sufficient to raise 0-163 gramme of water through 1° C. From this, which
is often called the caloriinetrical measure of conductivity., we must distin-
guish the thermometric measure of conductivity ; that is to say, the number
of degrees through which the cube in question would be heated when the
above quantity of heat passes through it under the given conditions. This
is obtained from the constants given, by dividing them by the reduced value
of the cube c, or the specific heat of unit volume ; that is, by the product of
its specific heat into its specific gravity.

406. Senarmont's experiment. — It is only in homogeneous bodies that
heat is conducted with equal facility in all directions. If an aperture be
made in a piece of ordinary glass covered with a thin layer of wax, and a
platinum wire ignited by a voltaic current be held through the aperture, the
wax will be melted round the hole in a circular form. Senarmont made, on

this principle, a series of experiments on the conductivity of
heat in crystals. A plate cut from a crystal of the regular
system was covered with wax, and a heated metaUic point
was held against it. The part melted had a circular form ;
but when plates of crystals belonging to other systems were
investigated in a similar manner, it was found that the form
of the isothermal line or line of equal temperature — that is,
the boundary of the melted part — varied with the different
systems and with the position of the axes. In plates of
uniaxial crystals cut parallel to the principal axis it was an
ellipse (fig. 365), the major axis of which was in the direction
of the principal axis. In plates cut perpendicular to the
principal axis it was a circle. In biaxial crystals, for which
F'g- 365- selenite is well adapted, the line was always an ellipse. The

isothermal surface agrees in general character with the wave surface of the
extraordinary ray.

Instead of wax the plate may be coated with the double iodide of mercury
and copper ; this substance is of a brick-red colour, which when heated
changes into a purplish black.

Rontgen makes the experiment very simply by breathing on the plate,
and then holding a hot steel point against it. When a space free from mois-
ture has been found about the point, the whole plate is dusted with lyco-
podium, which shows the outline of the figure with great sharpness.

Pfaff found the conductivity of rock crystal 50-3 in the direction of the
principal axis, and 39-1 in a direction at right angles thereto.

407. Conductivity of liquids. — The conductivity of liquids is very small,
as is seen from the following experiment : — A delicate thermoscope B, con-
sisting of two glass bulbs, joined by a tube w, in which there is a small
index of coloured liquid, is placed in a large cylindrical glass vessel, D (fig.

-407J

Conductivity of Liquids.

379

366). This vessel is filled with water at the ordinary temperature, and a tin

vessel, A, containing oil at a temperature of two or three hundred degrees,

is dipped in it. The bulb near the vessel A is J^

only very slightly heated, and the index m moves

through a very small distance. Other liquids give

the same result. That liquids conduct very badly

is also demonstrated by a simpler experiment. A

long test-tube is half filled with water, and some ice

so placed in it that it cannot rise to the surface.

By inclining the tube and heating the surface of

the liquid by means of a spirit lamp, the liquid at

the top may be made to boil, while the ice at the

bottom remains unmelted.

Despretz made a series of experiments with an
apparatus analogous to that here described, but he
kept the liquid in the vessel, A, at a constant tem- -=^^=--

perature, and arranged a series of thermometers Fig. 366.

one below the other in the vessel D. In this manner he found that the
conductivity of heat in liquid obeys the same'^laws as in solids, but is much
more feeble. For example, the conductivity of water is i that of copper.

Guthrie examined the conductivity of liquids in the following manner : —
Two hollow brass cones are placed near each other so that the top of one

points upwards, that of the other downwards (fig. 367). The distance of the
bases, which are of platinum, can be regulated by a micrometer screw. The
liquid to be examined is introduced between the bases by means of a pipette.
The lower cone is fitted with a glass tube which dips in a coloured liquid,
and thus constitutes an air thermometer. The base of the upper cone is
kept at a constant temperature by means of a current of hot water ; it thus

38o On Heat. [407-

warms the liquid, and the base of the lower cone, in consequence of which
the air in the interior is expanded and the column of liquid in the stem
depressed.

The bases of the cones were first brought in contact and the depression
of the column of hquid was observed. A layer of liquid of a given thick-
ness was then interposed and the depression observed after a certain time.
The same thicknesses of other liquids were then successively introduced,
and the corresponding depressions noted. The difference of the depressions
was a measure for the resistance which the liquid offered to the passage of heat.

The most complete researches on the conductivity of liquids are those of
Weber, who made use of the following method. A copper disc about 8
cm. in radius was separated from another similar one by three pieces of
glass, about 0'2 cm. thick. The space thus formed between the two is
filled with the liquid to be examined, and the system placed horizontally on
a smooth block of ice. The lower plate rapidly assumed the temperature of
the ice, and heat travelled through the hquid from the upper plate, the
changes in temperature of which were noted by a thermo-electrical arrange-
ment (413). He thus observed the following values for k (405) : —

Water

0-00124

Carbon bisu

Iphide

. 0-00042

Solution of CuSO.,

Q-OGIlS

Ether

. 0-00040

Solution of NaCl

0-00115

Olive oil .

. 0-00039

Glycerine .

0-00067

Chloroform

. O-OOO},']

Alcohol

-.pr HpH.irPrl frniT. hiq i

0-00049
p';parrhp'^ th

Benzole

p law that fnr

thp linilif

0-00032
q pvaminp

him, the conductivity divided by the specific heat of unit volume — that is to
say, the density multiplied by the specific heat — is an almost constant number.
408. IVIanner in wtaicli liquids are heated. — When a column of liquid
is heated at the bottom, ascending and descending currents are produced.
It is by these that heat is mainly distributed
thi-ough the hquid, and not by its conductivity.
These currents arise from the expansion of
the inferior layers, which, becoming less
dense, rise in the licjuid, and are replaced
by colder and denser layers. They may be
made visible by projecting bran or wooden
shavings into water, which rise and descend
with the currents. The experiment is
arranged as shown in fig. 368. The mode
in which heat is thus propagated in liquids
and in gases is said to be by co/ivectio/i.

409. Conductivity of g-ases. — It has
been a disputed question whether gases have
a true conductivity, that is to say, a conduc-
tion from layer to layer as with the metals ;
but certainly when they are restrained m
their motion their conductivity is very small.
All substances, for instance, between whose particles air remains stationary,
offer great resistance to the propagation of heat. This is well seen in straw,

Fig. 368.

-410] Applications. 381

eider-down, and furs. The propagation of heat in a gaseous mass is effected
by means of the ascending and descending currents formed in it, as is the
case with hcjuids.

The following experiment, a modification of one originally devised by
Sir W. Grove, is considered to prove that gases have a certain conductivity.

A glass tube, fig. 369, with two lateral tubes d and e opening into it at
one end, is closed in the middle by a cork, ^, through which a stout copper
wire passes. This is connected by thin platinum wires with similar stout
copper wires also passing through the corks a and c. When the current of
a Grove's battery is passed through the wires, both platinums are equall)'
incandescent. If, now, one half of the tube is filled with hydrogen by con-
necting one of the small tubes with a supply of that gas, and the current is
again passed, the wire in the hydrogen is scarcely luminous, while that in
air is still brightly incandescent.

This greater chilling of the wire in hydrogen than in air was considered
by Magnus to be an effect of conduction ; while Tyndall ascribes it to the
greater mobility of the particles of hydrogen.

Stefan found the value of k for air to be 0-0000558 in CGS units, so
that its conductivity is only J9I55 that of copper, and j^j that of iron. He

Fig. 369.

also found that hydrogen conducts seven times as well as air, and that
difference of density seems to have no influence on the conductivity.

410, Applications. — The greater or less conductivity of bodies meets
with numerous apphcations. If a liquid is to be kept warm for a longtime,
it is placed in a vessel and packed round with non-conducting substances,
such as shavings, straw, or bruised charcoal. For this purpose water-pipes
and pumps are wrapped in straw at the approach of frost. The same means
are used to hmder a body from becoming heated, Ice is transported in
summer by packing it in bran or folding it in flannel.

Double walls constructed of thick planks having between them any finely
divided materials, such as shavings, sawdust, dry leaves, &c., retain heat
extremely well ; and are likewise advantageous in hot countries, for they
prevent its access. Pure sihca in the state of rock crystal is a better con-
ductor than lead, but in a state of powder it conducts very badly. If a layer
of asbestos is placed on the hand, a red-hot iron ball can be held without
inconvenience. Red-hot cannon-balls can be wheeled to the gun's mouth in
wooden barrows partially filled with sand. Lava has been known to flow
over a layer of ashes underneath which was a bed of ice, and the non-
conducting power of the ashes has prevented the ice from melting.

The clothes which we wear are not warm in themselves ; they only
hinder the body from losing heat, in consequence of their spongy texture
and the air they enclose. The warmth of bed-covers and of counterpanes
is explained in a similar manner. Double windows are frequently used in

382 On Heat. [410-

cold climates to keep a room warm — they do this by the non-conducting-
layer of air interposed between them. During the night the windows are
opened, while during the day they are kept closed. It is for the same reason
that two shirts are warmer than one of the same material but of double the
thickness. Hence, too, the warmth of furs, eider-down, &c.

The small conducting power of felt is used in the North of Eui^ope in the
construction of the Norwegian stove, which consists merely of a wooden
box with a thick lining of felt on the inside. In the centre is a cavity in
which can be placed a stew-pan provided with a cover. On the top of this
is a lid, also made of felt, so that the pan is surrounded by a very badly
conducting envelope. Meat, with water and suitable additions, is placed in
the pan, and the contents are then raised to boiling point. The whole is then
enclosed in the box and left to itself ; the cooking will go on without fire,
and after the lapse of several hours it will be quite finished. The cooling
down is very slow, owing to the bad conducting power of the lining ; at the
end of three hours the temperature is usually not found to have sunk more
than from 10° to 15°.

That water boils more rapidly in a metallic vessel than in one of porcelain
of the same thickness ; that a burning piece of wood can be held close to
the burning part with the naked hand, while a piece of iron heated at one
end can only be held at a great distance, are easily explained by reference
to their various conductivities.

The sensation of heat or cold which we feel when in contact with certain
bodies is materially influenced by their conductivity. If their temperature is
lower than ours, they appear colder than they really are, because from their
conductivity heat passes away from us. If, on the contrary, their temperature
is higher than that of our body, they appear warmer from the heat which
they give up at different parts of their mass. Hence it is clear why carpets,
for example, are warmer than wooden floors, and why the latter again are
warmer than stone floors.

The closer the contact of the hand with a substance, the greater is the
difference of temperature felt. With smooth surfaces there are more points
of contact than with rough ones. A hot glass rod feels hotter than a piece
of rusted iron of the same temperature, although the latter is a better con-
ductor. The closer the substance is pressed, the more intimate the contact ;
an ignited piece of charcoal can be lifted by the fingers, if it is not closely
pressed.

-412] 383

CHAPTER VIII.

RADIATION 01^ HEAT.

411. Radiant heat,— It has been already stated (403) that heat can be
transmitted from one body to another without aUering the temperature of the
intervening medium, If we stand in front of a fire we experience a sensation
of warmth which is not due to the temperature of the air, for if a screen be
interposed the sensation immediately disappears, which would not be the
case if the surrounding air had a high temperature. Hence bodies can send
out rays which excite heat, and which penetrate through the air without
heating it, as rays of light through transparent bodies. Heat thus propagated
is said to be radiated ; and we shall use the terms ray of heat, or thcmial,
or calorific ray, in a similar sense to that in which we use the term ray of
tight, or luminous ray.

We shall find that the property of radiating heat is not confined to
luminous bodies, such as a fire or a red-hot ball, but that bodies of all tem-
peratures radiate heat. It will be convenient to make a distinction between
litniinous and obscure rays of heat.

412. Detection and measurement of radiant heat. — In demonstrating
the phenomena of radiant heat, very delicate thermometers are required, and
the thermo-electrical multiplier of Melloni is used for this purpose with great
advantage ; for it not only indicates minute differences of temperature, but
it also measures them with accuracy.

This instrument cannot be properly understood without a knowledge of
the principles of thermo-electricity, for which Book X. must be consulted.
It may, however, be stated here that when two different metals A and B are
soldered together at one end (figs. 370, 371), the free ends being joined by a
wire when the soldering
C is heated, a current

of electricity circulates ^ ___ -p^ C ^

through the system ; if,
on the contrary, the

soldering be cooled, a •" fU

current is also produced, '-g

but it circulates in exactly p.^ ^^^^_ ^.^ ^^^

the opposite direction.

This is called a thermo-electiic couple ox pair. If a number of such pairs be
alternately soldered together, as represented in fig. 371, the strength of the
current produced by heating the ends is increased ; or, what amounts to the
same thing, a smaller degree of heat will produce the same effect. Such an
arrangement of a number of thermo-electric pairs is called a thermo-electric
battery ox pile.

384

On Heat.

[412

Melloni's thermomultiplier consists of a thermo-electric pile connected
with a delicate galvanometer. The thermo-electric pile is constructed of a
number of minute bars of bismuth and antimony soldered together alternately,
though kept insulated from each other, and contained in a rectangular box
P (fig. 372). The terminal bars are connected with two binding screws in
and ;/, which in turn are connected with the galvanometer G by means of the
wires a and b.

The galvanometer consists of a quantity of fine insulated copper wire
coiled round a frame, in the centre of which a delicate magnetic needle is
suspended by means of a silk thread. When an electric current is passed
through this coil, the needle is deflected through an angle which depends on
the strength of the current. The angle is measured on a dial by an index
connected with the needle.

It may then be sufficient to state that the thermo-electric pile being con-
nected with the galvanometer by means of the wires a and ^, an excess of

temperature at one end of the pile causes the needle to be deflected through
an angle which depends on the extent of this excess ; and similarly if the
temperatui-e is depressed below that of the other end, a corresponding
deflection is produced in the opposite direction. By arrangements of this
kind Melloni was able to measure differences of temperature of s^joth of a
degree. The object of the cone C is to concentrate the thermal rays on the
face of the pile.

413. Itaws of radiation. — The radiation of heat is governed by three
laws : —

I. Radiation takes place in all directions round a body. If a thermometer
be placed in different positions round a heated body, it indicates everywhere
a rise in temperature.

II. In a homogeneous nieditun, radiation takes place in a right line. For,
if a screen be placed in a right line which joins the source of heat and the
thermometer, the latter is not affected.

Fig. 373-

-414] Catises zvJiich Modify the Intensity of Radimit Heat. 385

But in passing obliquely from one medium into another, as from air into
glass, calorific like luminous rays become deviated, an effect known as
refraction. The laws of this phenomenon are the same for
heat as for light, and they will be more fully discussed under
the latter subject.

III. Radiant heat is propagated in vacuo as welt as in
air. This is demonstrated by the following experiment : —

In the bottom of a glass ilask a thermometer is fixed in
such a manner that its bulb occupies the centre of the flask
(fig- 373)- The neck of the flask is carefully narrowed by
means of the blowpipe, and then the apparatus having been
suitably attached to an air-pump, a vacuum is produced in
the interior. This having been done, the tube is sealed at
the narrow part. On immersing this apparatus in hot water,
or on bringing near it some hot charcoal, the thermometer is
at once seen to rise. This could only rise from radiation
through the vacuum in the interior, for glass is so bad a
conductor that the heat could not travel with this rapidity through the sides
of the flask and the stem of the thermometer,

414. Causes which modify the intensity of radiant heat By the

intensity of radiant heat is understood the quantity of heat received on the
unit of surface. Three causes are found to modify this intensity : the tem-
perature of the source of heat, its distance, and the obliquity of the calorific
rays in reference to the surface which emits them. The laws which regulate
these modifications may be thus stated : —

I. The intensity of radiant heat is proportional to the temperature of the
source.

II. The ititensity is inversely as the square of the distance.

III. The ifttensity is less, the greater the obliquity of t lie rays with respect
to the radiatijig surface.

The first law is demonstrated by placing a metal box containing water
at 10^, 20°, or 30° successively at equal distances from the bulb of a differen-
tial thermometer. The temperatures indicated
by the latter are then found to be in the same
ratio as those of the box : for instance, if the
temperature of that corresponding to the box at
10° be 2°, those of others will be 4° and 6° re-
spectively.

The truth of the second law follows from the
geometrical principle that the surface of a sphere
increases as the square of its radius. Suppose
a hollow sphere ab (fig. 374) of any given radius,
and a source of heat, C, in its centre ; each unit
of surface in the interior receives a certain quan- '"''■ -^''^'

tity of heat. Now a sphere, ef of double the radius will present a surface
four times as great ; its internal surface contains, therefore, four times as
many units of surface, and as the quantity of heat emitted is the same, each
unit must receive one-fourth the quantity.

To demonstrate the same law experimentally, a narrow tin-plate box is

C C

386

Oit Heat.

[414-

taken (fig. 375), filled with hot water, and coated on one side with lampblack.
The thermopile with its conical reflector is placed so that its face is at
a certain definite distance, co, say 9 inches, from this box, and the cover

having been lowered, the needle of the galvanometer is observed to be de-
flected, through 80° for example.

If now the pile is removed to a distance, CO (fig. 376), double that o{ co^
the deflection of the galvanometer remains the same, which shows that
the pile receives the same amount of heat ; the same is the case if the

Fig. 376.

pile is removed to three or four times the distance. This result, though?
apparently in opposition to the second law, really confirms it. For at first
the pile only receives heat from the circular portion ab of the side of the
box, while, in the second case, the circular portion AB radiates towards it.
But, as the two cones ACB and acb are similar, and the height of ACB is-
double that of acb, the diameter AB is double that of ab, and therefore the

-415] Mobile Equilibrium. Theory of Exchanges. 387

area AB is four times as great as that of ab., for the areas of circles are pro-
portional to the squares of the radii. But since the radiating surface increases
as the square of the distance, while the galvanometer remains stationary,
the heat received by the battery must be inversely as this same square.

The third law is demonstrated by means of the following experiment,
which is a modification of one originally devised by Leslie (fig. ■yil) : — P

-'" 0 0

^*^

.W.

da' ^B

^^^

Fig. 377-

represents the thermomultiplier which is connected with its galvanometer,
and A a metal cube full of hot water. The cube being first placed in such
a position, A, that its front face, ac, is vertical, the deflection of the galvano-
meter is noted. Supposing it amounts to 45°, this represents the radiation
from ac. If this now be turned in the direction represented by A', the
galvanometer is still found to mark 45°.

The second surface is larger than the first, and it therefore sends more
rays to the mirror. But as the action on the thermometer is no greater
than in the first case, it follows that in the second case, where the rays
are oblique, the intensity is less that in the first case, where they are
perpendiculai\

In order to express this in a formula, let i be the intensity of the rays
emitted perpendicularly to the surface, and i' that of the oblique rays.
These intensities are necessarily inversely as the surfaces ac and a'c', for the
effect is the same in both cases, and therefore i' x surface a'c' = i x surface ac ;

hence z" = / '^^'^ -J^ =z'— =zcos. aoa' \ which signifies that the intensity
surf a'c ac

of oblique rays is proportional to the cosine of the angle which these rays form

with the normal to the surface ; for this angle is equal to the angle aoa'.

This law is known as the law of the cosine ; it is, however, not general ;

Desains and De la Provostaye have shown that it is only true within very

narrow limits ; that is, only with bodies which, like lampblack, are entirely

destitute of reflecting power (423).

415. Mobile equilibrium. Tbeory of exchang-es. — Prevost of Geneva

suggested the following hypothesis in reference to radiant heat, known as

Prevost's theory of exchanges, which is now universally admitted. All bodies,

whatever their temperatures, constantly radiate heat in all directions. If

we imagine two bodies at different temperatures placed near each other,

the one at a higher temperature will experience a loss of heat, its temperature

will sink, because the rays it emits are of greater intensity than those it

receives ; the colder body, on the contrary, will rise in temperature, because

it receives rays of greater intensity than those which it emits. Ultimately

c c 2

388 On Heat. [415-

the temperature of both bodies becomes the same, but heat is still exchanged
between them, only each receives as much as it emits, and the temperature
remains constant. This state is called the mobile eqidlibriiim of temperature.

416. Ta"ewton's law of cooling-. — A body placed in a vacuum is only
cooled or heated by radiation. In the atmosphere it becomes cooled or
heated by its contact with the air, according as the latter is colder or hotter
than the radiating body. In both cases the velocity of cooling or of heating
— that is, the qitantity of heat lost or gained in a second — is greater accord-
ing as the difference of temperature is greater.

Newton enunciated the following law in reference to the cooling or
heating of a body : — The quantity of heat lost or gained by a body in a second
is proportional to the difference between its temperature and that of the sui'-
roundijig medium. Dulong and Petit have proved that this law is not so
general as Newton supposed, and only applies where the differences of
temperature do not exceed 15° to 20°. Beyond that, the quantity of heat
lost or gained is greater than what is required by this law.

Two consequences follow from Newton's law : —

I. When a body is exposed to a constant source of heat, its temperature
does not increase indefinitely, for the quantity which it receives in the same
time is always the same ; while that which it loses increases with the excess
of its temperature over that of the surrounding medium. Consequently
a point is reached at which the quantity of heat emitted is equal to that
absorbed, and the temperature then remains stationary.

II. Newton's law, as applied to the differential thermometer, shows that
its indications are proportional to the quantities of heat which it receives.
If one of the bulbs of a differential thermometer receives rays of heat from
a constant source, the instrument exhibits, first, increasing temperature, but
afterwards becomes stationary. In this case, the quantity of heat which it
receives is equal to that which it emits. But the latter is proportional to the
excess of the temperature of the bulb above that of the surrounding atmo-
sphere— that is, to the number of degrees indicated by the thermometer ;
consequently, the temperature indicated by the differential thermometer is
proportional to the quantity of heat it receives.

REFLECTION OF HEAT.

417. Iiaws of reflection. — When thermal rays fall upon a body they are,

speaking generally, divided into two portions, one of which penetrates the body

while the other rebounds as if repelled from the

ID surface like an elastic ball. This is said to be

reflected.

If jnn be a plane reflecting surface (fig. 378),
CB an incident ray, DC a line perpendicular to
the surface called the ?tormal, and BA the re-
flected ray, the angle CBD is called the aiigle
of incidence, and DBA the angle of reflection.
The reflection of heat, like that of light, is
governed by the two following laws : —
I. The angle of reflection is equal to the angle of incidence.

-418] Experimental Demonstration of the Lazvs of Reflection. 389

II. Botli tJie iiicideiif and the refected ray are in the same plane with the
perpendicular to the refecting surface.

41S. Experimental demonstration of the laws of reflection of heat. —

This may be effected by means of Melloni's thermopile and also by the con-
jugate mirrors (420). Fig. 379 represents the arrangement adopted in the
former case. AIN is a horizontal bar, about a metre in length, graduated in
millimetres, on which slide various parts, which can be clamped by means
of screws. The source of heat, S, is a platinum spiral, kept at a white heat in
a spirit lamp. A screen K, when raised, cuts off the radiation from the source ;
a second screen, F, with an aperture in the centre, cuts off all rays except a
pencil which falls upon the mirror ;//. At the other end is an upright rod, I, with
a graduated dial, the zero of which is in the direction of MN, and therefore
parallel to the pencil S w. In the centre of the dial is an aperture, in which turns
an axis that supports a metallic mirror m. About this axis turns an index, R,

on which is fixed the thermopile, P, in connection with the galvanometer G ;
H is a screen, the object of which is to cut off any direct radiation from the
source of heat towards the pile. In order not to mask the pile, it is not re-
presented in the position it occupies in the experiment.

By lowering the screen K, a pencil of parallel rays, passing through the
aperture F, falls upon the mirror in, and is there reflected. If the index R
is not in the direction of the reflected pencil, this latter does not fall on
the pile, and the needle of the galvanometer remains stationary : but by
slowly turning the index R, a position is found at which the galvanometer
attains its greatest deviation, which is the case when the pile receives the
reflected pencil perpendicularly to its surface. Reading off then on the dial
the position of a small needle perpendicular to the mirror, it is observed that
this bisects the angle formed by the incident and the reflected pencil, which
demonstrates the first law.

The second law is also proved by the same experiment, for the various
pieces of the apparatus are arranged so that the incident and reflected rays

390 On Heat. [418-

are in the same horizontal plane, and therefore at right angles to the reflect-
ing surface, which is vertical.

419. Reflection from concave mirrors. — Concave mirrors ox reflectors
are polished spherical or parabolic surfaces of metal or of glass, which are
used to concentrate luminous or calorific rays in the same point.

We shall only consider the case of spherical mirrors. P'ig. 381 represents
two of these mirrors ; fig. 380 gives a medial section, which is called the

Fig. 380.

prmcipal section. The centre C of the sphere to which the mirror belongs
is called the centre of curvature ; the point A, the middle of the reflector, is
the centre of the flgure ; the straight line AB passing through these points,
is \\\& principal a.xis of the mirror.

In order to apply to spherical mirrors the laws of reflection from plane
surfaces, they are considered to be composed of an infinite number of in-
finitely small plane surfaces, each belonging to the corresponding tangent
plane ; the normals to these small surfaces are all radii of the same sphere,
and therefore meet at its centre, the centre of curvature of the mirror.

Suppose now, on the axis AB of the mirror MN, a source of heat so
distant that the rays EK, PH .... which start from it may be considered
as parallel. From the hypothesis that the mirror is composed of an infini-
tude of small planes, the ray EK is reflected from the plane K just as from
a plane mirror ; that is to say, CK being the normal to this plane, the
reflected ray takes a direction such that the angle CKF is equal to the
angle CKE. The other rays, PH, GI . . . . are reflected in the same
manner, and all converge approximately towards the same point F, on the
line AC. There is then a concentration of the rays in this point, and conse-
quently a higher temperature than at any other point. This point is called
the focus., and the distance from the focus to the mirror at A is the focal
distance.

In the above figure the heat is propagated along the lines EKF, LDF, in
the direction of the arrows ; but, conversely, if the heated body be placed at
F, the heat is propagated along the lines FKE, FDL, so that the rays emitted
from the focus are nearly parallel after reflection.

420. Verification of the laws of reflection. — The following experiment,
which was made for the first time by Pictet and Saussure, and which is
known as the expcrinient of the conjugate mirrors, demonstrates not only
the existence of the foci, but also the laws of reflection. Two reflectors,
M and N (fig. 380), are arranged at a distance of 4 to 5 yards, and so that

-420] Verification of the Laws of Reflection. 391

their axes coincide. In the focus of one of them, A, is placed a small wire
basket containing a red-hot iron ball. In the focus of the other is placed
B, an easily inflammable body, such as gun-cotton or phosphorus. The rays
emitted from the focus A are first reflected from the mirror M, in a direction
parallel to the axis (419), and impinging on the other mirror, N, are reflected
so that they coincide in the focus B. That this is so, is proved by the fact
that the gun-cotton at this point takes fire, which is not the case if it is above
or below it.

The experiment also serves to show that light and heat are reflected in
the same manner. For this purpose a lighted candle is placed in the focus
of A, and a ground-glass screen in the focus of B, when a luminous focus is
seen on it exactly in the spot where the gun-cotton ignites. Hence the
luminous and the calorific foci are produced at the same point, and the
reflection takes place in both cases according to the same laws, for it will be

afterwards shown that for light, the angle of reflection is equal to the angle
of incidence, and that both the incident and the reflected rays are in the same
plane perpendicular to the plane I'eflecting surface.

In consequence of the high temperature produced in the foci of concave
mirrors they have been called burning mirrors. It is stated that Archi-
medes burnt the Roman vessels before Syracuse by means of such mirrors.
Bufifon constructed burning mirrors of such power as to prove that the feat
attributed to Archimedes was not impossible. The mirrors were made of a
number of silver plane mirrors about 8 inches long by 5 broad. They
could be turned independently of each other in such a manner that the rays
reflected from each coincided in the same point. With 128 mirrors and a
hot summei-'s sun Bufifon ignited a plank of tarred wood at a distance of 70
yards.

392

On Heat.

[421-

421. Reflection in a vacuum.— Heat is reflected in a vacuum as well as
in air, as is seen from the following experiment (fig. 382), due to Sir Hum-
hpry Davy. Two small concave reflectors were placed opposite each other
under the receiver of an air-pump. In the focus of one was placed a delicate
thermometer, and in the focus of the other a platinum wire made incandescent
by means of a galvanic current. The thermometer was immediately seen to
rise several degrees, which could only be due to reflected heat, for the ther-
mometer did not show any increase of
temperature if it were not exactly in the
focus of the second reflector.

422. iLpparent rejection of cold.
If two mirrors are arranged as repre-
sented in fig. 381, and a piece of ice is
placed in one of the foci instead of the
red-hot ball, the surrounding tempera-
ture being greater than zero, a diffe-
rential thermometer placed in the focus
of the second reflector would exhibit a
decrease in temperature of several de-
grees. This appears at first to be
caused by the emission oi frigorific rays
from ice. It is, however, easily explained
from what has been said about the
mobile equilibrium of temperature (415).
There is still an interchange of tempera-
ture, but here the thermometer is the
warmest body. As the rays which the thermometer emits are hotter than
those emitted by the ice, the former gives out more heat than it receives,
and hence its temperature sinks.

The sensation of cold experienced when we stand near a plaster or stone
wall whose temperature is lower than that of our body, or when we stand in
front of a wall of ice, is explained in the same way.

423. Reflecting- power. — The reflecting power of a substance is its pro-
perty of throwing off a greater or less proportion of incident heat.

This power varies in different substances. In order to study this power
in different bodies without having recourse to as many reflectors, Leslie
arranged his experiment as shown in fig. 383. The source of heat is a
cubical canister, M, now known as Leslie's cube, filled with hot water. A
plate, a, of the substance to be experimented upon is placed on the axis of a
I'eflecting mirror between the focus and the mirror. In this manner the rays
emitted by the source are first reflected from the mirror and impinge on the
plate a, where they are again reflected and converge to the focus between the
plate and the mirror, at which point a differential thermometer is placed.
The reflector and the thermometer are always in the same position, and the
water of the cube is always kept at 100°, but it is found that the temperature
indicated by the thermometer varies with the nature of the plate. This
method gives a means of determining, not the absolute reflecting power of a
body, but its power relatively to that of some body taken as a standard of
comparison. For from what has been said on the application of Newton's law

Fig. 382.

-423]

Reflecting Pozuer.

393

to the differential thermometer (416), the temperatures which this instrument
indicates are proportional to the quantities of heat which it receives. Hence,
if in the above experiment a plate of glass causes the temperature to rise 1°
and a plate of lead 6°, it follows that the quantity of heat reflected by the
latter is six times as great as that reflected by the former. For the heat
emitted by the source remains the same, the concave reflector receives the
same portion, and the difference can only arise from the reflecting" power of
the plate a.

By this method Leslie determined the reflecting powers of the following
substances, relatively to that of brass, taken as 100 : —

Polished brass .

. 100

Indian ink

Silver

• 90

Glass

Steel

. 70

Oiled glass

Lead

. 60

Lampblack

The numbers only represent the relative reflecting power as compared
with that of brass. Thew absolute power is the relation of the quantity of
heat reflected to the quantity of heat received. Desains and De la Provostaye,
who examined the absolute reflecting power of certain metals, obtained the
following results by means of Melloni's thermomultiplier (412), the heat
being reflected at an angle of 50° : —

. 0-82
o-Si

■ 077

■ 074

Silver plate

• 0-97

Steel

Gold

. 0-95

Zinc

Brass

■ 0-93

Iron

Platinum

• 0-83

Cast iron

394 On Heat. [424-

424. Absorbing: power. — The absorbing powe}- of a body is its property
of allowing a greater or less quantity of the heat which falls upon it to pass
into its mass. Its absolute value is the ratio of the quantity of heat absorbed
to the quantity of heat received.

The absorbing power of a body is always inversely as its reflecting
power : a body which is a good absorbent is a bad reflector, and vice versa.
It was formerly supposed that the two powers were exactly complementary,
that the sum of the reflected and absorbed heat was equal to the total quan-
tity of incident heat. This is not the case ; it is always less : the incident
heat is divided into three parts — ist, one which is absorbed ; 2nd, another
which is reflected regularly — that is, according to laws previously demon-
strated (417) ; and a third, which is irregularly reflected in all directions,
and which is called scattered or diffused heat.

In order to determine the absorbing power of bodies, Leslie used the
apparatus which he employed in determining the reflecting powers (423).
But he suppressed the plate a^ and placed the bulb of the thermometer in
the focus of the reflector. This bulb being then covered successively with
lampblack, or varnish, or with gold, silver, or copper foil, &c., the thermo-
meter exhibited a higher temperature under the influence of the source ot
heat, M, according as the substance with which the bulb was covered
absorbed more heat. Leslie found in this way that the absorbing power of
a body is greater the less its reflecting power. In these exfJeriments, how-
ever, the relation of the absorbing powers cannot be deduced from that of
the temperatures indicated by the thermometer, for Newton's law is not
exactly applicable in this case, as it only prevails for bodies whose substance
does not vary, and here the covering of the bulb varied with each observa-
tion. But we shall presently show (426) how the comparative absorbing
powers may be deduced from the ratios of the emissive powers.

Taking, as a source of heat, a canister filled with water at 100°, Melloni
found, by means of the thermomultiplier, the following relative absorbing
powers : —

Lampblack . . .100 Indian ink . . . .85

White lead . . .100 Shellac 72

Isinglass ... 91 Metals 13

425. Radiating: power. — The radiating or emissive power of a body is
its capability of emitting, at the same temperature, and with the same extent
of surface, greater or less quantities of heat.

The apparatus represented in fig. 382 was also used by Leslie in deter-
mining the radiating power of bodies. For this purpose the bulb of the
thermometer was placed in the focus of the reflector, and the faces of the
canister M were formed of difterent metals, or covered with difterent
substances such as lampblack, paper, &c. The cube being filled with hot
water, at 100°, and all other conditions remaining the same, Leslie turned
each face of the cube successively towards the reflectors, and noted the
temperature each time. That face which was coated with lampblack caused
the greatest elevation of temperature, and the metal faces the least. Applying
Newton's law, and representing the heat emitted by lampblack as 100, Leslie
formed the following table of radiating powers : —

-426] Identity of the Absorbi?ig and Radiating Powers. 395

Lampblack

. 100

Tarnished lead .

White lead

. 100

Mercury ....

Paper

. 98

Polished lead .

Ordinary white glass

■ 90

Polished iron

Isinglass .

. 80

Tin, gold, silver, copper, &c.

It will be seen that, in this table, the order of the bodies is exactly the
reverse of that in the tables of reflecting powers.

The radiating powers of several substances were determined by Desains
and De la Provostaye, who used the thermomultiplier. They found, in this
manner, the following numbers compared with lampblack as 100 : —

Platinum foil .

Burnished platinum

Silver deposited chemically

Copper foil

Gold leaf.

Pure silver laminated

,, burnished

„ deposited chemically and burnished

io-8o
9-50
5-36
4-90
4-28
3-00
2-50

2-25

It appears, therefore, that the radiating power found by Leslie for the
metals is too large.

426. Identity of the absorbing- and radiating: powers. — The absorb-
ing power of a body cannot be accurately deduced from its reflecting power,
because the two are not exactly complementary. But the absorbing power
would be determined if it could be shown that in the same body it is ecjual
to the radiating power. This conclusion has been drawn by Dulong and
Petit from the following experiments : — In a large glass globe, blackened on
the inside, was placed a thermometer at a certain temperature, 1 5° for ex-
ample ; the globe was kept at zero by surrounding it with ice, and having
been exhausted by means of a tubulure connected with an air-pump, the time
was noted which elapsed while the thermometer fell through 5°. The experi-
ment was then made in the contrary direction : that is, the sides of the globe
were heated to 15°, while the thermometer was cooled to zero : the time was
then observed which the thermometer occupied in rising through 5°. It was
found that this time was exactly the same as that which the thermometer
had taken in sinking through 5°, and it was thence concluded that the
radiating power is equal to the absorbing power for the same body, and for
the same difference between its temperature and the temperature of the sur-
rounding medium, because the quantities of heat emitted or absorbed in the
same time are equal.

This point may also be demonstrated by means of the following apparatus
devised by Ritchie. Fig. 384 represents what is virtually a differential
thermometer, the two glass bulbs of which are replaced by two cylindrical
reservoirs B and C, of metal, and full of air. Between them is a third and
larger one A, which can be filled with hot water by means of a tubulure.
The ends of B and of A, which face the right, are coated with lampblack';
those of C and of A, which face the left, are either painted white, or are

396

On Heat.

[426-

Fig. 38

coated with silver foil. Thus one of the two faces opposite each other is
black, and the other white ; hence when the cylinder A is filled with hot
water, its white face radiates towards the black face of B, and its black face
towards the white face of C. In these circum-
stances the liquid in the stem does not move,
indicating that the two reservoirs are at the
same temperature. On the one hand, the
greater emissive power of the black face of A
is compensated by the smaller absorptive power
of the white face of C ; while, on the other
hand, the feebler radiating power of the white
face of A is compensated by the greater
absorbing power of the black face of B.

The experiment may be varied by replacing
the two white faces by discs, of paper, glass,
porcelain, &c.

427. Causes which modify the reflectingr,
absorbing-, and radiating: powers. — As the
radiating and absorbing powers are equal, any
cause which affects the one affects the other
also. And as the reflecting power varies in
an inverse manner, whatever increases it dimi-
nishes the radiating and absorbing powers, and
vice versa.

It has been already stated that these different powers vary with different
bodies, and that metals have the greatest reflecting power, and lampblack
the least. In the same body these powers are modified by the degree of
polish, the density, the thickness of the radiating substance, the obliquity of
the incident or emitted rays, and, lastly, by the nature of the source of heat.
It has been usually assumed that the reflecting power increases with the
polish of the surface, and that the other powers diminish therewith. But
Alelloni showed that by scratching a polished metaUic surface its reflecting
power was sometimes diminished and sometimes increased. This pheno-
menon he attributed to the greater or less density of the reflecting surface.
If the plate had been originally hammered, its homogeneity would be
destroyed by this process, the molecules would be closer together on the
surface than in the interior, and the reflecting power would be increased.
But if the surface is scratched, the interior and less dense mass becomes
exposed, and the reflecting power diminished. On the contrary, in a plate
which has not been hammered, and which is homogeneous, the reflecting
power is increased when the plate is scratched, because the density at the
surface is increased by the scratches.

Melloni found that when the faces of a cube filled with water at a constant
temperature were varnished, the emissive power increased with the number
of layers up to 16 layers, while above that point it remained constant, what-
ever the number. The thickness of the 16 layers was calculated to be
0-04 mm. With reference to metals, gold leaves of 0*008, 0*004, and 0-002
of a millimetre in thickness, having been successively applied on the sides
of a cube of glass, the diminution of radiant heat was the same in each case.

429]

Dynamical Theory of Heat.

397

It appears, therefore, that, beyond certain Hmits, the thickness of the ra-
diating layer of metal is without influence.

The absorbing power is greatest when the rays are at right angles, and
it diminishes in proportion as the incident rays deviate from the normal.
This is one of the reasons why the sun is hotter in summer than in winter,
because, in the former case, the sun's rays are less oblique.

The radiating power of gaseous bodies in a state of combustion is very
weak, as is seen by bringing the bulb of a thermometer near a hydrogen
flame, the temperature of which is very high. But if a platinum spiral be
placed in this flame, it assumes the temperature of the flame, and radiates
a great amount of heat, as is shown by the thermometer. For a similar
reason the flames of oil and of gas lamps radiate more than a hydrogen
flame in consequence of the excess of carbon which they contain, and
which, not being entirely burned, becomes incandescent in the flame.

428. nCelloni's researcbes on radiant heat. — For our knowledge of
the phenomena of the reflection, emission, and absorption of heat which
have up to now been described, science is indebted mainly to Leslie. But
since his time the discovery of other and far more delicate modes of de-
tecting and measuring heat has not only extended and corrected our
previous knowledge, but has led to the discovery of other phenomena of
radiant heat, which, without such improved means, must have remained
unknown.

This advance in science is due to an Italian philosopher, Melloni, who
first applied the thermo-electric pile, invented by Nobili, to the measurement
of very small diff"erences of temperature ; a method of which a preliminary
account has already been given (412).

In his ex-
periments Mel-
loni used five
sources of heat
— 1st, a Loca-
telli's lamp —
one, that is,
without a glass
chimney, but
provided with
a reflector (fig.

385) ; 2nd, an
Argand lamp,
that is, one with
a chimney and a

double draught ; 3rd, a platinum spiral, kept red hot by a spirit lamp (fig.

386) ; 4th, a blackened copper plate, kept at a temperature of about 400°
by a spirit lamp (fig. 387) ; 5th, a copper tube, blackened on the outside
and filled with water at 100° (fig. 388).

429. Dynamical theory of heat. — Before describing the results arrived
at by Melloni and others, it will be convenient to explain here the view now
generally taken as to the mode in which heat is propagated. For additional
information the chapter on the Mechanical Theory of Heat and the book on

398 On Heat. [429-

Light should be read. According to what has ah-eady been stated (292), a
hot body is nothing more than one whose pai'ticles are in a state of vibration.
The higher the temperature of the body, the more rapid are these vibrations,
and a diminution in temperature is but a diminished rapidity of vibration of
the particles. The propagation of heat through a bar is due to a gradual
communication of this vibratory motion from the heated part to the rest of
the bar. A good conductor is one which readily takes up and transmits the
vibratory motion from particle to particle, while a bad conductor is one which
takes up and transmits the motion with difficulty. But even through the best
conductors the propagation of this motion is comparatively slow. How then
are we to explain the instantaneous perception of heat experienced when a
screen is removed from a fire, or when a cloud drifts from the face of the
sun ? In this case, the heat passes from one body to another without affect-
ing the temperature of the medium which transmits it. In order to explain
these phenomena, it is imagined that all space, the interplanetary spaces as
well as the interstices in the hardest crystal or the heaviest metal — in short,
matter of any kind — is permeated by a medium having the properties of a
tluid of infinite tenuity, called ether. The particles of a heated body, being in
a state of intensely rapid vibration, communicate their motion to the ether
around them, throwing it into a system of waves which travel through space
and pass from one body to another with the velocity of light. When the un-
dulations of the ether reach a given body, the motion is again delivered up to
the particles of that body, which in turn begin to vibrate ; that is, the body
becomes heated. This process of motion through the hypothetical ether is
termed radiation, and what is called a ray of heat is merely one series of
waves moving in a certain direction.

It will facilitate the understanding of this to consider the analogous mode
in which sound is produced and propagated. A sounding body is one whose
entire mass is in a state of vibration (222) ; the more rapid the rate of vibra-
tion, the more acute the sound ; the slower the rate of vibration, the deeper
the sound. This vibratory motion is communicated to the surrounding air, by
means of which the vibrations reach the auditory nerve, and there produce
the sensation of sound. If a metal ball be heated, say, to the temperature
of boiling water, we can ascertain that it radiates heat, although we cannot
see any luminosity ; and if its temperature be gradually raised, we see it
becomes successively of a dull red, bright red, and dazzling white. At each
particular temperature the heated body emits waves of a definite length ; in
other words, its particles vibrate in a certain period. As its temperature
rises it sends out other and more rapid vibrations, which coexist, however,
with all those which it had previously emitted. Thus the motion at each
successive temperature is compounded of all preceding ones.

It has been seen that vibrations of the air below and above a certain rate
do not affect the auditory nerve (244) ; it can only take up and transmit to the
brain vibrations of a certain periodicity. So too with the vibrations which
produce light. The optic nerve is insensible to a large number of wave-
lengths. It can apprehend only those waves that form the visible spectrum.
If the rate of undulation be slower than the red or faster than the violet,
though intense motion may pass through the humours of the eye and fall
upon the retina, yet we shall be utterly unconscious of the fact, for the

-430] Thermal Analysis of Solar Light. 399

optic nerve cannot take up and respond to the rate of vibrations which exist
beyond the visible spectrum in both directions. Hence, these are termed
invisible or obsctcre rays. A vast quantity of these obscure rays is emitted
by flames which, though intensely hot, are yet almost non-luminous, such
as the oxy-hydrogen flame, or that of a Bunsen's burner ; for the vibra-
tions which these emit, though capable in part of penetrating the media
of the eye, are incapable of exciting in the optic nerve the sensation of
light.

430. Thermal analysis of solar ligrht. — When a beam of sunlight (fig.
389), admitted through an aperture in a dark room, is concentrated on a

prism of rock salt by means of a lens of the same material, and then, after
emerging from the prism, is received on a screen, it will be found to present
a band of colours in the following order : red, orange, yellow, green, blue,
and violet. This is called the spectrum (564).

If now a narrow and delicate thermopile be placed successively on the
space occupied by each of the colours, it will be scarcely affected on the
violet, but in passing over the other colours it will indicate a gradual rise of
temperature, which is greatest at the red. Painters, thus guided by a cor-
rect but unconscious feeling, always speak of blue and green colours as cold,
and of red and orange as warm tones. If the pile be now moved in the
same direction beyond the limits of the luminous spectrum, the temperature
will gradually rise up to CP, at which it attains its maximum. From this
point the pile indicates a decrease of temperature until it reaches a point, O,
where it ceases to be affected. This point is about as distant from R as the
latter is from V ; that is, there is a region in which thermal effects are pro-
duced extending as far beyond the red end of the spectrum in one direction
as the entire length of the visible spectrum in the other. In accordance
with what we have stated, the sun's light consists of rays of different rates of
vibration ; by their passage through the prism they are unequally broken or
refracted ; those of greatest wave-length or slowest vibrating period are least
bent aside, or are said to be the least refrangible, while those with shorter
wave-lengths are the most refrangible.

These non-luminous rays outside the red are called the extra or ultra-red
rays, or sometimes the Herschelian rays, from Sir W. Herschel, who first
discovered their existence.

400 On Heat: [430-

If, in the above case, prisms of other materials than rock salt be used,
the position of the maximum heat will be found to vary with the nature of
the prism, a fact first noticed by Seebeck. Thus with a prism of water it is
in the yellow, with one of crown glass in the middle of the red, and so on.
These changes are due to the circumstance that prisms of different materials
absorb rays of different refrangibility to unequal extents. But rock salt
practically allows heat of all kinds to pass with equal facility, and thus gives
a normal spectrum.

431. Tyndall's researches. — Tyndall investigated the spectrum pro-
duced by the electric light, by the following mode of experimenting : — The
electric light was produced between charcoal points by a Grove's battery of
fifty cells. The beam, rendered parallel by a double rock-salt lens, was
caused to pass through a narrow slit, and then through a second lens of rock
salt ; the slices of white light thus obtained being decomposed by a prism
of the same material. To investigate the thermal conditions of the spec-
trum a linear thermo-electric pile was used ; that is, one consisting of a
number of elements arranged in a line, and in front of which was a slit that
could be narrowed to any extent. The instrument was mounted on a
movable bar connected with a fine screw, so that by turning a handle the
pile could be pushed forward through the smallest space. On placing this
apparatus successively in each part of the spectrum of the electric light, the
heating effected at various points near each other was determined by the
indications of a very delicate galvanometer. As in the case of the solar
spectrum, the heating effect gradually increased from the violet end towards
the red, and was greatest in the dark space beyond the red. The position
of the greatest heat was about as far from the limit of the visible red as the
latter was from the green, and the total extent of the invisible spectrum was
found to be twice that of the visible.

The increase of temperature in the dark space is veiy considerable. If
thermal intensities are represented by perpendicular lines of proportionate
jj length, erected

at those parts of
the spectrum to
which they cor-
respond, on
passing beyond
the red end
these lines in-
crease rapidly
and greatly in
length, reach a
maximum, and
then fall some-
what more sud-
denly. If these

lines are connected, they form a curve (fig. 390), which beyond the red
represents a peak, quite dwarfing that of the visible spectrum. In fig. 391,
the dark parts at the end represent the obscure radiation. The curve is
based, in the manner above stated, on the results obtained by Tyndall with

Fig. 390.

-432]

Ljiminous and Obscure Radiation.

401

the electric light. The upper curve in fig. 391 represents the spectrum of
sunlight with a rock-salt prism, while the lower curve represents the results
obtained with a flint-glass prism, which is thus seen to absorb some of the
ultra-red radiation.

By interposing various substances, more especially water, in certain
thicknesses, in the path of the electric light, the ultra-red radiation was
greatly diminished. Now aqueous vapour, like water, absorbs the obscure
rays. And probably the reason why the obscure part of the spectrum of
sunlight is not so intense as in the case of the electric light is that the
obscure rays have been already partially absorbed by the aqueous vapour of
the atmosphere. If a solar spectrum could be produced outside the atmo-
sphere, it would probably give a spectrum more like that of the electric light,
which is unaffected by the atmospheric absorption.

This has been confirmed in other ways. Melloni observed that the
position of the maximum in the solar spectrum differs on different days ;
which is probably due to the varying absorption of the atmosphere, in con-
sequence of its varying hygrometric state. Secchi, in Rome, found the
same shifting of
the maximum to
occur in the dif-
ferent seasons
of the year ; for
in winter, when
there is least
moisture in the
atmosphere, the
maximum is far-
ther from the
red than in sum-
mer, when the '^'

aqueous vapour in the air is most abundant. An important observation on
the luminous rays has also been made by Cooke, in America, who found that
the faint black lines in the solar spectrum attributed to the absorption of light
by our atmosphere (see book on Optics) are chiefly caused by the presence
of aqueous vapour.

432. Iiuminous and obscure radiation. — The radiation from a luminous
object, a gas flame for example, is of a composite character ; a portion con-
sists of what we term light, but a far greater part consists of heat rays,
which are insensible to our eyes, being unable to affect the optic nerve.
When this mixed radiation falls upon the blackened face of a thermo-electric
pile, the whole of it is taken to be absorbed, the light by this act beino-
converted into heat, and affecting the instrument proportionally with the
purely calorific rays. The total radiation of a luminous source, expressed
in units of heat or force, can thus be measured. By introducing into the
path of the rays a body capable of stopping either the luminous or the
obscure radiation, we can ascei'tain by the comparative action on the pile
the relative quantities of heat and light radiated from the source. Melloni
sought to do this by passing a luminous beam through a layer of water
containing alum in solution ; a liquid which he found in previous experi-

D D

Luminous

Obscure

. O

lOO

. O

loo

• 3

• 4

. 4-6

95-4

. lO

402 071 Heat. [432-

ments absorbed all the radiation from bodies heated under incandescence.
Comparing the transmission through this liquid — which allowed the luminous
but not the obscure part of the beam to pass — with the transmission through
a plate of rock salt — which atfected neither the luminous nor the obscure
radiation, but gave the loss due to reflection — Melloni found that 90 per cent,
of the radiation from an oil flame and 99 per cent, of the radiation from an
alcohol flame consist of invisible calorific rays. This proportion has been
still further increased by the experiments of Tyndall, who employed a solu-
tion of iodine in bisulphide of carbon, which he found to be impervious to
the most intense light, but very pervious to radiant heat ; only a slight
absorption being effected by the bisulphide. By comparing the transmission
through the transparent bisulphide, and the transmission through the same
liquid rendered opaque by iodine, the value of the luminous radiation from
various sources was found to be as follows :—

Source

Red-hot spiral

Hydrogen flame

Oil flame ....

Gas flame ....

White-hot spiral

Electric light ....

Here by direct experiment the ratio of luminous to obscure rays in the
electric light is found to be 10 per cent, of the total radiation. By prismatic
analysis, the curve shown in fig. 390 was obtained, graphically representing
the proportion of luminous to obscure rays in the electric light ; by calculating
the areas of the two spaces in the diagram, the obscure portion, DCBA, is
found to be nearly 10 times as large as the luminous one, DCE.

433. Transmutation of obscure rays. — We shall find, in speaking of
the luminous spectrum, that beyond the violet there are rays which are in-
visible to the eye, but which are distinguished by their chemical action, and
are spoken of as the actinic or chemical rays ; they are also known as the
Ritteric rays, from the philosopher who first discovered their existence.

As we shall afterwards see in the book on Optics, Stokes has succeeded
in converting these rays into rays of lower refrangibility, which then become
visible ; so Tyndall has effected the corresponding but inverse change, and
has increased the refrangibility of the Herschelian or extra red rays, and
thus rendered them visible. The charcoal points of the electric light were
placed in front of a concave silvered glass mirror in such a manner that
the rays from the points after reflection were concentrated to a focus about
6 inches distant. On the path of the beam was interposed a cell full of a
solution of iodine in bisulphide of carbon, which (432) has the power of com-
pletely stopping all luminous radiation, but gives free passage to the non-
luminous rays. On now placing in the focus of the beam, thus sifted, a piece
of platinum, it was raised to incandescence by the impact of perfectly invisible
rays. In like manner a piece of charcoal iji vacuo was heated to redness.

By a proper arrangement of the charcoal points a metal may be raised
to whiteness, and the light now emitted by the metal yields on prismatic
analysis a brilliant luminous spectrum, which is thus entirely derived from

-434]

Transmission of Thermal Rays.

403

the invisible rays beyond the red. This transmutation of non-luminous into
luminous heat, Tyndall calls calorescence.

When the eye was cautiously placed in the focus, guarded by a small
hole pierced in a metal screen, so that the converged rays should only enter
the pupil and not affect the surrounding part of the eye, no impression of
light was produced, and there was scarcely any sensation of heat. A con-
siderable portion was absorbed by the humours of the eye, but yet a power-
ful beam undoubtedly reached the retina ; for, as Tyndall showed by a
separate experiment, about 18 per cent, of the obscure radiation from the
electric light passed through the humours of an ox's eye.

434. Transmission of thermal rays. — Melloni was the first who ex-
amined extensively and accurately the absorption of heat by solids and
liquids. The apparatus he employed is represented in fig. 392, where AB is

Fig. 392.

the thermo-electric pile ; rt; is a support for the source of heat, in this case a
Locatelli's lamp ; F and E are screens, and C is a support for the body ex-
perimented on ; while m is the support for the pile, and D the galvanometer.
To express the power which bodies have of transmitting heat, Melloni
used the term diathermancy : diathermancy bears the same relation to
radiant heat that transparency does to light ; and in like manner the power
of stopping radiant heat is called at/iermancy, which thus corresponds to
opacity for light. In experimenting on the diathermancy of hquids, Melloni
used glass troughs with parallel sides, the thickness of the liquid layer being
0-36 in. The radiant heat of an Argand lamp with a glass chimney was
first allowed to fall directly on the face of the pile, and the deflection pro-
duced in the galvanometer taken as the total radiation ; the substance under
examination was then interposed, and the deflection noted. This corre-
sponded to the quantity of heat transmitted by the substance. If t indicate
this latter number, and /' the total radiation, then
t' : t :: 100 : x,

which is the percentage of rays transmitted. Thus calling the total radiation
100, Melloni found that

D D 2

404

On Heat.

[434-

Bisulphide of carbon transmitted

Olive oil „

Ether „

Sulphuric acid „

Alcohol „

Solution of alum or sugar „

Distilled water „

In experimenting with solids they were cut into plates OT inch in thick-
ness, and it was found that of every loo rays there was transmitted by
Rock salt . . . .92 Selenite . . .20

Smoky quartz . . .67 Alum . . . .12

Transparent carbonate of lead 52 Sulphate of copper . o

The transmission of heat through liquids has been re-examined by Tyndall,
who used a cell consisting of parallel plates of rock salt separated by a ring
of brass with an aperture on the top through which the liquid could be
poured. As this ring could be changed at will, liquid layers of various
thicknesses were easily obtainable, the apparatus being merely screwed
together and made liquid-tight by paper washers. The instrument was
mounted on a support before an opening in a brass screen placed in front
of the pile. The source of heat employed was a spiral of platinum wire
raised to incandescence by an electric current, the spiral being enclosed in a
small glass globe with an aperture in front, through which the radiation
passed unchanged in its character, a point of essential importance overlooked
by Melloni. The following table contains the results of experiments made
with liquids in the various thicknesses indicated, the numbers expressing
the absorption per cent, of the total radiation. The transmission per cent,
can be found in each case by subtracting the absorption from 100. Thus a
layer of water 0-2 inch thick absorbs 807 and transmits 19-3 per cent, of the
radiation from a red-hot spiral.

Absorptio?i of heat by liquids.

Thickness of liquids in parts of an inch

Liquid

o-o.

o'o4

0-07

0-14

0-27

Bisulphide of carbon

5-5

8-4

12.5

15-2

17-3

Chloroform

i6-6

25-0

35 -o

40-0

44-8

Iodide of methyl

36-1

46-5

53-2

65-2

68-6

Benzole .

43-4

557

62-5

71-5

73-6

Amylene .

58-3

65-2

73-6

777

82-3

Ether

63-3

73-5

76-1

78-6

85-2

Alcohol .

67-3

78-6

83-6

85-3

89-1

Water .

807

86-1

88-8

91-0

It appears from these tables that there is no connection between diather-
mancy and transparency. The liquids, except olive oil, are all colourless
and transparent, and yet vaiy as much as 75 per cent, in the amount of heat
transmitted. Among solids, smoky quartz, which is nearly opaque to light.

-435]

Influence of the Nature of the Heat.

405

transmits heat very well ; while alum, which is perfectly transparent, cuts off
88 per cent, of heat rays. As there are different degrees of transparency, so
there are different degrees of diathermancy ; and the one cannot be predi-
cated from the other.

By studying the transmission of heat from different parts of the spec-
trum separately, the connection between light and heat becomes manifest.
With this view Masson and Jamin received the spectrum of the solar light
given by a prism of rock salt on a movable screen provided with an aperture,
so that by raising or lowering the screen the action of any given part of the
spectrum on different plates could be investigated. They thus found —

That glass, rock crystal, ice, and generally substances transparent for
light, are also diathermanous for all kinds of luminous heat ;

That a coloured glass, red, for instance, which only transmits the red rays
of the spectrum, and extinguishes the others, also extinguishes every kind of
luminous heat, excepting that of the red rays ;

That glass and rock crystal, which are diathermanous for luminous heat,
also transmit the obscure heat near the red— that is, the most refrangible —
but extinguish the extreme obscure rays, or those which are the least de-
flected by the prism. Alum extinguishes a still greater proportion of the
obscure spectrum, and ice stops it altogether.

Knoblauch has shown that very thin layers of gold, silver, and platinum,
which are known to transmit luminous rays of a definite colour, also allow
rays of heat to pass ; so that these substances are diathermanous, though in
a small degree. This is also the case with thin sheets of ebonite.

435. Influence of the nature of the heat. — The diathermanous power
differs greatly with the heat from different sources, as is seen from the
following table, in which the numbers express what proportion of every
100 rays from the different sources of heat incident on the plates is trans-
mitted : —

Locatelli's
lamp

Incandescent
platinum wire

Copper at 400°

Copper at 100°

Rock salt .

Fluor spar .

Plate glass

Black glass

Selenite

Alum ....

Ice .

0-5

These different sources of heat correspond to light from different sources.
Rock salt is here stated to transmit all kinds of heat with equal facility, and
to be the only substance which does so. It is analogous to white glass,
which is transparent for light from all sources. Fluor spar transmits 78 per
cent, of the rays from a lamp, but only -^jT, of those from a blackened surface
at 100°. A piece of plate glass only one-tenth of an inch thick, and perfectly
transparent to light, is opaque to all the radiation from a source of 100°,
transmits only 6 per cent, of the heat from a source at 400°, and but 39 of
the radiation from the lamp. Black glass, on the contrary, though it cuts

4o6 . On Heat. [435-

off all heat from a source at ioo°, allows 12 per cent, of the heat at 400° to
pass, and is equally transparent to the heat from the spiral, but on account
of its blackness is more opaque to the heat from the lamp. As we have
already seen, every luminous ray is a heat ray ; now as several of the sub-
stances in this table are pervious to all the luminous rays, and yet, as in the
case of ice, transmit about 6 per cent, of luminous heat, we have an apparent
anomaly ; which, however, is only a confirmation of the remarkably small
proportion which the luminous rays of a lamp bear to the obscure.

From these experiments Melloni concluded that as the temperature of
the source rose, more heat was transmitted. This has been confirmed by
some experiments of Tyndall. The platinum lamp (434) was used as the
source, the temperature of which could be varied from a dark to a brilliant
white heat, by a gradual augmentation of the strength of the electric current
which heated the platinum spiral. Instead of liquids, vapours were examined
in a manner to be described subsequently ; the measurements are given in
the following table : —

Absorption of Jicat by vapours.

Name of vapour

Source, platinum spiral

Barely visible Bright red

White hot

Near fusion

Bisulphide of carbon

Chloroform

Iodide of methyl

Benzole ....

Ether ....

Formic ether .

Acetic ether

6-5 i 47
9-1 6-3
12-5 9-6
26-4 20-6
43"4 3 1 '4
45-2 31-9
49 '6 1 34-6

2-9
5-6
7-8
i6-5
25-9
25-1
27-2

2-5
3-9

237
21-3

The percentage of rays absorbed is here seen to diminish in each case
as the temperature of the source rises. Mere elevation of temperature does
not, however, invariably produce a high penetrative power in the rays
emitted ; the rays from sources of far higher temperature than any of the
foregoing are more largely absorbed by certain substances than are the rays
emitted from any one of the sources as yet mentioned. Thus, the radia-
tion from a hydrogen flame was completely intercepted by a layer of water
only o'27 of an inch thick, the same layer transmitting 9 per cent, of the
radiation from the red-hot spiral, a source of much lower temperature. The
explanation of this is, that those rays which heated water emits (and water, •
the product of combustion, is the main radiant in a hydrogen flame) are the
very ones which this substance most largely absorbs. This statement, which
will become clearer after reading the analogous phenomena in the case of
light, was exemplified by the powerful absorption of the heat from a
carbonic oxide flame by carbonic acid gas. It will be seen presently (438)
that of the rays from a heated plate of copper, olefiant gas absorbs 10 times
the quantity intercepted by carbonic acid, whilst of the rays from a carbonic
oxide flame Tyndall found carbonic acid absorbed twice as much as olefiant
gas. A tenth of an atmosphere of carbonic acid, inclosed in a tube 4 feet
long, absorbs 60 per cent, of the radiation from a carbonic oxide flame.

-436] Influence of the Thickness and Nature of Screens. 407

Radiant heat of this character can thus be used as a dehcate test for the
presence of cai'bonic acid, the amount of which may even be accurately
measured by the same means. Prof. Barrett made in this way a physical
analysis of the human breath. In one experiment, the carbonic acid con-
tained in breath physically analysed was found to be 4"65 per cent, whilst
the same breath chemically analysed gave 4'66 per cent.

436. Influence of the tbickness and nature of screens. — It will be
seen from the table (435) that of every 100 rays rock salt transmits 92. The
other 8 may either ha\'e been absorbed or reflected from the surface of the
plate. According to Melloni, the latter is the case ; for if, instead of on one
plate, heat be allowed to fall on two or more plates whose total thickness
does not exceed that of the one, the quantity of heat arrested will be propor-
tional to the number of reflecting surfaces. He therefore concluded that
rock salt was quite diathermanous.

The experiments of later observers show that this conclusion is not
strictly correct ; rock salt does absorb a very small proportion of obscure
rays.

The quantity of heat transmitted through rock salt is practically the
same, whether the plate be i, 2, or 4 millimetres thick. But with other bodies
absorption increases with the thickness, although by no means in direct
proportion. This is seen to be the case in the table of absorption by liquids
at diflerent thicknesses. The following table tells what proportion of
1,000 rays from a Locatelli's lamp pass through a glass plate of the given
thickness : —

Thickness in millimetres 0-512345678
Rays transmitted . . 775 T-})}) 682 653 634 620 609 600 592

The absorption takes place in the first layers ; the rays which have passed
these possess the property of passing through other layers in a higher degree,
so that beyond the first layers the heat transmitted approaches a certain
constant value. If a thin glass plate be placed behind another glass plate
a centimetre thick, the former diminishes the transmission by little more
than the reflection from its surface. But if a plate of alum were placed be-
hind the glass plate, the result would be different, for the latter is opaque for
much of the heat transmitted by glass.

Heat, therefore, which has traversed a glass plate traverses another
plate of the same material with very slight loss, but is very greatly diminished
by a plate of alum. Of 100 rays which had passed through green glass
or tourmaline, only 5 and 7 were respectively transmitted by the same
plate of alum. A plate of blackened rock salt only transmits obscure rays,
while alum extinguishes them. Consequently, when these two substances
are superposed, a system impervious to light and heat is obtained.

These phenomena find their exact analogies in the case of light. The
different sources of heat correspond to flames of different colours, and the
screens of various materials to glasses of different colours. A red flame
looked at through a red glass appears quite bright, but through a green glass
it appears dim or is scarcely visible. So in like manner heat which has
traversed a red glass passes through another red glass with little diminu-
tion, but it is almost completely stopped by a green glass. Rock salt at 1 50°

4o8

On Heat.

[436-

emits only one kind of heat ; it is monothermal, just as sodium vapour is
monochromatic.

Different luminous rays being distinguished by their colours., Melloni
gave the name of therrnocrose or heat coloration to these different obscure
calorific rays. The invisible portion of the spectrum is accordingly mapped
out into a series of spaces, each possessing its own peculiar feature corre-
sponding to the coloured spaces which are seen in that portion of the spec-
trum visible to our eyes.

Besides thickness and colour, the polish of a substance influences the
transmission. Glass plates of the same size and thickness transmit more
heat as their surface is more polished. Bodies which transmit heat of any
kind very readily are not heated. Thus a window pane is not much heated
by the strongest sun's heat ; but a glass screen held before a common fire
stops most of the heat, and is itself heated thereby. The reason of this is
that by far the greater part of the heat from a fire is obscure, and glass is
opac[ue to this kind of heat.

437. Diffusion of beat. — When a ray of light falls upon an unpolished
surface in a definite direction, it is decomposed into a variety of rays which
are reflected from the surface in all directions. This irregular reflection is
called diffusion^ and it is in virtue of it that bodies are visible when light
falls upon them. A further peculiarity is, that all solar rays are not equally
diffused from the surface of bodies. Certain bodies diffuse certain rays and
absorb others, and accordingly appear coloured. The red colour of a gera-
nium is caused by its absorbing all the rays, excepting the red, which are
irregularly reflected. Just as is the case with transmitted light in transparent
bodies, so with diffused light in opaque ones ; for if a red body is illuminated
by red light it appears of a bright red colour, but if green light fall upon it
It is almost black. We shall now see that here again analogous phenomena
prevail with heat.

Various substances diffuse different thermal rays to a difterent extent ;
each possesses a peculiar thermocrose. Melloni placed a number of strips
of brass foil between the source of heat and the thermo-pile. They were
coated on the side opposite to the pile with lampblack, and on the other
side with the substances to be investigated. Representing the quantity ot
heat absorbed by the lampblack by 100, the absorption of the other bodies
was as follows : —

Incandescent
platinum

Copper at 400°

Copper at 100°

Lampblack ....

100

ICO

White lead ....

100

Isinglass

Indian ink ....

Shellac

Polished metal

13-5

Hence white lead absorbs far less of the heat radiated from incandescent
platinum than lampblack, but it absorbs the obscure rays from copper at
100° as completely as lampblack. Indian ink is the reverse of this ; it

-438] Relation of Gases and Vapours to Radiant Heat. 409

absorbs obscure rays less completely than luminous rays. Lampblack
absorbs the heat from all sources in equal quantities, and very nearly com-
pletely. In consequence of this property all thermoscopes which are used
for investigating radiant heat are covered with lampblack, as it is the best-
known absorbent of heat. The behaviour of metals is the reverse of that of
lampblack. They reflect the heat of different sources in the same degree.
They are to heat what white bodies are to light.

As coloured light is altered by diffusion from several bodies, so Knoblauch
has shown that the different kinds of heat are altered by reflection from dif-
ferent surfaces. The heat of an Argand lamp diffused from white paper
passes more easily through calcspar than when it has been diffused from
black paper.

The rays of heat, like the rays of light, are susceptible of polarisation
and double refraction. These properties will be better understood after
treating of light.

438. Relation of grases and vapours to radiant beat. — This subject
has been investigated by Tyndall ; the apparatus he used is represented in
the adjacent figure, the arrangement being looked upon from above.

A (fi?- 393) is a cylinder about 4 feet in length and 2\ inches in diameter,
placed horizontally, the ends of which can be closed with rock-salt plates :

by means of a lateral tube at r it can be connected with an air-pump and
exhausted ; while at / is another tube which serves for the introduction of
gases and vapours. T is a sensitive thermo-pile connected with an extremely
delicate galvanometer, M.

The deflections of this galvanometer were proportional to the degrees of
heat up to about 30° ; beyond this point the proportionality no longer held
good, and accordingly, for the higher degrees, a table was empirically con-
structed, in which the value of the higher deflections was expressed in units ;
the unit being the amount of heat necessary to move the needle through one
of the lower degrees.

C was a source of heat, which usually was either a Leslie's cube filled with
boiling water, or else a sheet of blackened copper heated by gas. Now,
when the source of heat was permitted to radiate through the exhausted
tube, the needle made a great deflection ; and in this position a very con-
siderable degree of absorption would have been needed to produce an
alteration of 1° of the galvanometer. And if to lessen this deflection a lower
source of heat had been used, the fraction absorbed would be correspondingly
less, and might well have been insensible. Hence Tyndall adopted the fol-
lowing device, by which he was enabled to use a powerful flux of heat, and at
the same time to discover small variations in the quantity falling on the pile.

410

On Heat.

[438-

The source of heat at C was allowed to radiate through the tube at the
end of which the pile was placed ; a deflection was produced of, say, 70° ;
a second source of heat, D, was then placed near the other face of the pile,
the amount of heat falling on the pile from this C07npensating cube being
regulated by means of a movable screen S. When both faces of the pile
are warmed, two currents are produced, which are in opposite directions,
and tend, therefore, to neutralise each other : when the heat on both faces
is precisely ec^ual, the neutralisation is perfect, and no current at all is pro-
duced, however high maybe the temperature on both sides. In the arrange-
ment just described, by means of the screen S, the radiation from the
compensating cube was caused to neutralise exactly the radiation from the
source C ; the needle consequently was brought down from 70° to zero, and
remained there so long as both sources were equal. If now a gas or vapour
be admitted into the exhausted tube, any power of absorption it may possess
will be indicated by the destruction of this equilibrium, and preponderance
of the radiation from the compensating cube, by an amount corresponding
to the heat cut off by the gas. Examined in this way, air, hydrogen, and
nitrogen, when dried by passing through sulphuric acid, were found to exert
an almost inappreciable effect ; their presence as regards radiant heat being
but little different from a vacuum. But with olefiant and other complex gases
the case was entirely different. Representing by the number i the quantity
of radiant heat absorbed by air, olefiant gas absorbs 970 times, and am-
moniacal gas 1,195 times, this amount. In the following table is given the
absorption of obscure heat by various gases, referred to air as unity : —

Name of gas

Air . . .

Oxygen

Nitrogen

H ydrogen

Chlorine

Hydrochloric acid

Absorption

under 30 inches

of pressure

Name of gas

Carbonic acid
Nitrous oxide
Marsh gas .
Sulphurous acid
Olefiant
Ammonia

Absorption 1

under 30 inches

of pressure.

335
403
710
970
1195

If, instead of comparing the gases at a common pressure of one atmo-
sphere, they are compared at a common pressure of an inch, their differences
in aljsorption are still more strikingly seen. Thus, assuming the absorption
by I inch of dry air to be i,the absorption by i inch of olefiant gas is 7,950,
and by the same amount of sulphurous acid 8,800.

439. Xnfluence of pressure and thickness on the absorption of heat
by g-ases. — The absorption of heat by gases varies with the pressure ; this
variation is best seen in the case of those gases which have considerable
absorptive power. Taking the total absorption by atmospheric air under
ordinary pressure at unity, the numbers of olefiant gas under a pressure of i,
3, 5, 7, and 10 inches of mercury are respectively 90, 142, 168, 182, and 193.
Thus one-thirtieth of an atmosphere of olefiant gas exerts 90 times the
absorption of an entire atmosphere of air. And the absorption, it is seen,
increases with the density, though not in a direct ratio. Tyndall showed.

-440]

A bsorptive Poiver of Vapo7irs.

411

however, by special experiments, that for very low pressures the absorption
does increase with the density. Employing as a unit volume of the gas a
quantity which measured only ^ of a cubic inch, and admitting succes-
sive measures of olefiant gas into the experimental tube, it Avas found that
up to 15 measures the absorption was directly proportionate to the density
in each case.

In these experiments the length of the experimental tube remains the
same whilst the pressure of the gas within it was caused to vary ; in subse-
quent experiments the pressure of the gas was kept constant, whilst the
length of the tube was, by suitable means, varied from o-oi of an inch up to
50 inches. The source was a heated plate of copper ; of the total radiation
from this nearly 2 per cent, was absorbed by a film of olefiant gas -oi of an
inch thick, upwards of 9 per cent, by a layer of the same gas ot of an inch
thick, -i)^ per cent, by a layer 2 inches thick, 68 per cent, by a column 20
inches long, and 11 per cent, by a column rather more than 4 feet long.

440. j^bsorptive power of vapours. — The absorptive power of olefiant
gas is exceeded by that of several vapours. The liquid from which the
vapours were to be produced was inclosed in a small flask, which could be
attached with a stop-cock to the exhausted experimental tube. The absorp-
tion was then determined after admitting the vapours into the tube in
quantities measured by the pressure of the barometer gauge attached to the
air-pump.

The following table shows the absorption of vapours under pressures
varying from o-i to ro inch of mercury : —

Name of vapours

Absorption under pressure in inches of mercury

o-i

o"S

I'D

Bisulphide of carbon

Benzole

Chloroform ....

Ether

Alcohol

Acetic ether ....

85
300

325
590

47
182-
182
710
622
980

62
267
236
870

I 195

These numbers refer to the absorption of a whole atmosphere of dry air
as their unit, and it is thus seen that a quantity of bisulphide of carbon
vapour, the feeblest absorbent yet examined, which only exerts a pressure of
y^Q of an inch of mercury, or the gi^ of an atmosphere, gave fifteen times the
absorption of an entire atmosphere of air ; and j^ of an inch of acetic ether
590 times as much. Comparing air at a pressure of o-i with acetic ether of
the same pressure, the absorption of the latter would be more than 17,500
times as great as that of the former.

Tyndall found that the odours from the essential oils exercised a marked
influence on radiant heat. Perfectly dry air was allowed to pass through a
tube containing dried paper impregnated with various essential oils, and
then admitted into the experimental tube. Taking the absorption of dry air
as unity, the following were the numbers respectively obtained for air scented
with various oils ; — Patchouli 31, otto of roses -^,1, lavender 60, thyme 68,

412 On Heat. [440-

rosemary 74, cassia 109, aniseed 372. Thus the perfume of a flower-
bed absorbs a large percentage of the heat of low refrangibility emitted
from it.

Ozone prepared by electrolysing water was also found to have a remark-
able absorptive effect. The small quantity of ozone present in electrolytic
oxygen was found in one experiment to exercise 136 times the absorption of
the entire mass of the oxygen itself.

But the most important results are those which follow from his experi-
ments on the behaviour of aqueous vapour to radiant heat. The experimen-
tal tube was filled with air, dried as perfectly as possible, and the absorption
it exercised was found to be one unit. Exhausting the tube, and admitting
the ordinary undried, but not specially moist, air from the laboratory, the
absorption now rose to 72 units. The difference between dried and undried
air can only be ascribed to the aqueous vapour the latter contains. Thus on
a day of average humidity the absorptive effect due to the transparent aque-
ous vapour present in the atmosphere is 72 times as great as that of the air
itself, though in quantity the latter is about 200 times greater than the former.
Analogous results were obtained on different days, and with specimens of
air taken from various localities. When air which had been specially purified
and dried was allowed to pass through a tube filled with fragments of moist-
ened glass and examined, it was found to exert an absorption 90 times that
of pure air.

In some other experiments Tyndall suppressed the use of rock-salt
plates in his experimental tube, and even the tube itself, and yet in every
case the results were such as to show the great power which aqueous vapour
possesses as an absorbent of radiant heat.

The absorptive action which the aqueous vapour in the atmosphere exerts
on the sun's heat has been established by a series of actinometrical observa-
tions made by Soret at Geneva and on the summit of Mont Blanc ; he found
that the intensity of the solar heat on the top of Mont Blanc is f of that
at Geneva ; in other words, that of the heat which is radiated at the height
of Mont Blanc, about | is absorbed in passing through a vertical layer of
the atmosphere 14,436 feet in thickness. The same observer has found that
with virtually equal solar heights there is the smallest transmission of heat
on those days on which the tension of aqueous vapour is greatest ; that is,
when there is most moisture in the atmosphere.

441. Radiating: power of gpases. — Tyndall also examined the radiating
power of gases. A red-hot copper ball was placed so that the current of
heated air which rose from it acted on one face of a thermo-pile ; this action
was compensated by a cube of hot water placed in front of the opposite face.
On then allowing a current of dry olefiant gas from a gasholder to stream
through a ring burner over the heated ball and thus supplant the ascending
current of hot air, it was found that the gas radiated energeticalljf. By com-
paring in this manner the action of many gases it was discovered that, as is
the case with solids, those gases which are the best absorbers are also those
which radiate most freely.

442. Dynamic radiation and absorption. — A gas when permitted to
enter an exhausted tube is heated in consequence of the collision of its par-
ticles against the sides of the vessel ; it thus becomes a source of heat, which

-443] Relation of A bsorption to Molecular State. 4 1 3

is perfectly capable of being measured. Tyndall calls this dynatiiic heathtg.
In like manner, when a tube full of gas or vapour is rapidly exhausted, a
chilling takes place owing to the loss of heat in the production of motion ;
this he calls dynamic cJiillitig or absorption.

He could thus determine the radiation or absorption of a gas without
any source of heat external to the gas itself An experimental tube was
taken, one end of which was closed with a polished metal plate, and the
other with a plate of rock salt ; in front of the latter was the face of the pile.
The needle being at zero, and the tube exhausted, a gas was allowed quickly
to enter until the tube was full, the effect on the galvanometer being noted.
This being only a transitoiy effect, the needle soon returned to zero ; the
tube was then rapidly pumped out, by which a sudden chilling was produced
and the needle exhibited a deflection in the opposite direction. Comparing
in this way the dynamic heating and chilling of various gases, those gases
which are the best absorbers were also found to be the best radiators.

Polished metallic surfaces are, as we have seen (427), bad radiators,
but radiate freely when covered with varnish. Tyndall made the curious
experiment of varnishing a metallic surface by a film of gas. A Leslie's
cube was placed with its polished metal side in front of the pile, and its effect
neutralised by a second cube placed before the other face of the pile. On
allowing a stream of olefiant or coal gas to flow from a gasholder over the
metallic face of the first cube, a copious radiation from that side was pro-
duced as long as the flow of gas continued. Acting on the principle indi-
cated in the foregoing experiment, Tyndall determined the dynamic radiation
and absorption of vapours. The experimental tube containing a vapour
under a small known pressure, air was allowed to enter until the pressure
inside the tube was the same as that of the atmosphere. In this way the
entering air, by its impact against the tube, became heated ; and its particles
mixing with those of the minute quantity of vapour present, each of them
became, so to speak, coated with a layer of the vapour. The entering air
was in this case a source of heat, just as in the above experiments the
Leslie's cube was. Here, however, one gas varnished another ; the radia-
tion and subsequently the absorption of \-arious vapours could thus be
determined.

It was found that vapours differed veiy materially in their power of
radiating under these circumstances ; of those which were tried bisulphide
of carbon vapour was the worst and boracic ether the best radiator. And in
all cases those which were the best absorbents were also the best radiators.

443. Relation of absorption to molecular state. — ^After examining the
absorption of heat by vapours, Tyndall tried the same substances in a liquid
form. The conditions of the experiments were in both cases the same ; the
source of heat was a spiral of platinum heated to redness by an electric cur-
rent of known strength ; and plates of rock salt were invariably employed to
contain both vapours and liquids. Finally, the absorption by the vapours
was re-measured ; in this case introducing into the experimental tube, not,
as before, equal quantities of vapour, but amounts proportional to the
density of the liquid. When this last condition had been attained, it was
found that the order of absorption by a series of liquids, and by the same
series when turned mto vapour, was precisely the same Thus the sub-

414 On Heat. [443-

stances tried stood in the following order as liquid and as vapour, beginning
with the feeblest absorbent, and ending with the most powerful : —

Liquids Vapours

Bisulphide of carbon .... Bisulphide of carbon.

Chloroform Chloroform.

Iodide of ethyl Iodide of ethyl.

Benzole Benzole.

Ether Ether.

Alcohol Alcohol.

Water

A direct determination of aqueous vapour could not be made, on account
of its low tension and the hygroscopic nature of the rock salt. But the un-
deviating regularity of the absorption by all the other substances in the list,
both as liquid and vapour, establishes the fact, which is corroborated by
the experiments already mentioned, that aqueous vapour is one of the most
energetic absorbents of heat.

In this table it will be noticed that those substances which have the
simplest chemical constitution stand first in the list, with one anomalous
exception, namely, that of water. In the absorption of heat by gases, Tyndall
found that the elementary gases were the feeblest absorbents, while the
gases of most complex constitution were the most powerful absorbents. Thus
it may be inferred that absorption is mainly dependent on chemical consti-
tution ; that is to say, that absorption and radiation are molecular acts
independent of the physical condition of the body.

Tyndall discovered that the radiation of powders is similar to that of the
solids from which they were derived, and therefore differs greatly iftter se.
The absorbent power of powders was also found to correspond with their
radiative power — which, as we have shown, is the case with solids and gases,
and, though as yet we have no experiments on the subject, is doubtless also
true for liquids. The powders were attached to the tin surfaces of a Leslie's
cube, in such a manner that radiation took place from the surface of the
powder alone. The following table gives the radiation in units from some of
the powders examined by Tyndall ; the metal surface of the cube giving a
deflection of 1 5 units : —

Radiation from powders.

Rock salt . . . 35-3 Sulphate of calcium . 777

Biniodide of mercury . 397 Red oxide of iron . . 78-4

Sulphur .... 40-6 Hydrated oxide of zinc . 80-4

Carbonate of calcium . 70-2 Sulphide of iron . . 817

Red oxide of lead . . 74-0 Lampblack . . . 84-0

These substances are of various colours. Some are white, such as rock
salt, carbonate and sulphate of calcium, and hydrated oxide of zinc ; some
are red, such as biniodide of mercury and oxide of lead ; whilst others are
black, as sulphide of iron and lampblack ; we have besides other colours.
The colours, therefore, have no influence on the radiating power : rock salt,

-444] Applications. 415

for example, is the feeblest radiator, and hydrated oxide of zinc one of the
most powerful radiators.

Nearly a century ago Franklin made experiments on coloured pieces of
cloth, and found their absorption, indicated by their sinking into snow on
which they were placed, to increase with the darkness of the colour. But
all the cloths were equally powerful absorbents of obscure heat, and the
effects noticed were only produced by their relative absorptions of light. In
feet, the conclusions to be drawn from Franklin's experiments only hold good
for luminous heat, especially sunlight, such as he employed.

444. Applications — The properties which bodies possess of absorbing,
emitting, and reflecting heat meet with numerous applications in domestic
economy and in the arts. Leslie stated in a general manner that white
bodies reflect heat very well, and absorb very little, and the contrary is
the case with black substances. As we have seen, this principle is not
generally true, as Leslie supposed ; for example, white lead has as great an
absorbing power for non-luminous rays as lampblack (437). Leslie's principle
applies to powerful absorbents like cloth, cotton, wool, and other organic
substances when exposed to luminous heat. Accordingly, the most suitable
coloured clothing for summer is just that which experience has taught us to
use, namely, white, for it absorbs less of the sun's rays than black clothing,
and hence feels cooler.

The polished fire-irons before a fire are cold, whilst the black fender is
often unbearably hot. If, on the contrary, a Hquid is to be kept hot as long
as possible, it must be placed in a brightly polished metallic vessel, for
then, the emissive power being less, the cooling is slower. Hence it is
advantageous that the steam pipes, &c., of locomotives should be kept
bright. In the Alps, the mountaineers accelerate the fusion of the snow by
covering it with earth, which increases the absorbing power.

In our dwellings, the outsides of stoves and of hot-water apparatus ought
to be black, and the insides of fireplaces ought to be lined with firebrick, in
order to increase the radiating power towards the apartment.

It is in consequence of the great diathermancy of dry atmospheric air
that the higher regions of the atmosphere are so cold, notwithstanding the
great heat which traverses them ; whilst the intense heat of the sun's direct
rays on high mountains is probably due to the comparative absence of
aqueous vapour at these elevations.

As nearly all the luminous rays of the sun pass through water, and the
sun's radiation as we receive it on the surface of the earth consists of a
large proportion of luminous rays, accidents have often arisen from the con-
vergence of these luminous rays by bottles of water which act as lenses. In
this way gunpowder could be fired by the heat of the sun's rays concen-
trated by a water lens ; and the drops of water on leaves in greenhouses
have, it is said, been found to act as lenses, and burn the leaves on which
they rest.

Certain bodies can be used (436) to separate the heat and light radiated
from the same source. Rock salt covered with lampblack, or still better
with iodine, transmits heat, but completely stops light. On the other hand,
alum, either as a plate or in solution, or a thin layer of water, is permeable
to light, but stops all the heat from obscure sources. This property is made

4i6 On Heat. [444-

use of in apparatus which are ilhiminated by the sun's rays, in order to sift
the rays of their heating power ; and a vessel full of water or a solution of
alum is used with the electric light when it is desirable to avoid too intense
a heat.

In gardens, the use of shades to protect plants depends partly on the
diathermancy of glass for heat from luminous rays and its athermancy for
obscure rays. The heat which radiates from the sun is largely of the former
quality, but by contact with the earth it is changed into obscure heat, which,
as such, cannot retraverse the glass. This explains the manner in which
greenhouses accumulate their warmth, and also the great heat experienced
in summer in rooms having glass roofs, for the glass in both cases acts, as
it were, as a valve which effectually entraps the solar rays. On the same
principle plates of glass are frequently used as screens to protect us from the
heat of a fire ; the glass allows us to see the cheerful light of the fire, but
intercepts the larger part of the heat radiated from the fire. Though the
screens thus become warm by the heat they have absorbed, yet, as they
radiate this heat in all directions towards the fire as well as towards us, we
finally receive less heat when they are interposed.

445. Attraction and repulsion arising^ from radiation. — Crookes has
discovered a highly remarkable class of phenomena which are due to the
radiant action of heated and of luminous bodies. These phenomena are
most conveniently illustrated by means of an instrument which he has
devised and which is called the radiometer^ the construction of which is as
follows : — A glass tube (fig. 393), with a bulb blown on it, is fused at the
bottom to a glass tube which at one end serves to rest the whole apparatus
in a wooden support. In the other end is fused a fine steel point. On this
rests a small vane or fly, consisting of four arms of aluminium wire fixed at
one end to a small cap, while at the others are fixed small discs or lozenges
of thin mica, coated on one side with lampblack. The weight of the fly is
not more than two grains.

In order to keep the fly on the pivot a tube is fused in the upper part of
the bulb which reaches down to and just surrounds the top of the cap, with-
out, however, touching it ; the other end of this tube is drawn out and con-
nected with an arrangement for exhausting the air by the Sprengel pump
(205) or by chemical means ; when the desired degree of exhaustion has been
attained this can be sealed. By keeping the apparatus during exhaustion in
a hot air bath at a temperature of 300°, the gases occluded on the inner surface
of the glass, and by the vanes, are got rid of

If a source of light or of heat, a candle for instance, is brought near the
fly, it is attracted, and the fly rotates slowly in a direction showing that the
blackened side moves towards the light ; this movement, indicating an
attraction, depends on a certain state of rarefaction. If, however, the appa-
ratus be connected with an arrangement which allows the pressure to be
varied, this rotation gradually diminishes in rapidity as the air within is
further rarefied, until a certain point is reached at which it ceases. If
now the rarefaction is pushed further, the highly remarkable phenomenon
is observed that repulsion succeeds to attraction, and that the fly now rotates
in the direction away from the source of heat. In a double radiometer, in

-445] Attraction and Repulsion arising from Radiation. 417

which two flys are pivoted independently one over the other, having their

blackened sides opposite each other, the flys rotate in opposite directions

on the approach of a lighted candle.

When a cold body, such as a piece of

ice, is brought near, instead of a hot one,

exactly the opposite effects are observed ;

when the vessel contains air a pith ball

suspended at one end of a light arm is

repelled, the neutral point is observed,

while at high degrees of rarefaction

attraction ensues.

One of the most important facts
brought to light by these experiments
is, that what has hitherto been looked
upon as a complete vacuum is not so in
reality ; the most perfect vacuum obtain-
able still contains a certain residue of
gas, as has been proved by the experi-
ments of Crookes and others, among
which that of Kundt may be mentioned.
The latter placed on the vanes a light
disc of mica, and at a little distance
above it a similar disc was arranged so
as to rotate freely, in a horizontal plane
independently of the first. When the
lower vane was made to rotate by bring-
ing a light near, it was found that the
upper disc was also put in rotation in the
same direction, being dragged by the
viscosity of the residual air. Accordingly
the explanation of the phenomena of the
radiometer must take into account the
existence of this gaseous residue.

The nature of the gas seems to have
no special influence on the pheno-
mena ; whether the vacuum be one of
hydrogen, of aqueous vapour, or of

iodine vapour, seems immaterial ; though fig- 394-

with hydrogen the exhaustion need not

l3e pushed so far as with air. The repulsion takes place with all the rays
of the spectrum, the intensity diminishing from the ultra red to the ultra
violet. When the chemical rays act, the interposition of a plate of alum has
no effect, while a solution of iodine in bisulphide of carbon diminishes the
repulsion. The rate at which the vane rotates depends on the intensity of
the source of light. With a strong light the rotation is so rapid that its rate
cannot be determined. With two candles at the same distance the rotation
is twice as rapid as with one. Two sources of light which, successively placed
at the same distance, produce the same rate of rotation, are ecjual in inten-
sity. If, when placed at different distances, they produce the same speed

41 8 On Heat. [445-

of rotation, their intensities are directly as the squares of these distances from
the radiometer. On this is based the use of the instrument as a photometer
(509) for comparing together various sources of artificial light. It may like-
wise be used for making comparative measurements of the intensity of
sunhght ; and the distribution of heat in the solar spectrum may be in-
vestigated by its means.

It is not difficult to understand that the attraction observed in the experi-
ments may be explained by the action of convection currents (408), as long
as the apparatus still contains air. For heat falling upon this blackened disc
would raise its temperature, and the temperature of a layer of air in im-
mediate contact with the disc would be raised too ; it would expand and
rise, flowing over into the space behind the disc, and would thus increase the
pressure there.

On the other hand the repulsion observed at the higher degrees of ex-
haustion, approaching a vacuum, is due to a reaction between the vane and
the crlass envelope, and is explained by reference to the modern views as
to the constitution of gases, of which it is at once an illustration and a
proof

The general nature of this theory is that a gas is an assemblage of in-
dependent molecules, which are perfectly elastic, and which move with great
rapidity ; their impacts against the sides of the vessel in which the gas is
contained are the cause of the pressure. The impact of the molecules
against each other is the mechanism by which the equal transmission of
pressure in gases is effected (294).

Crookes has calculated that the mechanical effect of the force of repulsion
is equal to about the -^ of a milligramme on a square centimetre, and Stoney
has shown that this force is sufficient to account for the effects observed, by
reference to admitted principles of the mechanical theory of gases.

The rays of heat pass through the thin glass without raising its tempera-
ture, and, falling on the blackened side of the vane, are absorbed by it ; the
consequence of this is, that it will become slightly hotter. The layer of ex-
tremely rarefied air in immediate contact with the blackened disc will also
become somewhat hotter, and the molecules will fly from the disc with
greater velocity. Under ordinary pressures or even at moderate degrees of
rarefaction these more rapid motions would be equalised by their impacts
ao-ainst other molecules, and a uniformity of pressure — that is, of temperature

would be established. But the frequency of these intramolecular shocks

diminishes rapidly with the increase of rarefaction ; and the consequence is,
that a great number of molecules, after having been heated by contact with
the blackened side of the palette, will strike against the cold glass. The effect
of this will be to cool these molecules— that is, to diminish their velocity ; it
will be chiefly molecules of this kind which fall on the back of the disc, and
on the regions behind it. An excess of force equal and opposite to that on
the glass acts against the front of the disc, and is sufficient to account for
the phenomena exhibited by Crookes.

It follows from this explanation that, other things being equal, a fly will
rotate more rapidly in a small than in a large bulb. This has been con-
clusively proved by Crookes, who constructed a double-bulb radiometer, the
two bulbs being very different insize, and so connected that, by dexterous

-446a] Viscosity of Gases. 419

manipulation, the fly could be transferred from the pivot of the one to that
of the other bulb.

The radiometer is well adapted for the lecture demonstration of many
phenomena in heat. Thus the law of the inverse square (414) may be illus-
trated by counting the number of rotations when the instrument is placed at
varying distances from the source of heat.

446. Internal friction or viscosity of grases. — In some recent experi-
ments in connection with the radiometer, Crookes used an arrangement con-
sisting of a long but light arm of straw suspended by a delicate glass fibre
in a sort of T tube turned upside down ; in this way even a greater degree
of delicacy was obtained than with the radiometer. Thus he was able to
get a deflection by moonlight, which does not move the fly of the radiometer.
He examined the internal friction or viscosity of the residual gas by causing
the arm to oscillate, and then observing the rate at which the oscillations
diminish under various pressures. He thus found that from ordinary pres-
sures down to a pressure of 0-19 mm., or what may be called a TorriceUian
vacuum, the viscosity is practically constant, only diminishing from 0-126 to
0-II2. It now begins to fall off, and at apressure of 0-000076 mm. it has
diminished to o-oi, or about j\. Simultaneously with this decrease in
viscosity the force of repulsion excited by a standard light on a blackened
surface varies. It increases as the pressure diminishes until the exhaus-
tion is about 0-05 mm., and attains its maximum at about 0-03 mm. It then
sinks veiy rapidly until it is at 0*000076 mm., when it is less than j^ of its
maximum.

The viscosity varies in different gases ; it is considerably less in hydrogen
than in air ; and hence with this gas it is not necessar^^ to drive the exhaus-
tion so far to produce a considerable degree of repulsion.

The researches of Crookes have opened the way to an entirely new field
of experimental inquiry into the phenomena which occur in what is called
the ultra-gaseous state of matter, or that in which the rarefaction of gases is
pushed to its utmost limits. The state in which molecular, as distinguished
from 7nolar, actions come into play, has been aptly termed Crookes's vacuum.
A further account of the researches requires too great an amount of detail
for the purposes of this work ; and it must also be added that the explana-
tions which have been given are still not beyond the range of controversy.

446^. Relation of radiant heat to sound.^This subject has of late
engaged the attention of several physicists, among whom may be particular-
ised Bell and Tainter, Tyndall, Preece, and Mercadier. A convenient way
of showing the phenomena is by means of an apparatus constructed by
Duboscq., the essential features of which are represented in fig. 396. It is
an arrangement by which an intermittent beam of radiant heat maybe made
to act on various bodies, and consists of a disc D mounted on a horizontal
axis, and which, by means of the multiplying wheels P and p', may be
rotated at any desired speed. In the disc is a series of holes, the numbers
of which are in some multiple of the ratio 4:5:6:8. This apparatus con-
stitutes in fact a syren (242), and is very convenient for lecture purposes.
If, while the disc is rotating with uniform speed, a current of air be succes-
sively directed against the rows of holes from the inside to the outside, we
get the fundamental note, the third, the fifth, and the octave.

E E 2

420

On Heat.

[446£

On the stand is a support on which the arrangement O may be fixed in
any position by means of the screw s ; it consists of a screen and wide tube
behind which is the source of radiant heat, not represented in the figure.
To this support may be fitted a double convex lens, if the rays are to be
concentrated on one line of holes, or a cylindrical lens when a slice of
thermal rays is to be used ; or the rays may be concentrated by a mirror, to
get rid of the effects of absorption by glass. The support S is for holding
various pieces of apparatus.

Tyndall found that when a flask like that represented in fig. 395, con-
taining a small quantity of ether, was placed so that the intermittent beam
arising from a lime-light could fall on it, and the top was connected with a
flexible tube, a distinct musical note was heard when the ear-trumpet was
held to the ear. Other liquids being tried it was found that those which his
other experiments had revealed as the best absorbers of heat (440) gave the
loudest sounds. The vapour was the operative cause, for when the beam
was caused to strike against the liquid instead of against the vapour no
sound was heard ; this was also the case when the rays fell on a rock-salt
cell filled with the liquid. The pitch of the note depended on the velocity
of rotation.

Dry air gave no sound, but air containing moisture did so ; and the
more moisture was present the louder was the sound. Other gases gave
sounds in the order of their absorption for heat ; and, indeed, all Tyndall's
results in this direction are most strikingly confirmed.

The investigations of the other experimenters, Preece, Bell and Tainter,

Fig. 397.

Y\% ^96

and' Mercadier, were chiefly directed to the eftects produced when the
intermittent beam is allowed to fall on solid bodies. A sort of an acoustic

-446a] Relation of Radiant Heat to Sonnd. 42 1

trumpet (fig. 397) was used by Mercadier, consisting of a movable piece ab
fitting over c d ?,o that plates L of various materials could be experimented
upon. The other end /is fitted with a flexible tube and bell so that it could
be applied to the ear.

When the intermittent beam is allowed to act on this plate it is set in
vibration and a sound is produced. This is not due, at any rate mainly, to
transverse vibrations of the plate, for neither the pitch nor the quality of the
note was altered when the thickness and nature of the plate were changed (282),
nor was it altered when the plate was slit. The best effects were obtained
when the diaphragm was of thin metal foil coated with lampblack on the
side next the rays. Marked effects were also obtained when a transparent
plate was used blackened on the side away from the rays. The effect is one
of radiant heat, and is essentially due to alternate expansions and contrac-
tions of the layer of air in contact with the surfaces which absorb the i^adiant
heat. The phenomenon may be very simply exhibited by blackening half
the inside of a test-tube R, the open end of which is provided with a flexible
tube which can be placed to the ear. When the rays fall on the blackened
part a loud sound is heard, but very little when the bright side is exposed.
The effect is also obtained when a blackened piece of foil is placed in the
tube.

422 On Heat. [447-

CHAPTER IX.

CALORIMETRY.

447. Calorimetry. Thermal unit. — The object of calorimetry is to
measure the quantity of heat which a body parts with or absorbs, when its
temperature sinks or rises through a certain number of degrees, or when it
changes its condition.

Quantities of heat may l)e expressed by any of its directly measurable
effects, but the most convenient is the alteration of temperature, and quan-
tities of heat are usually defined by stating the extent to which they are
capable of raising a known weight of a known substance, such as water.
The unit chosen for comparison, and called the tJiermal unit, is not ever)'-
where the same. In France it is the quantity of heat necessary to raise the
temperature of one kilogramme of water through 07ie degree Centigrade ; this
is called a calorie. In this book we shall adopt, as a thermal unit, the
quantity of heat 7tecessary to raise otte pound of water through one degree
Centigrade: i calorie = 1-2 thermal units, and one thermal unit = 0-45 calorie.

On the centimetre-gramme-second system of units the heat required to
raise one gramme of water through one degree is taken as the unit. This is
called the gramme-degree or 'wate7'-gramme-degree.

448. Specific heat.— When equal weights of two different substances, at
the same temperature, placed in similar vessels, are subjected for the same
length of time to the heat of the same lamp, or are placed at the same
distance in front of the same fire, it is found that their temperatures will A-aiy
considerably ; thus mercuiy will be much hotter than water. But as, from
the conditions of the experiment, they have each been receiving the same
amount of heat, it is clear that the quantity of heat which is sufficient to
raise the temperature of mercury through a certain number of degrees, will
raise the temperature of the same quantity of water only through a less
number of degrees ; in other words, that it requires more heat to raise the
temperature of water through one degree than it does to raise the temperature
of mercury by the same extent. Conversely, if the same quantities of water
and of mercury at 100° C. be allowed to cool down to the temperature of the
air, the water will require a much longer time for the purpose than the
mercury ; hence, in cooling through the same number of degrees, water
gives out more heat than does mercury.

It is readily seen that all bodies have not the same specific heat. If a
pound of mercury at 100° is mixed with a pound of water at zero, the tem-
perature of the mixture will be about 3° only ; that is to say, that while the
mercury has cooled through 97°, the temperature of the water has been raised
only 3°. Consequently the same weight of water requires about 32 times as
much heat as mercury does, to produce the same elevation of temperature.

-449] Measure of the Sensible Heat absorbed by a Body. 423

If similar experiments are made with other substances, it will be found
that the quantity of heat required to efifect a certain change of temperature
is different for almost every substance, and we speak of the specific heat, or
thermal or calorific capacity, of a body as the quantity of heat which it absorbs
when its temperature rises through a given range of temperature, from zero
to 1° for example, compared with the quantity of heat which would be
absorbed, in the same circumstances, by the same weight of water ; that is,
water is taken as the standard for the comparison of specific heats. Thus,
to say that the specific heat of lead is 0-0314, means that the quantity of
heat which would raise the temperature of any given weight of lead through
1° C. would raise the temperature of the same weight of water through only
0-0314° C.

Temperature is the vis viva of the smallest particles of a body ; in
bodies of the same temperature the atoms have the same vis viva, the
smaller mass of the lighter atoms being compensated by their greater
velocity. The heat absorbed by a body not only raises its temperature — that
is, increases the vis viva of the progressive motion of the atoms — but in over-
coming the attraction of the atoms it moves them further apart, and along
with the expansion which this represents, some external pressure is overcome.
In the conception of specific heat is included not merely that amount of heat
which goes to raise the temperature, but also that necessary for the internal
work of expansion, and that required for the external work. If these latter
could be separated, we should get the true heat of temperature, that which is
used solely in increasing the vis viva of the atoms. This is sometimes
called the true specific heat.

Three methods have been employed for determining the specific heats of
bodies : (i.) the method of the melting of ice, (ii.) the method of mixtures,
and (iii.) that of cooling. In the latter, the specific heat of a body is deter-
mined by the time which it takes to cool through a certain temperature.
Previously to describing these methods, it will be convenient to explain the
expression for the quantity of heat absorbed or given out by a body of known
weight and specific heat, when its temperature rises or falls through a certain
number of degrees.

449. Measure of the sensible heat absorbed by a body.— Let m be
the weight of a body in pounds, c its specific heat, and / its temperature.
The quantity of heat necessary to raise a pound of water through one degree
being taken as unity, vi of these units would be required to raise m pounds
of water through one degree, and to raise it through / degrees, / times as
much, or )nt. As this is the quantity of heat necessary to raise through /
degrees m pounds of water, whose specific heat is unity, a body of the same
weight, only of different specific heat, would require mtc. Consequentlj-,
when a body is heated through / degrees, the quantity of heat which it
absorbs is the product of its lueigkt into the range of tejnperature into its
specific heat. This principle is the basis of all the formulae for calculatmg
specific heats.

If a body is heated or cooled from / to /' degrees, the heat absorbed or
disengaged will be represented by the formula

;«(/' - t)c, or m{t — t')c.

424

On Heat.

[450-

450. iwethod of the fusion of ice. — This method of determining specific
heats is based on the fact that to melt a pound of ice 80 thermal units are
necessary, or more exactly 79"25. Black's calorimeter (fig. 398) consists of
a block of ice in which a cavity is made,
and which is provided with a cover of ice.
The substance whose specific heat is to be
determined is heated to a certain tempera-
ture, and is then placed in the cavity, which
is covered. After some time the body be-
comes cooled to zero. It is then opened, and
both the substance and the cavity wiped dry
with a sponge which has been previously
weighed. The increase of weight of this
sponge obviously represents the ice which
has been converted into water.
Now, since one pound of ice at 0° in melting to water at 0° absorbs 80
thermal units, P pounds absorbs 80 P units. On the other hand this cjuan-
tity of heat is equal to the heat given out by the body in cooHng from t° to
zero, which is nitc, for it may be taken for granted that in cooling from t° to
zero a body gives out as much heat as it absorbs in being heated from zero
to f- Consequently from

Fig. 398.

It is difficult to obtain blocks of ice as large and pure as those used by

Black in his experiments, and Lavoisier and Laplace replaced the block of
^^__ ice by a more complicated

apparatus which is called
the ice calorimeter. Fig.
399 gives a perspective,
view of it, and fig. 400
represents a section. It
consists of three concen-
tric tin vessels ; in the
central one is placed the
body M, whose specific
heat is to be determined,-
while the other two are
filled with pounded ice.
The ice in the compart-
ment A is melted by the
heated body, while the
ice in the compartment B
cuts off the heating influ-
ence of the surrounding

atmosphere. The two stopcocks E and D give issue to the water which

arises from the liquefaction of the ice.

In order to find the specific heat of a body by this apparatus, its weight,

w, is first determined ; it is then raised to a given temperature, /, by keeping

Fig. 399-

Fig

Bunsen's Ice Caloriinctcr.

425

-451]

it for some time in an oil or water bath, or in a current of steam. Having
been quickly brought into the central compartment, the lids are replaced
and covered with ice, as represented in the figure. The water which flows
out by the stopcock D is collected. Its weight, P, is manifestly that of the
melted ice. The calculation is then made as in the preceding
case.

There are many objections to the use of this apparatus.
From its size it requires some quantity of ice, and a body, M,
of large mass ; while the experiment lasts a considerable time.
A certain weight of the melted water remains adhering to the
ice, so that the water which flows out from D does not exactly
represent the weight of the melted ice.

451. Bunsen's ice calorimeter. — On the very considerable
diminution of volume which ice experiences on passing into
water (347), Bunsen has based a calorimeter which is particu-
larly suitable when only small quantities of a substance can
be used in determinations. A small test-tube a (fig. 401)
intended to receive the substance experimented upon is fused
in the wider tube B. The part ab contains pure freshly
boiled distilled water, and the prolongation of this tube BC,
together with the capillary tube d^ contains pure mercury.
This tube d is firmly fixed to the end of the tube C ; it is
g'raduated, and the value of each division of the graduation is
specially determined by calibration. When the apparatus is
immersed in a freezing mixture, the water in the part ab
freezes. Hence, if afterwards, while the apparatus is protected
against the excess of heat from without, a weighed quantity of
a substance at a given temperature is

introduced into the tube, it imparts ^ _^

its heat to this in sinking to zero. In
doing so it melts a certain quantity of
ice, which is evidenced by a corre-
sponding depression of the mercury
in the tube d. Thus the weight of
ice melted, and the weight and
original temperature of the sub-
stance experimented upon, furnish all
the data for calculating the specific
heat.

For heating the substance in this,
and also in other calorimetrical expe-
riments, the apparatus fig. 402 is well
adapted. The cylindrical metal ves-
sel G is narrower at the top, and a
glass test-tube R is fitted into a cork
which closes G. In this glass tube,
which is also closed by a cork K, the

substance is placed which is to be heated. The greater part of the vessel is
covered by a thick mantle of felt, B. The water in the vessel is boiled, the

Fig. 401.

426 071 Heat. [451-

steam emerging at d, until the substance has acquired the temperature of
boiling water, for which about twenty minutes is required. The mantle and
the lamp having been taken away, the tube R is rapidly removed, and its
contents tipped into the tube a of the calorimeter (fig. 399).

For this method of determining specific heat a new determination of the
latent heat of ice was made, and it was found to be 80*025. ^t was also in con-
nection with these experiments that Bunsen made his determination of the
specific gravity of ice, which he found to be in the mean 0-91674.

By the above method Bunsen determined the specific heat of several of
the rare metals for which a weight of only a few grains could be used.

452. iMCethod of mixtures. — In determining the specific heat of a solid
body by this method, it is weighed and raised to a known temperature, by
keeping it, for instance, for some time in a closed place heated by steam ;
it is then immersed in a mass of cold water, the weight and temperature of
which are known. From the temperature of the water after mixture the
specific heat of the body is determined.

Let M be the weight of the body, T its temperature, c its specific heat ;
and let tn be the weight of the cold water, and / its temperature.

As soon as the heated body is plunged into the water, the temperature of
the latter rises until both are at the same temperature. Let this temperature
be 6. The heated body has been cooled by T — ^ ; it has, therefore, lost a
quantity of heat, M (^ — &)c. The cooling water has, on the contrary, ab-
sorbed a quantity of heat equal to )ii{Q - 1), for the specific heat of water is
unity. Now the quantity of heat given out by the body is manifestly equal
to the quantity of heat absorbed by the water ; that is, M{T — 6{c = m{6 - 1),
from which

M(T-^'

An example will illustrate the application of this formula. A piece of
iron weighing 60 ounces, and at a temperature of 100° C, is immersed in
180 ounces of water, whose temperature is 19° C. After the temperatures
have become uniform, that of the cooling water is found to be 22° C. What
is the specific heat of the iron ?

Here the weight of the heated body, M, is 60, the temperature, T, is 100°,
c is to be determined ; the temperature of mixture, ^, is 22°, the weight of
the cooling water is 180, and its temperature 12°. Therefore

i8oi2^-i9)_^ ^0-1153.
60(100-22) 7?,

453. Corrections. — The vessel containing the cooling water is usually
a small cylinder of silver or brass, with thin polished sides, and is supported
by some badly conducting arrangement. It is obvious that this vessel, which
is originally at the temperature of the cooling water, shares its increase of
temperature, and in accurate experiments this must be allowed for. The
decrease of temperature of the heated body is equal to the increase of
temperature of the cooling water, and of the vessel in which it is contained.
If the weight of this latter be in', and its specific heat c', its temperature, like
that of the water, is / : consequently the previous equation becomes

Mf(T - ^) = m{6 - /) + 7n'c\6 - 1) ;

-454J Apparatus for Deterviiniiig Specific Heats. 427

from which, by obvious transformations,

_{m + 7n'c') {6-t)

Generally speaking, the value f/i'c' is put = fx ; that is to say, /x is the
weight of water which would absorb the same quantity of heat as the vessel.
This is said to be the reduced value in water of the vessel, or the water-equi-
valent. This expression accordingly becomes

(m-t-M)(^_zl)

M(T-^) ■

In accurate experiments it is necessary to allow also for the heat absorbed
by the glass and mercury of the thermometer, by introducing into the equa-
tion their values reduced on the same principle.

In order to allow for the loss of heat due to radiation, a preliminary experi-
ment is made with the body whose specific heat is sought, the only object
of which is to ascertain approximately the increase of temperature of the
cooling water. If this increase be 10°, for example, the temperature of the
water is reduced by half this number — that is to say, 5° — below the tempera-
ture of the atmosphere, and the experiment is then carried out in the
ordinary manner.

By this method of compensation, first introduced by Rumford, the water
receives as much heat from the atmosphere, during the first part of the
experiment, as it loses by radiation during the second part.

454. Re^nault's apparatus for determining: specific heats. — Fig. 403
represents one of the forms of apparatus used by Regnault in determining
specific heats during the method of mixtures.

The principal part is a water bath, AA, of which fig. 404 represents a
section. It consists of three concentric compartments ; in the central one
there is a small basket of brass wire, t-, containing fragments of the substance
whose specific heat is to be determined, in the middle of which is placed a
thermometer, T. The second compartment is heated by a current of steam
coming through the tube, e, from a boiler B, and passing into a worm, a.,
where it is condensed. The third compartment, z z, is an air chamber, to
hinder the loss of heat. The water bath, AA, rests on a chamber, K, with
double sides, EE, forming a jacket, which is kept full of cold water, in order
to exclude the heat from AA, and from the boiler, B. The central compart-
ment of the water bath is closed by a damper, r, which can be opened at
pleasure, so that the basket, 6", can be lowered into the chamber, K.

On the left of the figure is represented a small and very thin brass vessel,
D, suspended by silk threads on a small carriage, which can be moved out
of, or into, the chamber, K. This vessel, which serves as a calorimeter, con-
tains water, in w-hich is immersed a thermometer, /. Another thermometer
at the side, /', gives the temperature of the air.

When the thermometer T shows that the temperature of the substance
in the bath is stationary, the screen, ^, is raised, and the vessel, D, moved to
just below the central compartment of the water bath. The damper, r, is
then withdrawn, and the basket, c, and its contents are lowered into the water
in the vessel, D, the thermometer, T, remaining fixed in the corn. The

428

On Heat.

[454-

carriage and the vessel, D, are then moved out, and the water agitated until
the thermometer, T, becomes stationary. The temperature which it indicates
is 6. This temperature known, the rest of the calculation is made in the
manner described in art. 449, care being taken to make all the necessary
corrections.

In determining the specific heat of substances — phosphorus, for instance
— which could not be heated without causing them to melt, or undergo some
change which would interfere with the accuracy of the result, Regnault
adopted an inverse process : he cooled them down to a temperature con-
siderably below that of the water in the calorimeter, and then observed the
diminution in the temperature of the latter, which resulted from immersing
the cooled substance in it.

In determining the specific heat of substances, which, like potassium,
would decompose water, some other liquid, such as turpentine or benzole,

Fi-.

must be used. These liquids have the additional advantage of having a
lower specific heat than water, which has the highest of any liquid, so that an
error in determining the temperature of the cooling liquid has a less influence
on the value of the specific heat. With this view use has been made of
mercury, the specific heat of which is only one-thirtieth that of water.

-456] Method of Cooling. 429

455. Method of cooling-. — Equal weights of different bodies whose
specific heats are different, will occupy different times in cooling through
the same number of degrees. Dulong and Petit applied this principle in
determining the specific heats of bodies in the following manner : — A small
polished silver vessel is filled with the substance in a state of fine powder,
and a thermometer placed in the powder, which is pressed down. This
vessel is heated to a certain temperature, and is then introduced into a
copper vessel, in which it fits hermetically. This copper vessel is exhausted,
and maintained at the constant temperature of melting ice, and the time
noted which the substance takes in falling through a given range of tem-
perature, from 1 5° to 5'^ for example. The times which equal weights of dif-
ferent bodies require for cooling, through the same range of temperature,
are directly as their specific heats.

Regnault has proved that with solids this method does not give trust-
worthy results ; it assumes, which is not quite the case, that the cooling in
all parts is equal, and that all substances part with their heat to the silver
case with equal facility. The method may, however, be employed with
success in the determination of the specific heat of liquids.

In an investigation of the specific heats of various soils, Pfaundler found
that a soil of low specific heat heats and cools rapidly, while earth of higher
specific heat undergoes slow heating and slow cooling ; that moist earths
rich in humus have a high specific heat, amounting in the case of turf to as
much as 0-5 ; while diy soils free from humus, such as lime and sand, have
a low specific heat, not more than about 0-2.

456. Specific heat of liquids — The specific heat of liquids may be
determined either by the method of cooling, by that of mixtures, or by that
of the ice calorimeter. In the latter case they are contained in a small
metal vessel, or a glass tube, which is placed in the central compartment
(fig. 404), and the experiment then made in the usual manner.

A method devised by Pfaundler of determining the specific heat of
liquids, which under certain circumstances is advantageous, depends on a
property of the electrical current of heating any conductor through which
it passes.

In two equal calorimeters containing the liquids to be tested, together
with suitable thermometers and stirrers, two equal spirals of fine platinum
wire are placed. These are connected with a voltaic battery by means of
copper wires, and if the same current of electricity be simultaneously
passed through each of them, which can be very accurately done, the heat
produced in the wires will be equal, and the rise in tem.perature in the
liquids will then be inversely as the specific heats. One of the liquids is
usually water.

It will be seen from the table in the following article that water and oil
of turpentine have a much greater specific heat than other substances, and
more especially than the metals. It is from its great specific heat that water
requires a long time in being heated or cooled, and that for the same weight
and temperature it absorbs or gives out far more heat than other substances.
This double property is applied in the hot-water apparatus, of which we
shall afterwards speak, and it plays a most important part in the economy of
nature.

430 On Heat. [457-

457. Specific heats of bodies. — The list contained in the next article
(458) gives the specific heats of a great number of elementary substances.
We give here the specific heats of a few substances, mostly liquids : —

Specific heat Specific heat

Turpentine . . . 0-426 Bisulphide of carbon . o"245

Alcohol. . . . 0-062 Thermometer glass . 0-198

Ether . . . .0-516 Steel . . . . o-ii8

Glycerine . . -0-555 Brass .... 0-094

The specific heat of water is commonly taken at unity, which is not
strictly correct. According to the most recent determinations the 7nean
specific heat between 0° and / is expressed by the formula i +0-00015/.

These numbers, as well as the numbers in (458), represent the mean
specific heats between 0° and 100°. It was shown by Dulong and Petit
that the specific heats increase with the temperature. Those of the metals,
for instance, are gi-eater between 100° and 200° than between 0° and 100°,
and are still greater between 200° and 300° ; that is to say, a greater amount
of heat is required to raise a body from 200° to 250'^ than from 100° to 150"^,
and still more than from 0° to 50°. For silver, the mean specific heat
between 0° and 100° is 0-057, while between 0° and 200° it is 0-061 1. The
following table gives the specific heats at various temperatures : —

Copper ....... 0-0910 + 0-000046/

Zinc 0-0865+0-000088/

Lead 0-0286 + 0-000038/

Platinum ....... 0-0317 + 0-0000062/

Water i + 0-00030/

The increase of specific heat with the temperature is greater as bodies
are nearer their fusing point. Any action which increases the density and
molecular aggregation of a body, diminishes its specific heat. Thus hard
steel with the density 7-798 has the sp. heat o-i 175 ; while that of soft steel
of density 7-861 is o-i 165. The specific heat of copper is diminished by its
being hammered, but it regains its original value after the metal has been
again heated.

The specific heat of a liquid increases with the temperature much more
rapidly than that of a solid. Water is, however, an exception : its specific
heat increases less rapidly than does that of solids.

The most remarkable examples of the influence of temperature on the
specific heat are afforded by carbon, boron, and 'sihcon. Weber has found
that at 600° the specific heat of carbon is 7 times, and that of boron 2\ times,
as great as their respective specific heats at — 50°. The specific heat of
diamond is 0-0635 ^^ —50°, 0-1318 at '^'^°, 0-2218 at 140°, and 0-3026 at 247°.
Although the specific heat increases thus rapidly between - 50'' and 250°,
beyond that point the rate of increase is slower ; and beyond 600°, or at an
incipient red heat, it seems to be pretty constant, or at any rate to exhibit
no greater variations with the temperature than are afforded by other sub-
stances. Thus while at 600° the specific heat is 0-441, at 985° it is 0-459.
Graphite also has at 22° the specific heat 0-168 ; this increases, but at a
gradually diminishing rate, to 642°, where its specific heat is 0-445. Like

-457] Specific Heats of Bodies. 43 1

diamond, an incipient red heat seems to be a limiting temperature beyond
which graphite exhibits only the ordinary variation with the temperature.
Weber has also found that, in their thermal deportment, there are only two
essentially different modifications of carbon— the transparent one (diamond),
and the opaque ones (graphite, dense amorphous carbon, and porous amor-
phous carbon).

Crystallised boron is similar in its deportment to carbon ; its specific
heat increases from 0-1915 at -40° to 0-2382 at 27°, and to 0-3663 at 233°.
The rate of increase is very rapid up to 80° ; it increases beyond that
temperature, but at a gradually diminished rate, and, no doubt, tends to an
almost constant value of 0-5.

The specific heat of silicon also varies with the temperature ; between
-40° and 200° it increases from 0-136 to 0-203 ; the rate of increase is less
rapid with higher temperatures, being at 200° only ^^ what it is at 10°. At
200° it reaches its limiting value.

The specific heat of substances is greater in the liquid than in the solid
state, as will be seen by the following table : —

Solid Liquid

Water 0-502 i-qoo

Sulphur 0-203 0-234

Bromine 0-084 o-iio

Iodine 0-054 o-oo8

Mercury 0-031 0-033

Phosphorus . . . . . .0-190 0-212

Tin 0-056 0-064

Lead 0-031 0-040

It also differs with the allotropic modification ; thus the specific heat of
red phosphorus is 0-19, and that of white 0-17; of crystallised arsenic
0-083, and of amorphous 0*058 ; of crystallised selenium 0-084, and of
amorphous 0-0953 ; of wood charcoal 0-241 5 of graphite 0-202 ; and of
diamond 0-147.

Pouillet used the specific heat of platinum for measuring high decrees of
heat. Supposing 200 ounces of platinum had been heated in a furnace and
had then been placed in 1,000 ounces of water, the temperature of which it
had raised from 13° to 20°. From the formula we have M = 200, in 1000 •
6 is 20, and / is 13. The specific heat of platinum is 0-033, and we have
therefore, from the equation —

yicij-e) = m{e-t)

^ ^ i)i{6-f) + M6-g ^ 7000+132 ^ 7232 ^
Vlc 6-6 6-6

It is found, however, that the mean specific heat of platinum at tempera-
tures up to about 1200° is 0-0377 ; if this value, therefore, be substituted for
c in the equation, we have —

T = 7J-5^S = 948°C.

7-54

By this method, which requires great skill in the experimenter, Pouillet
determined a series of high temperatures. He found, for example, the tem-
perature of melting iron to be 1500° to 1600° C.

432 On Heat. [458-

458. Dulong and Petit's law. — A knowledge of the specific heat of
bodies has become of great importance, in consequence of Dulong and Petit's
discovery of the remarkable law, that the product of the specific heat of any
solid element into its atomic weight is approximately a constant number, as
will be seen from the following table : —

Specific heat

Atomic weight

Atomic heat

Aluminium

0-2143

27-4

5-87

Antimony

0-0513

122

6-26

Arsenic .

0-0822

6-17

Bismuth .

0-0308

210

6-47

Bromine .

0-0843

6-74

Cadmium

0-0567

112

6-35

Cobalt .

0-1067

58-7

6-26

Copper .

0-0939

63-5

5 "99

Gold .

0-0324

197

6-38

Iodine .

0-0541

127

6-87

Iron

O-II38

6-37

Lead .

0-0314

207

6-50

Magnesium

0-2475

5-94

Mercury .

0-0332

200

6-64

Nickel .

0-1092

58-7

6-41

Phosphorus

0-1740

31-0

5-39

Platinum

0-0324

197-5

6-40

Potassium

0-1655

39-1

6-47

Silver .

i 0-0570

108-0

6-i6

Sulphur .

0-178

570

Tin

0-0555

118

6-55

Zinc

0-0950

65-2

6-23

It will be seen that the number is not a constant, but varies between 5-39
and 6-87. These variations may depend partly on the difficulty of getting
the elements in a state of perfect purity, and partly on errors incidental
to the determination of the specific heats, and of the atomic weights. Again,
the specific heats of bodies vary with the state of aggregation of the bodies,
and also with the temperatures at which they are determined ; some, such
as potassium, have been determined at temperatures very near their fusing
points ; others, like platinum, at temperatures much removed from them. A
prominent cause, therefore, of the discrepancies is doubtless to be found in
the fact that all the determinations have not been made under correspondmg'
physical conditions.

The atomic weights of the elements represent the relative weights of equal
numbers of atoms of these bodies, and the product, pc, of the specific heat,
c, into the atomic weight, p, is the atomic heat, or the quantity of heat
necessary to raise the temperature of the same number of atoms of different
substances by one degree ; and Dulong and Petit's law may be thus ex-
pressed : the same quantity of heat is needed to heat an atom of all simple
bodies to the same extent.

The atomic heat of a body, when divided by its specific heat, gives the

-459] Specific Heat of Compound Bodies. 433

atomic weight of a body. Regnault proposed to use this relation as a
means of determining the atomic weight, and it certainly is of great service
in deciding on the atomic weight of a body in cases where the chemical
relations permit a choice between two or more numbers.

According to modern views, the heat imparted to a body is partly expended
in external work, which in the case of a solid would be extremely small, be-
ing only that required for raising the pressure of the atmosphere through a
distance representing the expansion ; secondly, the internal work, or the heat
used in overcoming the attraction of the atoms for each other, and forcing
them apart ; and thirdly, there is the true specific heat., or the heat applied in
increasing the temperature — that is, in increasing the vis viva of the molecules
(448). By far the most considerable of these is the latter ; the amount of
heat consumed in the two former operations is small, and the variations
with different bodies must be inconsiderable. Until, however, the relation
between the various factors is made out, absolute identity in the numbers
for the atomic specific heat cannot be expected. Weber holds that even
when due allowance has been made for these circumstances, the variations
are too great to be accounted for, and he considers that they point for their
explanation to an alteration in the constitution of the atom, and render
probable a changing valency of the atom of carbon.

459. specific beat of compound bodies. — In compound bodies the law
also prevails : the product of the specific heat into the equivalent is an al-
most constant number, which varies, however, with different classes of bodies.
Thus, for the class of oxides of the general formula RO, it is 11 -30 ; for the
sesquioxides R-'O^ it is 27-15 ; for the sulphides RS, it is i8-88 ; and for the
carbonates RCO^, it is 21-54. The law, which is known as Neiimamis law.,
maybe expressed in the following general manner: — With compounds of
the same fynnula, and of a similar chemical constitution, the product of the
atomic weight into the specific heat is a consta?it qiui7itity. This includes
Dulong and Petit's law as a particular case.

Kopp propounded the following law, which is an extension of that of
Neumann : — The molecular heats of all solid bodies are equal to the sum or
thfi molecular heats of the elements contained iii them. Dulong and Petit's
law that all elements have the same atomic heat he does not consider uni-
versally valid. He assigns the number 6-4 to all elements excepting the fol-
lowing ; with sulphur and phosphorus it is 5-4, fluorine 5-0, oxygen 4-0
siUcon 3-8, boron 2-7, hydrogen 2-3, and carbon rS.

Even with this modification it is found that the calculated heats of com-
pounds differ more from the observed ones than can be ascribed to errors in
the determination of the specific heats. This is probably due to the fact that
some of the heat is expended in internal work, and that it is this which brino-s
about the discrepancies.

With mixtures of alcohol and water in certain proportions, the specific
heat is greater than that of the water ; thus, that of a mixture containing 20
per cent, of alcohol was found by Dupre and Page to be 1-0456. No general
law can be laid down for solutions of acids or of salts in water ; though the
specific heat is most frequently less than that calculated from the consti-
tuents.

434

On Heat.

[460

460. Specific heat of g-ases. — The specific heat of a gas may be re-
ferred either to that of water or to that of air. In the former case it repre-
sents the quantity of heat necessary to raise a given weight of the gas through
one degree, as compared with the heat necessary to raise the same weight
of water one degree. In the latter case it represents the quantity of heat
necessary to raise a given volume of the gas through one degree, compared
with the quantity necessary for the same volmne of air treated in the same
manner.

De la Roche and Berard determined the specific heats of gases in re-
ference to water by causing known volumes of a given gas under constant
pressure, and at a given temperature, to pass through a spiral glass tube
placed in water. From the increase in temperature of this water, and from
the other data, the specific heat was determined by a calculation analogous;
to that given under the method of mixtures. They also determined the
specific heats of different gases relatively to that of air, by comparing the
quantities of heat which equal volumes of a given gas, and of air at the same
pressure and temperature, imparted to equal weights of water. Subsequently
to these researches, De la Rive and Marcet applied the method of cooling to
the same determination ; and more recently Regnault made a series of in-
vestigations on the calorific capacities of gases and vapours, in which he
adopted, but with material improvements, the method of De la Roche and
Berard. He thus obtained the following results for the specific heats of the
various gases and vapours, compared first with the specific heat of an equal
weight of water taken as unity ; secondly, with that of an ecjual volume of
air, referred, as before, to its own weight of water taken as unity : —

Specific heats

Equal

weights

volumes

Air ....

. 0-2374

0-2374

■ Oxygen ....

. 0-2I74

0-2405

Simple

Nitrogen

. 0-2438

0-2370

gases

Hydrogen

3-4090

0-2359

Chlorine

. 0-I2I0

0-2962

/ Binoxide of nitrogen .

• 0-2315

0-2406

Carbonic oxide

. 0-2450

0-2370

Compound

Carbonic acid

. 0-2163

0-3307

gases

Hydrochloric acid

. 0-1845

0-2333

Ammonia

. 0-5083

0^2966

>01efiant gas .

. 0-4040

0-4106

/Water ....

. 0-4805

0-2984

Ether ....

. 0-4810

1-2296

Vapours

Alcohol.

• 0-4534

0-7171

Turpentine .

. 0-5061

2-3776

Bisulphide of carbon .

. 0-1570

0-4140

Benzole.

• 0-3754

I -01 14

In making these determinations the gases were under a constant pressure,
but variable volume ; that is, the gas as it was heated could expand, and
this is called the specific heat under co7istant pressure. But if the gas when
being heated is kept at a constant volume, its pressure or elastic force then

-461] Latent Heat of Fusion. 43 5

necessarily increasing, it has a different capacity for heat ; this latter is
spoken of as the specific heat imder constant volume. That this latter is less
than the former is evident from the following considerations : —

Suppose a given quantity of gas to have had its temperature raised /"
while the pressure remained constant, this increase of temperature will have
been accompanied by a certain increase in volume. Supposing now that
the gas is so compressed as to restore it to its original volume, the result of
this compression will be to raise its temperature again to a certain extent,
say t'°. The gas will now be in the same condition as if it had been heated
and had not been allowed to expand. Hence, the same quantity of heat which
is required to raise the temperature of a given weight of gas, /°, while the
pressure remains constant and the volume alters, will raise the temperature
t-^f degrees if it is kept at a constant volume but variable pressure. The
specific heat, therefore, of a gas at constant pressure, c, is greater than the
specific heat under constant volume, t;, and they are to each other as /+ /': /,

that IS = .

c, t
It is not possible to determine by direct means the specific heat of gases
under constant volume with much approach to accuracy ; and it has been
determined by some indirect method, of which the most accurate is based
on the theory of the propagation of sound (229). A critical comparison of
the most accurate recent determinations gives the number i -405 for the value

of ^ , which is usually designated by the symbol k. *

461. Xiatent heat of fusion. — Black was the first to observe that during
the passage of a body from the solid to the liquid state, a cjuantity of heat
disappears, so far as thermometric effects are concerned, and which is
accordingly said to become latent.

In one experiment he suspended in the room at a temperature 8-5° two
thin glass flasks, one containing water at 0°, and the other the same weight
of ice at 0°. At the end of half an hour the temperature of the water had
risen 4°, that of the ice being unchanged, and it was \o\ hours before the
ice had melted and attained the same temperature. Now the temperature
of the room remained constant, and it must be concluded that both vessels
received the same amount of heat in the same time. Hence 21 times as
much heat was required to melt the ice and raise it to 4° as was sufficient
to raise the same weight of water through 4°. So that the total quantity of
heat imparted to the ice was 21x4 = 84; and as only 4 of this was used in
raising the temperature, the remainder, 80, was used in simply melting the
ice.

He also determined the latent heat by immersing 119 parts of ice at 0°
in 135 parts of water at 877° C. He thus obtained 254 parts of water at
1 1 '6° C. Taking into account the heat received by the vessel in which the
liquid was placed, he obtained the number 79*44 as the latent heat of lique-
faction of ice.

We may thus say

Water at 0°= Ice at 0° + latent heat of liquefaction.

The method which Black adopted is essentially that which is now used

436 On Heat. [461-

for the determination of latent heats of Uquids ; it consists in placing the
substance under examination at a known temperature in the water (or other
Hquid) of a calorimeter, the temperature of which is sufficient to melt the
substance if it is solid, or to solidify it if liquid ; and when uniformity of
temperature is established in the calorimeter, this temperature is determined.
Thus, to take a simple case, suppose it is required to determine the latent
heat of the liquidity of ice. Let M be a certain weight of ice at zero, and in
a weight of water at f sufficient to melt the ice. The ice is immersed in
the water, and as soon as it has melted, the final temperature 6° is noted.
The water, in cooling from f to 6°, has parted with a quantity of heat,
m {t-6). If X be the latent heat of the ice, it absorbs, in liquefying, a
quantity of heat M.i" ; but, besides this, the water which it forms has risen
to the temperature 6°, and to do so has required a quantity of heat, repre-
sented by M^°. We thus get the equation

from which the value x is deduced.

By this method Desains and De la Provostaye found that the latent heat
of the liquefaction of ice is 7Q'2 5 : that is, a pound of ice, in liquefying,
absorbs the quantity of heat which would be necessary to raise 79"25 pounds
of water i°, or, what is the same thing, one pound of water from zero to
79-25°. Bunsen's most recent determination gives 80-025 (450-

This method is thus essentially that of the method of mixtures : the same
apparatus may be used, and the same precautions are required, in the two
cases. In determining the latent heat of liquefaction of most solids, the diffe-
rent specific heats of the substance in the solid and in the liquid state require
to be taken into account. In such a case, let ;// be the weight of the water
in the calorimeter (the water ecjuivalents of the calorimeter and thermometer
supposed to be included) ; M the weight of the substance worked with ; / the
origmal and 6 the final temperature of the calorimeter ; T the original tem-
perature of the substance ; C its melting (or freezing) point ; C the specific
heat of the substance in the solid state between the temperature % and 6 ; c
its specific heat in the liquid state between the temperatures T and % ; and
let L be the latent heat sought.

If the experiment be made on a melted substance which gives out heat
to the calorimeter and is thereby solidified (it is taken for granted that a
body gives out as much heat in solidifying as it absorbs in liquefying), it is
plain that the quantity of heat absorbed by the calorimeter, ;;z(^-/), ismade
up of three parts ; first, the heat lost by the substance in cooling from its
original temperature T to the solidifying point C ; secondly, the heat given
out in solidification, ML ; and, thirdly, the heat it loses in sinking from its
solidifying point €", to the temperature of the water of the calorimeter.
That is :

;«(^_/) = M r(T-r)6- + L + ((r-^)c1

whence, i^J<Q^t)^^T-^)c-{^-b)Q.

The following numbers have been obtained for the latent heats of
fusion : —

-462] Dcteruiination of the Latent Heat of Vapour. 437

Water .

. 80-03

Cadmium

. 13-66

Nitrate of Sodium

. 62-97

Bismuth

. 12-64

„ „

Potassium

• 47-37

Sulphur

• 9-37

Zinc

• 28-13

Lead .

■ 5-37

Platinum

. 27-18

Phosphorus .

• 5-03

Silver .

. 21-07

D'Arcet's alloy

• 4-50

Tin

• 14-25

Mercury

. 2-83

These numbers represent the number of degrees through which a pound
of water would be raised by a pound of the body in question in passing
from the liquid to the solid state ; or, what is the same thing, the number of
pounds of water that would be raised i^ C. by one of the bodies in solidi-
fying.

On modern views the heat expended in melting is consumed in moving
the atoms into new positions ; the work, or its equivalent in heat required
for this — the potential energy they thus acquire, is strictly comparable to the
expenditure of work in the process of raising a weight. When the liquid
solidifies, it reproduces the heat which had been expended in liquefying the
solid : just as when a stone falls it produces by its impact against the ground
the heat, the equivalent of which in work had been expended in raising it,
and a similar explanation applies to the latent heat of gasification.

462. netermination of the latent beat of vapour. — Liquids, as we
have seen, in passing into the state of vapour, absorb a very considerable
quantity of heat, which is termed
latent heat of vaporisation. In deter-
mining the heat absorbed in vapours,
it is assumed that a vapour in liquefy-
ing gives out as much heat as it had
absorbed in becoming converted into
vapour.

The method employed is essentially
the same as that for determining the
specific heat of gases. Fig. 405 repre-
sents the apparatus used by Despretz.
The vapour is produced in a retort,
C, where its temperature is indicated
by a thermometer. It passes into a
worm SS immersed in cold water,
where it condenses, imparting its
latent heat to the condensing water in the vessel B.
is collected in a vessel, A, and its weight represents the quantity of vapour
which has passed through the worm. The thermometers in B gi^•e the
change of temperature.

Let M be the weight of the condensed vapour, T its temperature on
entering the worm, which is that of its boiling point, and x the latent heat of
vaporisation. Similarly, let vi be the weight of the condensing water (com-
prising the weight of the vessel B and of the worm SS reduced va water), let
t° be the temperature of the water at the beginning, and 6° its temperature
at the end of the experiment.

Fig. 405.

The condensed vapour

438

On Heat.

[462-

It is to be observed that, at the commencement of the experiment, the
condensed vapour passes out at the temperature /°, while at the conclusion
its temperature is 6° ; we may, however, assume that its mean temperature

during the experiment is ^ '. The vapour M after condensation has

therefore parted with a quantity of heat M

(t-~)

f, while the heat

disengaged in liquefaction is represented by yix. The quantity of heat
absorbed by the cold water, the worm, and the vessel is m{Q — t). There-
fore,

M;i-+ J

M ('T-^^^y- = ;/<^-/),

from which x is obtained. Despretz found that the latent heat of aqueous
vapour at ioo° is 540 ; that is, a pound of water at 100° absorbs in vaporising
as much heat as would raise 540 pounds of water through 1°. Regnault
found the number 537, and Favre and Silbermann 538-8.
As in the case of the latent heat of water we may say,

Steam at 100° = water at 100° + latent heat of gasification.

Bertholet uses the veiy convenient
apparatus represented in fig. 406, for deter-
mining latent heats of vaporisation. The
liquid in the flask D is heated by the ring
burner B, and the vapour which forms passes
through the tube ab into the serpentine S>
where it condenses and collects in the bulb
R. These are contained in the calorimeter
C, the top of which is closed by a wooden
cover HH , and a layer of felt, NN' ; they
cut off any heat from the flask D and from
the burner B. As the serpentine SR can
be detached from ab, it is easy to deter-
mine the weight of the distillate ; from this,
and from the rise in temperature of the water
in the calorimeter, the latent heat can be
readily calculated.

In the conversion of a body from the
liquid into the gaseous state, as in the
analogous process effusion (461), one part of
the heat is used in increasing the temperature
and another in internal -work. For vaporisation, the greater portion is con-
sumed in the internal work of overcoming the reciprocal attraction of the
particles of liquid, and in removing them to the far greater distances apart
in which they exist in the gaseous state. In addition to this there is the
external work — namely, that required to overcome the external pressure,
usually that of the atmosphere : and as the increase of volume in vaporisa-
tion is considerable, this pressure has to be raised through a greater space.
Vaporisation may take place without having external work to perform,
as when it is effected in \acuo ; but whether the evaporation is under a high

-463J

Favre and Silba'inami s Calorimeter.

439

or under a low pressure, on the surface of a liquid or in the interior, there
is always a great consumption of heat in internal work.

463. Pavre and Sllbermann's Calorimeter. — The apparatus (fig. 407)
furnishes a very delicate means of determining the calorific capacity of
liquids, latent heats of evaporation, and the heat disengaged in chemical
actions.

The principal part is a spherical iron reservoir, A, full of mercury, of
which it holds about 50 pounds, and represents, therefore, a volume of more
than half a gallon. On the left there are two tubulures, B, in which are
fitted two sheet-iron tubes or iimffles, projecting into the interior of the bulb.
Each can be fitted with a glass tube for containing the substance experl-

Fig. 407.

mented upon. In most cases one muffle and one glass tube are enough ;
the two are used when it is desired to compare the quantities of heat pro-
duced in two different operations. In a third vertical tubulure, C, there is
also a muffle, which can be used for determining calorific capacities by
Regnault's method (454), in which case it is placed beneath the ?■ of fig. 403.
The tubulure d contains a steel piston ; a rod turned by a handle, ;?/,
and which is provided with a screw thread, transmits a vertical motion to
the piston ; but, by a peculiar mechanism, gives it no rotatory motion. In
the last tubulure is a glass bulb, a, in which is a long capillary glass tube, bo,
divided into parts of equal capacity.

440

On Heat.

[463-

It will be seen from this description that the mercury calorimeter is
essentially a thermometer with a very large bulb and a capillary stem : it
is therefore extremely delicate. It dififers, however, from a thermometer in
the fact that the divisions do not indicate the temperature of the mercury
in the bulb, but the number of thermal units imparted to it by the substances
placed in the muffle.

This graduation is effected as follows ; — By working the piston the
mercuiy can be made to stop at any point of the tube, bo^ at which it is
desired the graduation should commence. Having then placed in the iron
tube a small quantity of mercury, which is not afterwards changed, a thin

glass tube, e, is inserted,
which is kept fixed against
the buoyancy of the mer-
cury by a small wedge
not represented in the
figure. The tube being
thus adjusted, the point
of a bulb tube (see fig.
408) is introduced, con-
taining water which is
raised to the boiling
point : turning the posi-
tion of the pipette, then,
as represented in n\ a
quantity of the liquid flows
into the test tube.

The heat which is thus imparted to the mercury makes it expand ; the
column of mercury in bo is lengthened by a number of divisions, which we
shall call n. If the water poured into the test glass be weighed, and if its
temperature be taken when the column bo is stationary, the product of the
weight of the water into the number of degrees through which it has fallen
indicates the number of thermal units which the water gives up to the entire
apparatus (447). Dividing, by n, this number of thermal units, the quotient
gives the number, «, of thermal units corresponding to a single division of
the tube bo.

In determining the specific heat of liquids, a given weight, M, of the
liquid in question is raised to the temperature T, and is poured into the tube
C. Calling the specific heat of the liquid t", its final temperature ^, and 71
the number of divisions by which the mercurial column bo has advanced, we
have

Mt-(T ■

«rt, from which c

M(T-^)

The boards represented round the apparatus are hinged so as to form a
box, which is lined with eider-down or wadding, to prevent any loss of heat.
It is closed at the top by a board, which is provided with a suitable case,
also lined, which fits over the tubulures d and a. A small magnifying glass
which slides along the latter, enables the divisions on the scale to be read

-464] Examples. 441

464. Examples.— I. What weight of ice at zero must be mixed with g
pounds of water at 20° in order to cool it to 5° ?

Let M be the weight of ice necessary ; in passing from the state of ice
to that of water at zero, it will absorb 80M thermal units ; and in order to
raise it from zero to 5'^, 5M thermal units will be needed. Hence the total
heat which it absorbs is 80M + 5M = 85M. On the other hand, the heat
given up by the water in cooling from 20° to 5° is 9 x (20-5)= 135. Con-
sequently,

85M = 135 ; from which M = 1-588 pounds.

II. What weight of steam at 100° is necessary to raise the temperature
of 208 pounds of water from 14° to 32° ?

Let^ be the weight of the steam. The latent heat of steam is 540°, and
consequently^ pounds of steam in condensing into water give up a quantity
of heat, 540^, and form^ pounds of water at 100°. But the temperature of
the mixture is 32^, and therefore p gives up a further quantity of heat
p (100- 32) = 68/, for in this case c is unity. The 208 pounds of water in
being heated from 14° to 32° absorb 208(32 - 14) = 3744 units. Therefore

540/ + 68/ = 3744 ; from which/ = 6-58 1 pounds.

442 On Heat. [465-

CHAPTER X.

STEAM ENGINES.

465. Steam Eng-ines. — Steam engines are machines by which heat
energy, obtained by the combustion of some fuel, is turned into mechanical
work, aqueous ^•apour being used as a working fluid for effecting the trans-
formation. In all but a few very exceptional cases the mechanical means
used for the transformation of the one form of energy into the other are as
follows : — the heat of combustion is, as far as possible, imparted to water in
a closed vessel called a boiler ; the water is thereby converted into steam,
occupying an enormously greater volume, and this steam is allowed to pass
from the boiler as fast as it is formed, and to act alternately on the two sides
of a movable piston working backwards and forwards in a cylinder. As soon
as the piston has been pushed to either end of the cylinder by the incoming
steam acting on one side of it, the communication between that side and the
boiler is shut off, and another communication opened either to a condenser
or to the atmosphere. In either case the steam rushes out of the cylinder
and the pressure against the piston falls, so that it can be pushed back by
fresh steam from the boiler acting on its opposite side. If the purpose of
the engine is merely to work pumps, or any other apparatus requiring only a
reciprocating motion, a rod from the piston can be connected directly, or
through a lever, to the pump to be worked. If, however, as in a majority of
cases, the engine has to drive something having a rotary motion, a simple
mechanism is used to change the reciprocating motion of the piston into the
rotation of a crank. In this change itself there is no loss of work or energy
(471), the work of the steam on the piston being exactly equal to the work
done at the rotating crank-pin, minus only the lost work spent in overcoming
the friction of the joints of the mechanism.

We shall first consider the boiler, or apparatus for generating steam, and'
then the engine itself.

466. Steam boiler. — Figs. 409 and 410 show one of the forms of boiler
most commonly used in this country for supplying steam to stationary engines.
This type of boiler is called Cornish, having been first used for the pumping
engines in Cornwall. Fig. 409 shows a longitudinal section of the boiler and
the brick flues in which it is set, and fig. 410 shows on the left a half- front
view of the boiler and on the right a half cross section. The boiler consists
of an outer cylindrical shell A of wrought iron or steel plates riveted together,,
and a smaller internal flue or furnace B. The latter is open at both ends,
and is crossed by a series of vertical tubes C, called Galloway tubes, which
allow the water to circulate from the lower to the upper part of the boiler.
The fire is placed on a grate D in the front part of the flue and ending
in a ■ firebrick ^?7Vi^^ over which the gases have to pass. These hot gases

-466]

Steam Boiler.

443

find their way past the tubes to the back of the boiler and then are com-
pelled to diverge sideways and return by the side flues K to nearly the front
of the shell where the flues are diverted downwards, as shown in fig. 410,
and thence they return by the lower flue L to the chimney M. By thus

,-^

-^^-

WATCR LIME

QODOQH

Fig. 4og.

encircling the boiler with flues it is endeavoured to get all the heat possible
from the gases before they are allowed to pass away up the chimney. The
principal yf/Z/V/o-j- or inoimthtgs of the boiler are indicated in the figures and
are as follows : G is a dome on which stands the stop-valve N through which
the steam is carried to the engine. The object of the dome is to take the
steam from a point as far away from the
water line as possible, so as to dry it. P is
a safety valve., held down on its seat by the
action of a weighted lever, and so adjusted
that as soon as the pressure of steam reaches
its intended maximum and tends to rise
beyond it, the valve is lifted and the steam
rushes away into the air. Q is a manhole
door by which access is had to interior of the
boiler, when it is empty and out of use, for
cleaning and repair. R is a pressure gauge
or indicator, standing in front of the shell,
showing, by a hand working in front of a dial
plate, the 'boiler pressure' or amount which
the pressure of steam inside the boiler ex-
ceeds that of the atmosphere surrounding it. S is a water gatige, a glass
tube connected at top and bottom to the boiler, its upper end to the steam
space, and the lower end to the water space. The water stands in the glass
tube at the same level as in the boiler, and the fireman can see at a glance
whether it is at the right height. This matter is of great importance,
because an accidental fall of water-level is a frequent cause of boiler explo-
sions. If, for instance, the water fell so low as to leave the top of the furnace
B uncovered, the plates would get red-hot and soften so much as to collapse

Fig. 41

444

On Heat.

[466-

under the action of the steam pressure, with consequences that might be
most serious.

In marine boilers, when it is of the greatest importance to get as much
heating surface as possible into a small space, and similarly in the locomotive
boiler to be presently described, the hot gases after leaving the furnace are
made to pass through a number of small tubes instead of one large one as in
fig. 409. Such boilers are called multiticbidar boilers.

Of late years the shells of large boilers have frequently been made of
' mild steel,' produced by the Bessemer or Siemens-Martin processes, rather
than of wrought iron. In locomotive boilers, where the combustion is very
rapid and intense, the fire-boxes are frequently made of copper, a much
better conductor of heat than either iron or steel.

467. Cornish eng-ine. — Fig. 411 shows the oldest of all the types of
engines still in use, the Cornish piunping engine., which is worth examina-
tion both for its historical interest and on account of the special way in
which it works. (In the figure all details except those absolutely necessary
to illustrate the action of the engine are omitted.) The engine has a vertical

Fig. 411.

cylinder A (often of very great size, and with as much as 10 or 11 ft. stroke),
in which works a piston P, whose rod is connected by a chain to a sector on
the end of a beam B. Beside the cylinder is a chamber C containing the
valves for admitting and discharging steam, whose mode of working will be
presently described. At the further end of the beam a second sector is

-467] Cornish Engine. 445

connected with the pump-rod, at the upper end of which is placed a hea\y
counterweight Q. Below the cylinder a pipe AI leads to a chamber N called
the condejiser^ into which a jet of water from the tank in which it stands
continually plays. The condenser in its turn is connected with a pump
called an air-pump, worked from the beam by the rod E, and fitted with
suction and discharge valves, and valves in its piston in the usual way.

We can follow the working of the engine easily by supposing the piston
to start at the top of its stroke. The valves are then in the position shown,
ni open, n and 0 closed. Steam passes from the boiler through the pipe T
to the top of the piston, and forces it down against the small pressure of the
steam below it, this steam escaping into the condenser through the valve o
and the pipe M. The pump-rods or pit work., and the weight Q, are thus
lifted to the top of their stroke. When the piston arrives at the bottom of
its stroke the valves w and 0 are shut and n is opened. This allows free
communication between the two sides of the piston, and so puts it into
equilibrium. The counter-weight Q, together with the pump-rods, is made
somewhat heavier than the piston and rod plus the whole weight of the
column of water to be hfted. It therefore falls slowly (the whole affair thus
becommg an Attwood's machine ij"]) on an enormous scale), and forces
up the water through the pumps. As soon as the piston has once more
got to the top of its stroke, by which time of course all the steam has been
transferred to its under side, the position of the valves is again reversed,
and the piston once more begins to fall. The steam below the piston is
suddenly put into communication with the condenser N, into which a jet of
cold water is always playing. It is therefore reduced in temperature almost
instantaneously, much of it is condensed into water, and the rest, which still
fills the space below the piston, is necessarily reduced to a pressure of only
about 3 pounds per square inch or about \ of an atmosphere. As the pres-
sure of the steam coming direct from the boiler in such engines is often 50
pounds per sq. inch above that of the atmosphere, it follows that the differ-
ence of pressure on the two sides of the piston in such a case, is 50 -t- 15 - 3
= 62 pounds per square inch, and it is this difference of pressure which
compels the piston to move downwards and lift all the weight at the other
end of the beam. The condensed steam and the condensing water fall
together at the bottom of the condenser, and are continually removed (along
with the uncondensed steam and any air that may be present) by the air
pump., which is a simple lift pump with a valve in its piston (216).

In all modern Cornish engines the beams are of iron and the sector and
chains are replaced by an arrangement of iron links forming ?i. pai-allel motio7t
which it is not necessary here to describe. The simple arrangement for
working the valves, shown in outline in the figure, is also replaced by a much
more complicated apparatus in which, by means of cataracts., any required
length of pause can be made between the strokes of the engine, a matter
which is sometimes of importance in heavy pumping work. It will be
noticed that by the peculiar single-acting method of working adopted in
the Cornish engine, the velocity of the down stroke (also called the steam
stroke., or the indoor stroke) depends — other things being equal — upon the
steam pressure, but the velocity of the up stroke {eqiiilibriuni or outdoor
stroke) depends solely on the overplus weight put on the outer end of the

446

On Heat.

[467-

beam. In this way a slow and quiet upward motion can be given to the
water, no matter how quickly the steam may move the piston.

468. Ordinary horizontal engine.- — The engines now most largely
used in factories for driving machinery differ altogether in their action from
the Cornish engine. In them the cylinder is generally horizontal, and the
crank is driven through a connecting rod only, without the intervention of
any beam. Such an engine is shown in fig. 412. Here A is the steam

Fig. 4

cylinder, B the valve chest, or chamber in which works the valve whose mode
of action is described in the next article. D is the main shaft, on the inner
end of which is the crank driven by the connecting rod E. C is an eccetitric
(fig. 414), which works the valve by the rod N. F is ?i governor controlling
the admission of steam to the cylinder by the valve H. M is the bedplate
or frame of the engine, and L the flywheel.

A few words are necessary about the governor. This apparatus, an
invention of James Watt's, consists of two weighted arms hinged at the top,
which fly outward when the speed of rotation is increased and drop together
when it is reduced. The outward or inward motion of the arms is caused
by a simple arrangement to turn the spindle G and so to close or open the
valve H, which admits steam through K to the cylinder. In this way the
engine automatically controls its own speed (471).

469. Distribution of the steam. Slide valves. — Figs. 413 and 414
show details as to the working of the valve and the chstribution of the steam
in the engine just described. The former is a longitudinal section of the
cylinder shown m fig. 412. A is the cylinder itself, B the piston, C the
piston-rod, D the stuffing-box through which the piston passes steam-tight.
It will be seen that deport or passage L communicates between each end of
the cylinder and the surface on which the valve works, or valve face. On
this face, and between the two steam-ports, comes a third port M, communi-
cating directly with the atmosphere or with a condenser as the case may be.
The valve G is shaped in section something like an irregular D, and is often

-469]

Distribution of Steam. Slide Valves.

447

called a ' D ' valve in consequence. It is moved continuously backwards
and forwards upon the valve face by the valve rod H working in the stuffing-
box K. When in the position shown in the figure the steam enters by F,
and passes into the left-hand end of the cylinder (past the edge of the
valve) and pushes the piston from left to right. The steam at present in
the cylinder (as shown by the arrows) passes out at L, and through the
under part of the valve G to the exhaust port M. As the piston moves on,
the valve at first moves in the same direction, opening the port a little wider,
then gradually moves back again and closes the admission port altogether.

The point at which this occurs is called the point oi cut off. No more steam
is allowed to enter the cylinder for that stroke, the piston being pushed
forward by the pressure of the elastic steam expanding behind it. By the
time the piston has got to the end of its stroke, the position of the valve is
just reversed from that in which it is shown, and steam passes into the
cylinder through the right-hand port, driving the piston from right to left,
while the steam which has already done duty in the left-hand end of the
cylinder passes away, in its turn, through the exhaust.

The eccentric from which the valve receives its motion (lettered C in fig.
412) is shown in detail in fig. 414. Here D is the crank-shaft and A a disc
(solid or ribbed) fixed eccentrically on it so as to revolve with it. Encircling
this disc (which is the eccentric) is a strap or ring B (made in two pieces for
the sake of getting on and off), rigidly connected with a rod C, which is
coupled by a pin to the valve-rod E. In each revolution of the eccentric
the valve-rod is moved backwards and forwards through a space equal to
twice the eccentricity of the eccentric, or distance between the centres of D
and of A. The eccentric is thus equivalent exactly to a crank having a
radius equal to its eccentricity. It is used instead of a crank because it
does not require any gap to be left in the shaft, as a crank would do, but
allows it to be carried continuously on.

In locomotive or marine engines two eccentrics are commonly used, one
so placed as to give the valve the right motion when the shaft rotates in
one direction, and one rightly placed for the other. By apparatus called
reversing gear either one or the other can be caused to move the valve, so
that the engine can be made, at pleasure, to turn the shaft in one or the
other direction.

448

On Heat.

[470-

470. a^ocomotives. — Locomotive engines, or simply locomotives, are
steam engines which, mounted on a carriage, propel themselves by trans-
mitting their motion to wheels. The whole machine, fig. 415, boiler and
engine, is fixed to a wrought-iron frame, which, therefore, is made strong

enough to carry the whole weight, and which in turn transmits that weight
to the axle-boxes (or bearings in which the axles turn), by means of springs,
and thence through the wheels to the rails. The boiler is of a special type,
adopted in order to get the greatest possible heating surface in a very limited

-470] Locomotives. 449

space. It consists of three parts — \h.& fire-box, barrel, and s7noke-box. The
fire-box, in the left of the engraving, is generally a more or less rectangular
box, with a flat top, placed inside a second box of somewhat similar shape,
but with a semi-cylindrical, or, as in the figure, domed top. In the inner
fire-box are the fire-bars, on which the fuel is placed through a door in front.
The space between the inner and outer boxes is filled with water to a height
considerably over the top of the inner one, and communicates freely with a
long cylindrical barrel, closed at the other end by the smoke-box. This
barrel, which forms the main bulk of the boiler, is filled with water to within
nine or ten inches of its upper side. It is traversed from end to end by a
great number of small tubes (about i^ inch in diameter) which communicate
with the inner fire-box at the one end, and with the smoke-box at the other.
They, therefore, are entirely immersed in the water from end to end. The
gases of combustion, formed in the inner fire-box, pass through these tubes
to the smoke-box, and thence up the chimney, and impart most of their heat
to the water as they pass along. There are two steam cylinders, one on each
side of the frame, each one with its piston and connecting rod, etc., being
simply an ordinary high-pressure horizontal engine. Their exhaust steam
is discharged through a blast pipe into a nozzle inside the chimney near its
base, and this serves to excite the fierce draught which is required in order
that the necessary heat may be developed by the very small furnace. The
two cylinders work cranks at right angles to each other, so that one may be
in full action when the other is at its dead point.

A locomotive such as that shown in the figure is called an outside
cylinder engine, on account of the position of its cylinders. In England
many engines have cylinders placed inside the frames, which are then called
inside cylinder locomoti\'es. In express engines the cylinders frequently
dri\e only one very large pair of wheels, as is shown in the figure. These
are called driving -wheels, those on the front axle being leading wheels and
on the rear axle trailing wheels. In the case of goods engines, however (as
well as in many other instances), when less speed but a greater pull is re-
c[uired, two or more pairs of wheels of the same diameter are connected
together by coupling rods, so that two or more axles may be directly or
indirectly actually dri\-en by the engine. Such engines are called coupled
engines.

The action of the engine upon the wheels may cause them either to slip
round on the rails (in which case the engine, of course, does not move
onwards) or to roll on them in the usual way. To prevent slipping occurring
it is necessary to make the friction between the wheels and the rails as
great as possible. This is done by making as large a proportion of the
whole weight as possible rest on the driving or the coupled wheels, and also
— when bad weather causes the rails to be greasy or otherwise unusually
slippery — by increasing the coefficient of friction (47) between the wheels
and the rails by pouring sand on the latter. All locomotives are furnished
with a sand-box for this purpose.

The steam pressure in locomotives is greater than that commonly used
in any other engines, being often 120 to 130 lbs. per square inch above the
atmosphere. In marine engines 70 to 80 lbs. is often used, in stationary
engines seldom cpite so much.

G G

450 On Heat. [471-

The following is an explanation of the reference letters in fig. 415 : — A,
the main steam-pipe, conveying steam to the cylinder F, in which works a
piston P, driving the crank M through the connecting rod K, rr are the
piston-rod guides, V the stuffing-box. The exhaust steam is discharged
through the pipe E. (It will be remembered that the cylinder and all this
gear are duplicated on the other side of the engine.) D Z is the outer fire-
box and X the barrel of the boiler, both covered with felt and wood or sheet
iron to prevent loss of heat by radiation. The small tubes are seen at a,
Y is the smoke-box, and Q the chimney or funnel. TT are the springs
which transmit the weight of the frame to the axle-boxes. Of the smaller
details, G I is the arrangement for closing or openmg the steam-admission
\'alve, 'BbC the reversing gear, RR feed-water pipes, N coupling rod for
attaching tender and rest of train, ci safety valves, g whistle, ni steps, tt
water gauge, / cocks for blowing water out of cylinders, H cock for blowing
out boiler when necessary.

It is perhaps hardly necessary to explain that the breaking away of part
of the fire-box, cylinder, etc., is done in the drawing only for the sake of
showing clearly the internal construction.

471. Various kinds of steam eng-ine. — Three types of steam engine
have been described ; the Cornish engine, the ordinary horizontal engine,
and the locomotive engine. Others ought to be mentioned, although they
cannot be here described in detail. Compound engines are those in which
the steam is first used in the ordinary way in one cylinder and then trans-
ferred— of course at a comparatively low- pressure — to another cylinder and
used in it before being sent away to the condenser. This type is practically
uni\ersal for marine purposes, and is very common for stationary engines.
Its main advantage is a thermodynamic one. In an ordinary engine the
cylinder walls are exposed alternately to the hot steam from the boiler
and the cool vapour passing to the condenser. The latter so reduces the
temperature of the iron, that when the first rush of fresh steam comes into
the cylinder, much of it is immediately condensed on the cool metal, and an
enormous quantity of heat is thereby lost. By passing the steam through
an intermediate, or loiu-pressiire^ cylinder on its way to the condenser, the
sides of the first or Mgh-p?'essiire cylinder are never exposed to condenser
temperature, but only to that of the steam as it passes to the low-pressure
cylinder ; they therefore are not so much cooled, and the loss of steam by
condensation on them is very much reduced. There is no mechanical gain,
as has sometimes been stated, in the use of two cylinders instead of one.

Sometimes the cylinder of an engine is inclosed in a second, slightly
larger, cylinder, and fresh steam at boiler pressure admitted to the annular
space so formed outside the working cylinder. The object of this is to re-
duce still further the condensation in the cylinder just alluded to. Such an
engine is said to be steam-jacketed.

A surface-condensing engine is one in which the steam is condensed by
contact with the surface of a number of small tubes through which cold
water is kept continually circulating without being itself actually mixed with
the condensing water. By this arrangement the condensed steam is kept
by itself, and being distilled water it can be used very advantageously to feed
the boiler again. Compound marine engines are almost invariably surface-

-472] Work of an Engine. Horse-poiver. 451

condensing. In this case the air pump only takes away the condensed
steam, a separate pump, called a circulating pump, being- used to force the
condensing water through the tubes.

Engines without any condenser, like that shown in fig. 414, in which the
steam is exhausted directly into the atmosphere after it has done its work,
are often called //^^//-/r^j'«/';r engines, but high pressures (of 80 to 90 pounds
per square inch) are now frequently used in condensing engines, so that the
name may be somewhat misleading.

In such an engine as is shown in fig. 414 we have seen that the governor
keeps the speed constant, by closing or opening an exterior valve through
which the steam passes on its way to the main valve. An artificial resist-
ance is in this way opposed to the passage of the steam, by increasing
which the pressure can be reduced, and therefore the work done by the
steam, so that the engine will not run too fast if the resistance to its motion
be diminished (as by the disconnecting of some of the machines it is driving,
etc). The actual weight of steam passing into the cylinder at each stroke
remains unchanged, but the amount of useful work the steam can do is
diminished artificially by giving it some useless work to do in addition, in
forcing its way through a constricted passage. This is now known to be a
wasteful way of controlling speed. In modern engines, therefore, the
governor is frequently made to act by regulating the quantity of steam ad-
mitted by each stroke, and thus making the consumption of steam as nearly
as possible proportional to the work done. Engines so arranged, of which
the Corliss engine is one of the best-known examples, are said to be fitted
with automatic cut-off gear.

There is a popular misconception, that somehow or other work is lost in
an engine of the ordinary type between the piston and the crank, the latter
receiving less work than is done on the former in consequence of the nature
of the mechanism connecting them. It is probably unnecessary to point
out here the fallacy of this notion, but it has received sufficient acceptance
to lead to the invention of a host oi rotary engines, it which it is endeavoured
to obtain the desired rotary motion in a somewhat more direct fashion,
Reuleaux has shown that in almost every case the mechanisms used in the
rotary engines are the same as those of ordinary engines, although disguised
in form, so that the idea of mechanical advantage is doubly a mistake, while
in almost every case the rotary engines possess such grave mechanical
defects that none of them have practically come into use.

472. "Work of an eng-ine. Horse-power. — The unit of work by which
the performance of an engine is measured is in this country always the foot-
pound. The number of foot-pounds of work done by the engine in any
given time is equal to the average effective pressure upon its piston during
that time, multiplied by the total distance through which the piston has
moved under that pressure. By average effective pressure is meant the
average value of the difference between the pressures on its two sides.
Taking the time as one minute, this quantity of work in foot-pounds is
equal to : —

Area of piston x jnean intensity of pressure on piston x length of stroke
X number of strokes per minute.

The stroke must be taken in feet. If the area is in square feet, the

G G 2

452 On Heat. [473-

pressure must be in pounds per square foot : if the area is in square inches,
the pressure must be in pounds per square inch. If the strokes are double
strokes, each corresponding, that is, to one whole revolution of the shaft, the
length of stroke must be multiplied by 2. To find, for example, the work
done in one minute by an engine with cylinder 16 inches diameter and 24
inches stroke, making 50 (double) strokes per minute with a mean pressure
of 52 pounds per square inch, we have

(8- X 3-1416) ;< 52 X ( "'^ " " j X 50 =2,09 1,000 ft. -lbs.

The rate at which an engine does work is often measured in /lorse-porue?- of
33,000 ft.-lbs. per minute, an arbitrary unit supposed to represent the maxi-
mum rate at which work could actually be done by a horse. In the case

supposed the horse-power would be "' ^ ' = 63-4.

33,000

On the Continent the unit of work is a kilogrammetre, which is very
closely equal to y\ ft.-lbs. The horse-power used abroad, of 75 kilo-
grammetres per second, is nearly 2 per cent, smaller than that in use in this
country.

473. Indicator. Brake. — By the expression work done by au ciigitie we
may mean either of two things, viz. — the total work done by the engine, or
what is called its useful, or effective, work. The total work is the actual work
done by the steam on the piston and obtained by calculation, as described
in the last paragraph. The useful work is what remains of this total after
deduction has been made of the work necessary to drive the engine itselt
against its own frictional resistances. The total work of an engine is mea-
sured by means of an apparatus called an indicato7% in\ented by Watt, of
which fig. 414 shows one of the most recent forms (Richard's) omitting a
number of constructional details. The steam-engine indicator consists of a
small cylinder A, half a square inch in area, in which works a piston B, the
under side of which can be put into full communication with the cylinder
of the engine by opening the cock C. Between the top side of the piston
and the under side of the cylinder-cover is a spiral spring. The motion
of the piston-rod is transferred to a parallel motion DD, and so causes a
point E to move in a straight line up and down, its stroke being about
four times as great as that of the small piston. The indicator is fixed on to
the cylinder of the steam engine near one end, so that when the cock C is
opened, there is the same pressure of steam on the indicator piston as on the
engine piston. This pressure forces up the piston, and the amount of com-
pression of the spring so caused is proportionate to the pressure causing it.
The upward motion of E, therefore, is proportional to the steam pressure.
In front of E is a vertical drum F on which a strip of paper can be fixed,
and this drum is caused to rotate about its axis by attaching the cord G
to any suitable part of the engine. The paper thus moves horizontally
under the pencil, with a motion proportional to the stroke of the engine,
while the pencil moves up and down on the paper with a motion proportional
to the steam pressure on the piston. The two motions occurring simul-
taneously, the pencil traces on the paper a curv'e whose horizontal and
vertical ordinates are proportional to the two quantities just named, and

-473] Indicator. Brake. 453

whose area is therefore proportional to the product of these quantities, or,
which IS the sime thing, to the work done by the piston as defined in the
last paia^aiph The lui\ e ib c illed an indicator card, or indicator diagram.

A B

Fig. 417.

■*

^^.._

■^

" "~ C

■^

Fig. 416. Fig. 41S.

and while its whole area shows the whole work done by the steam, \X.s form
shows the engineer what is happening within the cylinder at each point of
the stroke, which he may often require to know.

Figs. 417 and 418 show two forms of indicator diagram. The curves
themselves, as drawn by the indicators, are lettered ABCD. Beside them
a scale of pressure in atmospheres is placed. In fig. 417 the steam is ex-
panded about seven times, and the back pressure is about \ of an atmo-
sphere, the pressure during admission being five atmospheres. The engine
is a condensing one, and the diagram is fairly good. Fig. 418 is for a non-
condensing engine, the back pressure being above that of the atmosphere.
The steam is cut off (at B) only at about f of the stroke, so that it is not
working economically, and from the roundness of its corners the diagram
would be considered a poor one.

The useful work of an engine is measured by an entirely different piece
of apparatus, called a dynamometer. This is used in many forms, but
fig. 417 shows the principle upon which the majority act. The apparatus
shown in the figure is known as a Pronfs friction bratce. A is the shaft,
the usual work transmitted by which we require to find. Upon the shaft is
a fixed pulley B, einbraced by two blocks Bj and B,, which can be tightened
up by the screws at C^ and C. To the lower block is fixed a lever D, from
which hangs a weight, and which has at its extremity a small pointer work-
ing against a short scale F. If such an apparatus be set in motion by
turning the shaft A, one of two things must happen ; either the pulley must

454

On Heat.

[473-

slip round in the blocks, or it must so grip them as to carry both them and
the lever D round its own axis. The moment of resistance to the former is
r F, if r be the radius of the pulley and F the frictional resistance at its

.r^

Fig. 419.

periphery ; that of the latter is RW, where R is the radius of the weight
and W the weight itself. In practice the screw C., is loosened just suffi-
ciently to keep the weight just lifted from the ground, while the pulley is
always turning round in the blocks, so that, therefore,
rF = RW.

The work done at the brake per minute is equal to the frictional resistance
multiplied by the distance through which it is overcome in the same time,
or, if;/ be the number of revolutions per minute,
= 27rrF« = 27rRW«.
It is therefore just the same as if a resistance = W were continually being
overcome at the periphery of a wheel of radius R, making n turns per minute.
As the values of all the quantities in the expression 27rRW« are very readily
determined, it will be seen that this brake affords a very simple way of
measuring the net work transmitted through the shaft of an engine.

™, ^- useful work work shown by brake • n j .1, zk •

The ratio --, or , — , — ^--r. , is called the cfflci-

total work work shown by mdicator

ency of the engine as a machine, or its mccJiaiiical efficiojcy. It is often as
much as 0-85, and sometimes even higher than 0-9 or 90 per cent., being
generally greatest in large engines.

474. Efficiency of heat engrines. — There is another ratio of efficiency
connected with the steam engine, namely the ratio
Total work done by engine
Total heat expended

which is called the efficiency of the e?tgine as a heat engine or its thermo-
dynamic efficiency. If T, and T., be respectively the absolute temperatures
(496) of the steam and the feed water in any engine, then it can be shown

-476] Gas Engines. 455

that such an engine, if working quite perfectly, could transform no more

than ( — lZ — 2jof the heat which it receives into work. This fraction in the

case of a steam engine is seldom more than about o'25. The value of the
actual efficiency of the engine is often from o"io to 0'i4 ; while, therefore,
an ordinary steam engine, with such an efficiency, turns into work only from
~~ to I of the whole heat it receives, yet it may be turning into work h or
more of the whole heat which it could possibly transform into work if it
were perfect.

To increase the economy of steam engines we require to make the value

of i -^-^ — ^j larger. This is done either by raising Tj or by lowering Tg, or
\ T[ /

both. The chief difficulty is that we cannot raise Tj without increasing the

steam pressure, which it is often not convenient to do, while we cannot lower

T., below such a temperature, 50^ to 60° F., as can readily be obtained

naturally at all seasons of the year.

475. Hot-air engines. — The difficulty as to T, just mentioned is got over
by the use of some fluid whose pressure is not a function of its temperature,
and naturally air is the most convenient fluid for the purpose. Many ' hot-
air' engines have been designed, and some have found a considerable
measure of success commercially, as Rider's, Hock's, and Lehmann's. In
all cases the engines consist essentially of one (or two) chambers placed so
that one end can be heated by a furnace and the other cooled by a refrige-
rator. The air is compelled to move from the cold space to the hot and back
again continually. When hot it is allowed to expand and push forward a
piston, when cold it is compressed by pushing back the piston again to its
original position. The difference between these two quantities of work is
the whole work done by the engine. By making T^ a very high temperature,

(T - T \
— L -j of an air engine may be made much

higher than that of a steam engine. But it is so much more difficult to attain
the theoretical efficiency in the air than in the steam engine, that its actual
efficiency is generally much lower than that of a steam engine. There are
constructive difficulties connected with the hot-air chambers, and with the
regulation of the speed, and these, as well as with the large bulk of most air
engines in proportion to their power, have stood greatly in the way of their
development. No doubt, however, much more improvement would ha\'e
taken place in these engines had not gas engines come into prominence of
late years and proved much more convenient.

476. Gas engines. — Gas engines, like steam engines and air engines, are
heat engines, but in them the working fluid is ordinary coal gas mixed with
air, in the proportion of about i to 1 1 by volume. The principle of action
is very simple : — The explosive mixture after being drawn into the cylinder
is set light to, the heat generated by the very rapid combustion which
we call an explosion causes the mixed gases to expand and drive forward
the piston. The great difficulty for many years was that the explosion was
so rapid that the comparatively slow-going piston could not keep up with it,
and the greater part of the energy of the explosion was lost by radiation and
conduction. In the more modern gas engines, however (Otto's and Clerk's

456

On Heat.

[476-

and others), this difficulty is got over by compressing the charge before
igniting^ it, a treatment which is found to decrease very much the rapidity
of the explosion and so greatly increase the actual efficiency of the engine.
Fig. 420 shows the principal parts of an Otto 'Silent' gas engine, as now made.
A is the cylinder, open at front and single-acting, in which works a deep
piston F, driving a crank in the usual manner. The cylinder is surrounded
by a water jacket, to prevent it from getting too hot. At the back of the
cylinder is a slide valve B, worked by a cam, not shown in drawing, on the

lay shaft G. The valve B is kept up against its face by spiral springs E.
D is a chamber in which a small jet of gas for igniting the mixture is con-
tinually burning. C, is the cock for admission of gas, and C, an india-
rubber bag to equalise the gas pressure. The working of the engine is as
follows : — the piston moves from left to right and draws into the cylinder the
explosive mixture. On the return stroke it compresses the mixture to about
3 atmospheres. The igniting flame is then allowed to come for an instant
into contact with the compressed mixture, which burns very rapidly (or
explodes slowly, whichever expression be preferred) and pushes the piston
forward again, the pressure rising to 10 or 12 atmospheres. On the next
return stroke the burnt gases are pushed out through the opening shown in
the drawing, and the process begins again once more. There are many
ingenious arrangements about this type of engine which our space will not
allow us to mention in detail. It must suffice to say that the engine has
proved distinctly economical, and has such very great conveniences as may
fairly account for the rapid way in which its use (and that of other gas
engines) has extended.

In conclusion, it is as well to point out that, as long as they work between
the same temperatures, there is no difference between steam, air, and gas
engines as to theoretical economy. The last two gain by the possibility of
using higher limits of temperature than can be employed in a steam engine,
but, so far, have lost by constructive and mechanical difficulties which pre-
vent their theoretical efficiency from being attained.

-478J 457

CHAPTER XI.

SOURCES OF HEAT AND COLD.

477. Different sources of beat. — The following difterent sources of
heat may be distinguished : i. the mechanical sources, comprising friction,
percussion, and pressure ; ii. the physical sources —thaX is, solar radiation,
terrestrial heat, molecular actions, change of condition, and electricity ;
iii. the chemical sources, or molecular combinations, and more especially
combustion.

In what follows it will be seen that heat may be produced by reversing
its effects ; as, for instance, when a liquid is solidified or a gas compressed
(479) ; though it does not necessarily follow that in all cases the reversal of
its effects causes heat to be produced — instead of it, an equivalent of some
other form of energy may be generated.

In like manner heat may be forced to disappear, or cold be produced
when a change such as heat can produce is brought about by other means,
as when a liquid is vaporised or a solid liquefied by solution ; though here
also the disappearance of heat is not always a necessary consequence of
the production, by other means, of changes such as might be effected by
heat.

MECHANICAL SOURCES.

478. Heat due to friction. — The friction of two bodies, one against the
other, produces heat, which is greater the graater the pressure and the more
rapid the motion. For example, the axles of carriage wheels, by their fric-
tion against the boxes, often become so strongly heated as to take fire. By
rubbing together two pieces of ice in a vacuum below zero. Sir H. Davy
partially melted them. In boring a brass cannon Rumford found that the
heat developed in the course of 2h hours was sufficient to raise 26^ pounds
of water from zero to 100^, which represents 2,650 thermal units (447). Mayer
raised water from 12° to 13° by shaking it. At the Paris Exhibition, in 1855,
Beaumont and Mayer exhibited an apparatus, which consisted of a wooden
cone covered with hemp, and moving with a velocity of 400 revolutions in a
minute, in a hollow copper cone, which was fixed and immersed in the water
of an hermetically-closed boiler. The surfaces were kept covered with oil.
By means of this apparatus 88 gallons of water were raised from 10 to 130
degrees in the course of a few hours.

In the case of flint and steel, the friction of the flint against the steel
raises the temperature of the metallic particles, which fly off, heated to such
an extent that they take fire in the air.

The luminosity of aerolites is considered to be due to their friction
against the air, and to their condensation of the air in front of them (479),
their velocity attaining as much as 150 miles in a second.

458

On Heat.

[478-

Tyndall has devised an experiment by which the great heat developed by
friction is illustrated in a striking manner. A brass tube (fig. 421), about
7 inches in length and f of an inch in diameter, is fixed on a small wheel.
By means of a cord passing round a much larger wheel, this tube can be
rotated with any desired velocity. The tube is three parts full of water, and
is closed by a cork. In making the experiment, the tube is pressed between
a wooden clamp, while the wheel is rotated with some rapidity. The water
rapidly becomes heated by the friction, and its temperature soon exceeding
the boiling-point, the cork is projected to a height of several yards by the
elastic force of the steam.

479. Heat due to pressure and percussion. — If a bady be so com-
pressed that its density is increased, its temperature rises according as the

Fig. 421.

volume diminishes. Joule has verified this in the case of water and of oil,
which were exposed to pressures of 15 to 25 atmospheres. In the case of
water at i •2°C., increase of pressure caused lowering of temperature — a result
which agrees with the fact that water contracts by heat at this temperature.
Similarly, when weights are laid on metallic pillars, heat is evolved, and
absorbed when they are removed. So in like manner the stretching of a
metallic wire is attended with a diminution of temperature.

The production of heat by the compression of gases is easily shown by
means of the piieiimatic syringe (fig. 422). This consists of a glass tube
with thick sides, closed hermetically by a leather piston. At the bottom of
this there is a cavity in which a small piece of cotton, moistened with
ether or bisulphide of carbon, is placed. The tube being full of air, the
piston is suddenly plunged downwards ; the air thus compressed disengages
so much heat as to ignite the cotton, which is seen to burn when the piston
is rapidly withdrawn. The ignition of the cotton in this experiment indicates
a temperature of at least 300°.

The elevation of temperature produced by the compression in the above
experiment is sufficient to effect the combination, and therefore the detona-
tion, of a mixture of hydrogen and oxygen.

A curious application of the principle of the pneumatic syringe is met

-479]

Heat due to Pressure a)id Percussion.

459

with in the A.vntnc3.n ^oiuder nun for pile-driving. On the pile to be driven
is fixed a powder mortar, above which is suspended at a suitable distance an
iron rammer, shaped like a gigantic stopper, which just fits in the mortar.
Gunpowder is placed in the mortar, and when the rammer is detached it
foils into the mortar, compresses the air, producing so much heat that the

Fig. 422.

powder is exploded. The force of the gases projects the rammer into its
original position, where it is caught by a suitable arrangement ; at the same
time the reaction of the mortar on the pile drives this in with far greater
force than the fall of the rammer. After adding a fresh charge of powder,
the rammer is again allowed to fall, again produces heat, explosion, and so
forth, so that the driving is effected in a surprisingly short time.

Percussion is also a source of heat. In firing shot at an iron target, a
sheet of flame is frequently seen at the moment of impact ; and Sir J. Whit-
worth has used iron shells which are exploded by the concussion on striking
an iron target. A small piece of iron hammered on the anvil becomes very
hot. The heat is not simply due to an approximation of the molecules —
that is, to an increase in density — but arises from a vibratory motion im-
parted to them ; for lead, which does not increase in density by hammering,
nevertheless becomes heated.

The heat due to the impact of bodies is not difficult to calculate. When-
ever a body moving with a velocity v is suddenly arrested in its motion,
its vis viva is converted into heat. This holds equally whatever be the
cause to which the motion is due : whether it be that acquired by a stone
falling from a height, by a bullet fired from a gun, or the rotation of a
copper disc by means of a turning-table. The vis viva of any moving body

is expressed by — "- or in foot-pounds by -r , where/ is the weight in

pounds, v the velocity in feet per second, and g is about 32 (29) ; and if the
whole of this be converted into heat, its equivalent in thermal units will be

— £- Suppose, for instance, a lead ball weighing- a pound be fired

2^^x 1390 ^^ ' sal

from a gun, and strike against a target, what amount of heat will it produce ?

We may assume that its velocity will be about 1,600 feet per second ; then

its vis viva will be

1 600'

7^:

_ = 40,000 foot-pounds. Some of this will ha\e

been consumed in producing the vibrations which represent the sound of the
shock, some of it also in its change of shape ; but neglecting these two, as
being small, and assuming that the heat is equally divided between the ball

460

On Heat.

[479-

and the target, then, since 40,000 foot-pounds is the equivalent of 287
thermal units, the share of the ball will be 14-3 thermal units ; and if, for
simplicity's sake, we assume that its initial temperature is zero, then, taking
its specific heat at 0'03i4, we shall have

I X 0-0314 X /= 14-3 or ^ = 457°,

which is a temperature considerably above that of the melting point of
lead (338).

By allowing a lead ball to fall from various heights on an iron plate, both
experience an increase of temperature which may be measured by the
thermopile ; and from these increases it may be easily shown that the heat
is directly proportional to the height of fall, and therefore to the square of
the velocity.

By similar methods INIayer has calculated that if the motion of the earth
were suddenly arrested the temperature produced would be sufficient to melt
and even volatilise it ; while, if it fell into the sun, as much heat would be
produced as results from the combustion of 5,000 spheres of carbon the size
of our globe.

PHYSICAL SOURCES.
480. Solar radiation. — The most intense of all sources of heat is the
sun. Difterent attempts have been made to determine the quantity of heat

which it emits. Pouillet made the first
accurate measurements of the heat of
the sun by means of an instrument
called the pyroheliometer. The form
represented in fig. 423 consists of a
flat cylindrical metal box 3 inches in
diameter and i an inch deep, contain-
ing a known weight of water. To it is
fitted a metal tube which contains the
stem of a delicate thermometer, the
bulb of which dips in the liquid of the
box, being fitted by means of a cork.
The tube works in two collars, so that
by means of a milled head it can be
turned, and with it the vessel, and the
liquid thus be uniformly mixed. The
face of the vessel is coated with lamp-
black, and is so adjusted that the
sun's rays fall perpendicularly upon it.
This can be ascertained by observing
when the shadow exactly covers the
lower disc which is fitted to the same
axis.

The instrument was exposed for
five minutes at a time to the sun's
rays ; knowing the weight of the water, its rise m temperature could be easily
calculated (449). Corrections were necessary for the heat reflected by the
lampblack, and also for the heat absorbed by the air.

-481] Terrestrial Heat. 46 1

Pouillet calculated from the results of experiments with this apparatus
that if the total quantity of heat which the earth receives from the sun in the
course of a year were employed to melt ice, it would be capable of melting a
layer of ice all round the earth of 35 yards in thickness. Another state-
ment is that the heat emitted by the sun is equal to that produced by the
combustion of 1,500 pounds of coal in an hour on each square foot of its
surface. But from the surface which the earth exposes to the solar radia-
tion, and from the distance which separates the earth from the sun, the
quantity of heat which the earth receives can only be Ta-gfi];;;^^ of the heat
emitted by the sun.

Viotti calculated the thickness of ice melted by the sun's heat at the
equator, apart from absorption by the atmosphere, at 55 metres in thickness ;
and, deducting this absorption, at yj metres.

Faraday calculated that the average amount of heat radiated in a day on
each acre of ground in the latitude of London is equal to that which would
be produced by the combustion of sixty sacks of coal.

The heat of the sun cannot be due to combustion, for even if the sun
consisted of hydrogen, which of all substances gives the most heat in com-
bining with oxygen, it can be calculated that the heat thus produced would
not last more than 3,000 years. Another supposition is that originally put
forth by Mayer, according to which the heat which the sun loses by radiation
is replaced by the fall of aerolites against its surface. One class of these is
what we know as shooting stars, which often appear in the heavens with
great brilliancy, especially on August 14 and November 15 ; the term meteoric
stone or aer-olite being properly restricted to the bodies which fall on the
earth. They are often of considerable size, and are even met with in the
form of dust. Although some of the sun's heat may be restored by the
impact of such bodies against the sun, the amount must be very small, for
Sir W. Thomson has proved that a fall of 0-3 gramme of matter in a second
on each square metre of surface would be necessary for this purpose. The
effect of this would be that the mass of the sun would increase, and the
velocity of the earth's rotation about the sun would be accelerated to an
extent which would be detected by astronomical observations.

Helmholtz considers that the heat of the sun was produced originally by
the condensation of a nebulous mass, and is kept up by a continuance of
this contraction. A sudden contraction of the primitive nebular mass of the
sun to its present volume would produce a temperature of 28 millions of
degrees Centigrade ; and a contraction of jj^,^-- of its mass would be
sufficient to supply the heat radiated by the sun in 2,000 years. This amount
of contraction could not be detected even by the most refined astronomical
methods.

48 1. Terrestrial heat. — Our globe possesses a heat peculiar to it, which
is called the tetyestrial heat. The variations of temperature which occur at
the surface gradually penetrate to a certain depth, at which their influence
becomes too slight to be sensible. It is hence concluded that the solar heat
does not penetrate below a certain internal layer, which is called the layer of
constant annual temperature ; its depth below the earth's external surface
varies, of course, in different parts of the globe ; at Paris it is about 30 yards,
and the temperature is constant at 1 1 -8' C.

462

On Heat.

[481-

Below the layer of constant temperature, the temperature is observed to
increase, on the average, 1° C. for every 90 feet. The most rapid increase
is at Irkutsk in Siberia, where it is 1° for 20 feet, and the slowest in the mines
at Mansfield, where it is about 1° C. for 330 feet. This increase has been
verified in mines and artesian wells. According to this at a depth of 3,000
yards, the temperature of a corresponding layer would be 100°, and at a
depth of 20 to ■^:^o miles there would be a temperature sufficient to melt all
sulDstances which exist on the surface. Hot springs and volcanoes confirm
the existence of this central heat.

Various hypotheses have been proposed to account for the existence of
this central heat. The one usually admitted by physicists is that the earth
was originally in a liquid state in consequence of the high temperature, and
that by radiation the surface has gradually solidified, so as to form a solid
crust. The thickness of this crust is not believed to be more than 40 to 50
miles, and the interior is probably still in a liquid state. The cooling must
be very slow, in consequence of the imperfect conductivity of the crust. For
the same reason the central heat does not appear to raise the temperature
of the surface more than i of a degree.

Fourier calculated that the heat given off by the earth in 100 years would
be sufficient to melt a layer of ice 3 metres in thickness, which therefore is
only -j7^,,^i of that received by the sun in the same time.

482. Heat produced by absorption and imbibition. — Molecular phe-
nomena, such as imbibition, absorption, capillary actions, are usually accom-
panied by disengagement of heat. Pouillet found that whenever a liquid is
poured on a finely- divided solid, an increase of temperature is produced
which varies with the nature of the substances. With inorganic substances,
such as metal, the oxides, the earths, the increase is /^ of a degree ; but with
organic substances, such as sponge, flour, starch,,
roots, dried membranes, the increase varies from I
to 10 degrees.

The absorption of gases by solid bodies presents,
the same phenomena. Dobereiner found that when
platinum, in the fine state of division known as
platinum black, is placed in o.xygen, it absorbs
many hundred times its volume, and that the gas
is then in such a state of density, and the tempera-
ture so high, as to give rise to intense combustions.
Spongy platinum produces the same effect. A jet
of hydrogen directed on it takes fire.

The apparatus known as Dobereiner'' s Lamp
depends on this property of finely-divided platinum.
It consists of two glass vessels (fig. 424). The
first. A, fits in the lower vessel by means of a
tubulure which closes it hermetically At the end
of the tubulure is a lump of zinc, Z, immersed in
li.;. 4--4- dilute sulphuric acid. By the chemical action of

the zinc on the dilute acid hydrogen gas is gene-
rated, which, finding no issue, forces the liquid out of the vessel B into the
vessel A, so that the zinc is not in contact with the liquid. The stopper of

-483] Chemical Combination. Combustion. 463

the upper vessel is raised to give exit to the air in proportion as the water rises.
On a copper tube, H, fixed in the side of the vessel B, there is a small
cone, cz, perforated by an orifice ; above this there is some spongy platinum
in the capsule, c. As soon now as the cock, which closes the tube, H, is
opened, the hydrogen escapes, and, coming in contact with the spongy
platinum, is ignited.

The condensation of vapours by solids often produces an appreciable
increase of temperature. This is particularlj' the case with humus, which, to
the benefit of plants, is warmer in moist air than the air itself.

Favre has found that when a gas is absorbed by charcoal the amount of
heat produced by the absorption of a given weight of sulphurous acid, or of
protoxide of nitrogen, greatly exceeds that which is disengaged in the licjue-
faction of the same weight of gas ; for carbonic acid, the heat produced by
absorption exceeds even the heat which would be disengaged by the solidi-
fication of the gas. The heat produced by the absorption of these gases
cannot, therefore, be explained by assuming that the gas is licjuefied, or even
solidified in the pores of the charcoal. It is probable that it is in part due to
that produced by the liquefaction of the gas, and in part to the heat due to
the imbibition in the charcoal of the liquid so produced.

CHEMICAL SOURCES.

483. Chemical combination. Combustion, — Chemical combinations
are usually accompanied by a rise of temperature. When these combinations
take place slowly, as when iron oxidises in the air, the heat produced is im-
perceptible ; but if they take place rapidly, the disengagement of heat is very
intense. The same quantity of heat is produced in both cases, but when
evolved slowly it is dissipated as fast as formed.

Co7nbiistio7i is chemical combination attended with the evolution of light
and heat. In ordinary combustion in lamps, fires, candles, the carbon and
hydrogen of the coal, or of the oil, etc., combine with the oxygen of the .air.
But combustion does not necessarily involve the presence of oxygen. If
either powdered antimony or a fragment of phosphorus be placed in a vessel
of chlorine, it unites with chlorine, producing thereby heat and flame.

Many combustibles burn with flame. A /lame is a gas or vapour raised
to a high temperature by combustion. Its illuminating power varies with
the nature of the product formed. The presence of a solid body in the flame
increases the illuminating power. The flames of hydrogen, carbonic oxide^
and alcohol are pale, because they only contain gaseous products of com-
bustion. But the flames of candles, lamps, coal gas, have a high illuminating-
power. They owe this to the fact that the high temperature produced de-
composes certain of the gases, with the production of carbon, which, not
being perfectly burnt, becomes incandescent in the flame. Coal gas, when
burnt in an arrangement by which it obtains an adequate supply of air, such
as a Bunsen's burner, is almost entirely devoid of luminosity. A non-lumi-
nous flame may be made luminous by placing in it platinum wire or asbestos.
The temperature of a flame does not depend on its illuminating power.
A hydrogen flame, which is the palest of all flames, gives the greatest
heat.

464

On Heat.

[483-

Clionical decomposiiion, in which the attraction of heterogeneous mole-
cules for each other is overcome, and they are moved further apart, is an
operation recjuiring- an expenditure of work or an equivalent consumption of
heat ; and conversely, in chemical combination, motion is transformed into
heat. When bodies attract each other chemically their molecules move
towards each other with gradually increasing velocity, and when impact has
taken place the progressive motion of the molecules ceases, and is converted
into a rotating, vibrating, or progressive motion of the molecules of the new
body.

The heat produced by chemical combination of two elements may be
compared to that due to the impact of bodies against each other. Thus the
action of the atoms of oxygen, which in virtue of their progressive motion,
and of chemical attraction, rush against ignited carbon, has been likened by
Tyndall to the action of meteorites which fall into the sun.

484. Heat disengaged during chemical action. — Many physicists,
more especially Lavoisier, Rumford, Dulong, Despretz, Hess, Favre and
Silbermann, Berthelot, Thomsen, and Andrews, have investigated the
quantity of heat disengaged by various bodies in chemical actions.

Lavoisier used in his experiments the ice calorimeter already described.
Rumford used a calorimeter known by his name, which consists of a rect-
angular copper canister filled with water. In this canister there is a worm
which passes through the bottom of the box, and terminates below in an
inverted funnel. Under this funnel is burnt the substance experimented

upon. The products of combustion,
in passing through the worm, heat
the water of the canister, and from
the increase of its temperature the
quantity of heat evolved is calculated.
Despretz and Dulong successively
modified Rumford's calorimeter by
allowing the combustion to take
place, not outside the canister, but
in a chamber placed in the liquid
itself; the oxygen necessary for the
combustion entered by a tube in the
lower part of the chamber, and the
products of combustion escaped by
another tube placed at the upper
part and twisted in a serpentine form
in the mass of the liquid to be
heated. Favre and Silbermann have
improved this calorimeter very
greatly (463), not only by avoiding
or taking account of all possible
^' sources of error, but b)' arranging it
for the determination of the heat
evolved in such chemical actions as
take place between gases and vapours. The gases enter by tubes BB' and
CC, fig. 425, into a metal chamber A, where the reaction takes place, the

-484]

Heat discnrnzed during Combustion.

465

course of which can be watched through a glass plate which closes a wider
tube FK. The gaseous products before passing into the air traverse a long
serpentine tube H, at the lower end of which is a small box G which receives
the liquids arising from the condensation of the vapours. The cylinder A
and the serpentine are contained in a known mass of water contained in a
calorimeter, and from the rise in temperature of this water the heat developed
can be calculated. To avoid any loss of heat this is placed within a metal
case containing swan's down. The whole is contained in a vessel of water
NN in which is a thermometer, to eliminate the influence of changes in the
temperature of the air.

The experiments of Favre and Silbermann are the most trustworthy, as
having been executed with the greatest care. They agree very closely with
those of Dulong. Taking as thermal unit the heat necessary to raise the
temperature of a pound of water through one degree Centigrade, the following-
table gives the thermal units in round numbers disengaged by a pound of
each of the substances while burning in o.xygen : —

Hydrogen .
Marsh gas .
Olefiant gas
Oil of turpentine
OHve oil
Ether .
Anthracite
Charcoal
Coal .
Tallow
Graphite

Bunsen's calorimeter (451) has been used with advantage for studying
the heat produced in chemical reactions, for cases in which only very small
quantities are available.

All chemical actions, whether of combination or of decomposition, are
attended by a. disturbance of the thermal equilibrium ; and the quantity of
heat disengaged is a measure of the physical and chemical work.

In most cases the act of chemical combination is attended by a rise of
temperature, and the quantity of heat is a measure of the energy developed
in the reaction. Thus in the formation of one molecule of water there are
liberated 68,924 thermal units, which may be written thus,

Hj + O = H„0 + 68,924.

Those reactions which take place with disengagement of heat are said to
be exothermic ; there are, however, cases where bodies do not directly com-
bine without the intervention of extraneous heat — for instance, iodine and
hydrogen to form hydriodic acid ; the equation for this is

I + H+6,ooo=IH.

Such reactions called endothermic.

Those bodies are most stable in the formation of which most heat is

H H

34,462

Diamond

7,770

13,063

Absolute alcohol .

7,180

11,858

Coke .

7,000

10,852

Phosphorus .

5,750

9,860

Wood, dried at 120'

3,616

9,030

Bisulphide of carbon

3,401

8,460

Wood, ordinary .

2,756

8, 080

Carbonic oxide

2,400

8,000

Sulphur

2,220

8,000

Iron

1,181

7,797

Zinc

1,300

466 On Heat. [484-

developed ; thus the oxides of iron and zinc, in the formation of which i,iSi
and 1,300 units are respectively developed, are much more stable than oxide
of silver, m the formation of which only 27 units are developed. The heat
of decomposition is the reciprocal of that of combination ; those bodies
which develop most heat in their formation require conversely an equivalent
quantity to decompose them ; decompositions which require an expenditure
of heat to produce them are called etidothermic. Those compounds, on the
contrary, which absorb heat in their formation, develop an equivalent
quantity in being decomposed, and the reactions are exot/icnntc ; they often
take place with explosive violence, as in the case of the chlorides and iodide of
nitrogen. An exothermic reaction gives rise to an endothermic compound ;
and, conversely, an endothermic reaction forms an exothermic compound.

If there be any system of bodies which act on each other without the
supply of extraneous energy, then that body, or set of bodies, results in
the formation of which most heat is produced. This is called the principle
of greatest cJieiiiical actioti.

The heat developed in any chemical reaction depends on the relation
between the initial and the final products, and is independent of the nature
and succession of the intermediate stages. It is equal to the sum of the
quantities of heat produced in each stage, regard being had to the negative
quantities produced in such processes as solution and gasification.

Thus a unit weight of carbon in burning to carbonic acid produces 8,080
units. If the same weight of carbon burns so as to form carbonic oxide it
forms 2,473 ; a^rid the combustion of the carbonic oxide resulting from this
reaction yields 5,607, making together 8,080.

Potassium combines directly with chlorine to form potassium chloride,
the heat of formation of which is 1 5,000 and is equal to that produced by the
same weight of salt, whether this be formed by the direct union of hydro-
chloric acid and potash, or whether it be produced by the action of potassium
on aqueous solution of hydrochloric acid.

The heat of combustion of a compound is not equal to the sum of that of
each of its constituents. The heat of combustion of bisulphide of carbon is
3,401, while that calculated from its constituents is 3,145 ; the compound
accordingly possesses more energy than its constituents, and, its formation
is due to an endothermic reaction.

Metameric bodies are those which contain the same number of elements
but in different groupings ; thus acetic acid and methylic formate have
each the composition C^H^Oo ; but the heat of combustion of the latter
is 4,157, and that of the former 3,505 ; from this it is to be inferred that the
grouping of the atoms to form acetic acid has been attended with the expendi-
ture of more energy than in the case of methylic formate.

Polymeric bodies are those which have the same elements and the same
percentage composition but differ in the number of atoms which form a
molecule. Thus the more complex the molecule the smaller is the quantity
of heat. That of amylene, for instance, CjH,o, is 11,401, and that of
metamylene, C.,(,H_i,„ is 10,908.

Many chemical elements, such as carbon, sulphur, and phosphorus, exist
in modifications which are essentially different from each other in their
physical properties, iDut which form when they enter into combination with

-485]

Auiiual Heat. 467

other elements identical chemical products. Such bodies are said to exist
in an allotropic form. A given weight of carbon produces the same weight of
carbonic acid when it combines with oxygen, whether it be diamond or char-
coal, but the heat produced is different, and this difference corresponds to the
heat which represents the transformation from one modification into another.

The temperature of combustion., or, in the case of gases, the temperature
of the flame, is the upper limit of the temperature which can be attained by
the combustion- of a body. This can be deduced from the heat of combus-
tion, and from the specific heats of the bodies produced. The theoretical
temperature of combustion of hydrogen in oxygen is calculated at 6,715° ;
this, however, is never even approximately reached, for at much lower tem-
peratures aqueous vapour is dissociated (389) into its constituents, and the
combustion cannot exceed a certain limit.

485. iVnimal heat. — In all the organs of the human body, as well as
those of all animals, processes of oxidation are continually going on. Oxygen
passes through the lungs into the blood, and so into all parts of the body. In
like manner the oxidisible bodies, which are principally hyrocarbons, pass
by the process of digestion into the blood, and likewise into all parts of the
body, while the products of oxidation, carbonic acid and water, are ehminated
by the skin, the lungs, etc. Oxidation in the muscle produces motions of the
molecules, which are changed into contraction of the muscular fibres ; all
other oxidations produce heat directly. When the body is at rest, all its
functions, even involuntary motions, are transformed into heat. When the
body is at work, the more vigorous oxidations of the working parts are
transferred to the others. Moreover, a great part of the muscular work is
changed into heat, by friction of the muscle and of the sinews in their sheaths,
and of the bones in their sockets. Hence the heat produced by the body
when at work is greater than when at rest. The blood distributes heat
uniformly through the body, which in the normal condition has a temperature
of yj'^ C. = 98-6 F. The blood of mammalia has the same temperature, that of
birds is somewhat higher. In fever the temperature rises to 42° -43°, and in
cholera, or when near death, sink as low as 35°.

The function of producing work in the animal organism was formerly con-
sidered as separate from that of the production of heat. The latter was
held to be specially due to the oxidation of the hydrocarbons of the fat, while
the work was ascribed to the chemical activity of the nitrogenous matter.
This view has now been generally abandoned ; for it has been found that
during work there is no increase in the secretion of urea, which is the result
of the oxidation of nitrogenous matter ; moreover, the organism while at
rest produces less carbonic acid, and requires less oxygen than when it is at
work ; and the muscle itself, both in the living organism and also when
removed from it and artificially stimulated, requires more oxygen in a state
of activity than when at rest. For these reasons the production of work is
ascribed to the oxidation of the organic matter generally.

The process of vegetation in the living plant is not in general connected
with any o.xidation. On the contrary, under the influence of the sun's rays,
the green parts of plants decompose the carbonic acid of the atmosphere
into free oxygen gas and into carbon, which, uniting with the elements of
water, form cellulose, starch, sugar, and so forth. In order to effect this, an

H H 2

468

On Heat.

[485-

expenditure of heat is required which is stored up in the plant, and which
reappears duriny the combustion of the wood, or of the coal arising from its
decomposition.

At the time of blossoming a process of oxidation goes on, which, as in
the case of the blossoming of the Victofia regta, is attended with an appreci-
able rise of temperature.

HEATING.

486. Different kinds of heating-. — Heating is the art of utilising for
domestic and industrial purposes the sources of heat which nature offers to
us. Our principal source of artificial heat is the combustion of coal, coke,
turf, wood, and charcoal.

487. Pireplaces Fireplaces are open hearths built against a wall under

a chimney, through which the products of combustion escape.

However much they may be improved, fireplaces will always remain the
most imperfect and costly mode of heating, for they only render available
13 per cent, of th-e total heat yielded by coal or coke, and 6 per cent, of that
by wood. This enormous loss of temperature arises from the fact that the
current of air necessary for combustion always carries with it a large quan-
tity of the heat produced, which is dissipated in the atmosphere. Hence
Franklin said 'fireplaces should be adopted in cases where the smallest
quantity of heat was to be obtained from a given quantity of fuel.' Not-
withstanding their want of economy, however, they will always be preferred
as the healthiest and pleasantest mode of heating, on account of the cheerful
light which they emit, and the ventilation which they ensure.

488. Braugrht of fireplaces. — The draught of a fire is the upward cur-

rent in the chimney caused by the ascent of
the products of combustion; when the current
is rapid and continuous, the chimney is said
to draiv well.

The draught is caused by the difference
between the temperature of the inside and
that on the outside of the chimney ; for, in
consequence of this difference, the gaseous
bodies which fill the chimney are lighter
than the air of the room, and consequently
equilibrium is impossible. The weight of the
column of gas CD, fig. 426, in the chimney
being less than that of the external column
of air AB of the same height, there is a
pressure from the outside to the inside which
causes the products of combustion to ascend
the more rapidly in proportion as the differ-
ence in weight of the two gaseous masses is
greater.
The velocity of the draught of a chimney may be determined theoreti-
cally by the formula

t ig. 420.

-489J Stoves. 469

ill which g is the acceleration of gravity, a the coefficient of the expansion
of air, h the height of the chimney, /' the mean temperature of the air inside
the chimney, and t the temperature of the surrounding air.

The currents caused by the difference in temperature of two communi-
cating gaseous masses may be demonstrated by placing a candle near the
top and near the bottom of the partially- opened door of a warm room. At
the top, the flame will be turned from the room towards the outside, while
the contrary effect will be produced when the candle is placed on the
ground. The two effects are caused by the current of heated air which
issues by the top of the door, while the cold air which replaces it enters at
the bottom.

In order to have a good draught, a chimney ought to satisfy the following
conditions : —

i. The section of the chimney ought not to be larger than is necessary to
allow an exit for the products of combustion ; otherwise ascending and de-
scending currents are produced in the chimney, which cause it to smoke. It
is advantageous to place on the top of the chimney a conical pot narrower
than the chimney, so that the smoke may escape with sufficient velocity to
resist the action of the wind.

ii. The chimney ought to be sufficiently high, for, as the draught is
caused by the excess of the external over the internal pressure, this excess is
greater in proportion as the column of heated air is longer.

iii. The external air ought to pass into the chamber with sufficient
rapidity to supply the wants of the fire. In an hermetically-closed room
combustibles would not burn, or descending currents would be formed which
would drive the smoke into the room. Usually air enters in sufficient
quantity by the crevices of the doors and windows.

iv. Two chimneys should not communicate, for if one draws better than
the other, a descending current of air is produced in the latter, which carries
smoke with it.

For the strong fires recjuired by steam boilers and the like, very high
chimneys are needed : of course the increase in height would lose its effect
if the hot column above became cooled down. Hence chimneys are often
made with hollow walls — that is, of separate concentric layers of masonry
or brickwork — the space between them containing air.

489. Stoves. — Sieves are apparatus for heating with a detached fire,
placed in a room to be heated, so that the heat radiates in all directions
round the stove. At the lower part is the draught-hole by which the air
necessary for combustion enters. The products of combustion escape by
means of iron chimney-pipes. This mode of heating is one of the most
economical, but it is by no means so healthy as that by open fireplaces, for
the ventilation is very bad, more especially where, as in Sweden and in
Germany, the stoves are fed from the outside of the room. These stoves
also emit a bad smell, arising in part from the decomposition of organic sub-
stances which are always present in the air by their contact with the heated
sides of the chimney-pipes ; or possibly, as Deville and Troost's researches
seem to show, from the difitusion of gases through the heated sides of the
stove.

The heating is very rapid with blackened metal stoves, but they also

470 On Heat. [489-

cool very rapidly. Stoves constructed of polished earthenware, which are
common on the Continent, heat more slowly, but more pleasantly, and they
retain the heat longer.

490. Heating by steam. — Steam, in condensing, gives up its latent heat
of vaporisation, and this property has been used'^in heating baths, workshops,
public buildings, hothouses, &c. For this purpose steam is generated in
Ijoilers similar to those used for steam-engines, and is then made to circulate

in pipes placed in the room
to be heated. The steam
condenses, and in doing so
imparts to the pipes its latent
heat, which becomes free,
and thus heats the surround-
ing air.

491. Heating- by hot
air. — Heating by hot air
consists in heating the air in
the lower part of a building,
from whence it rises to the
higher parts in virtue of its
lessened density. The appa-
ratus is arranged as repre-
sented in fig. 427.

A series of tubes, AB,
only one of which is shown
in the figure, is placed in a
Fig. 427. furnace F, in the cellar. The

air passes into the tubes
through the lower end, A, where it becomes heated, and, rising in the direc-
tion of the arrows, reaches the room M by a higher aperture, B. The
various rooms to be heated are provided with one or more of these aper-
tures, which are placed as low in the room as possible. The conduit O is
an ordinary chimney. These apparatus are more economical than open fire-
places, but they are less healthy, unless special provision is made for venti-
lation.

492. Heating- by hot -water. — This consists of a continuous circulation
of water, which, having been heated in a boiler, rises through a series of tubes,
and then, after becoming cool, passes into the boiler again by a similar
series.

Fig. 428 represents an apparatus for heating a building of several
storeys. The heating apparatus, which is in the basement, consists of a
bell-shaped boiler, 0 o, with an internal flue, F. A long pipe, M, fits in
the upper part of the boiler, and also in the reservoir Q, placed in the
upper part of the building to be heated. At the top of this reservoir there
is a safety valve, j-, by which the pressure of the vapour in the interior can
be regulated.

The boiler, the pipe M, and a portion of the reservoir Q, being filled with
water, as it becomes heated in the boiler an ascending current of hot water
rises to the reservoir Q, while at the same time descending currents of colder

-494]

Cold produced by Expansion of Gases.

47^

and denser water pass from the lower part of the reservoir Q into receivers,
i, d,J\ filled with water. The water from these passes again through pipes
into other receivers,
a, c, e^ and ultimately
reaches the lower
part of the boilei'.

During this circu-
lation the hot watei
heats the pipes and
the receivers, which
thus become true
water-stoves. The
number and the di-
mensions of these
parts are determined
from the fact that a
cubic foot of watei
in falling through a
temperature of one
degree can theoreti-
cally impart the same
increase of tempera-
ture to 3,200 cubic
feet of air (460). In
the interior of the re-
ceivers, a, b, c, d, e, /,
there are cast-iron
tubes which commu-
nicate with the outside by pipes, P, placed underneath the flooring. The air
becomes heated in these tubes, and issues at the upper part of the receiver.

The principal advantage of this mode of heating is that of giving a tem-
perature which is constant for a long time, for the mass of water only cools
slowly. It is much used in hothouses, baths, artificial incubation, drying
rooms, and generally wherever a uniform temperature is desired.

SOURCES OF COLD.

493. Various sources ot cold. — Besides the cold caused by the passage
of a body from a solid to the liquid state, of which we have already spoken,
cold is produced by the expansion of gases, by radiation in general, and more
especially by radiation at night.

494. Cold produced by the expansion of grases. Ice machines. — We
have seen that when a gas is compressed the temperature rises. The reverse
of this is also the case : when a gas is rarefied, a reduction of temperature
ensues, because a quantity of sensible heat disappears when the gas becomes
increased to a larger volume. This may be shown by placing a delicate
Breguet's thermometer under the receiver of an air-pump, and exhausting ;
at each stroke of the piston the needle moves in the direction of zero, and
regains its original position when air is admitted.

A72 On Heat. [494-

The production of cold when a gas is expanded has been extensively
applied in machines for artificial refrigeration on a large scale. By Wind-
hausen's ice machine, from 15,000 to 150,000 feet of air can be cooled in an
hour, through 40 to 100 degrees in temperature, by means of a steam-engine
of from 6 to 20 horse-power. The essential parts of this machine are repre-
sented in fig. 429. The piston B in the cylinder A is worked to the right by
a steam-engine and to the left by a steam-engine and by the compressed air.
As it moves towards the right the valve a opens, and air under the ordinary
atmospheric pressure enters the space A,. When this is full the piston moves
towards the left, the air in A is compressed to about 2 atmospheres, the
valve a is closed, the valve b opens, and air passes in the direction of the
arrows into the cooler, C. By its compression it has become strongly
heated, and the necessary cooling is effected by means of pipes through
which cold water circulates, entering at 5 and emerging at 6. The air, thus
compressed and cooled, passes out through the valve c, which is automatically
worked by the machine, into the space Ao, where, in conjunction with the
steam-engine, it moves the piston to the left, and compresses the air in A, ;

Fig. 429.

^^^

for at a certain position of the piston the valve c is closed, the compressed
air in the cylinder A., expands, and thereby is cooled far below the freezing
point. As the piston moves again to the right, the valve d is opened by the
working of the machine, and the cooled air emerges through the tube 4 to
its destination. If it passes into an ordinary room it fills it with snowflakes.
Machines of this kind are extensively employed in the arts ; in breweries,
oil refineries, in the artificial production of ice, and in cooling rooms for the
transport of dead meat, &c., on board ship.

In the Linde machine the material used is ammoniacal gas, which is
liquefied by compression and surface condensation. This lic|uid ammonia
being allowed to evaporate takes the heat for this change of state from the
surrounding bodies, which are thereby cooled. The ammonia vapour thus
formed is again liquefied, and flowing back to the refrigerator is again
evaporated, so that a small quantity of ammonia is always passing through
the same cycle of operations.

A machine of this kind worked by a steam-engine of half a horse-power
can cool in an hour 3,400 cubic yards of air from 10° to 5° C, or 1,400 cubic

-496] Absolute Zero of Temperature. 473

yards from 6° to -4° C. ; or it will produce i cwt. of ice in the same time.
The larger machines are relatively more advantageous.

495. Cold produced by radiation at nigrht. — During the day the
ground receives from the sun more heat than radiates into space, and the
temperature rises. The reverse is the case during night. The heat which
the earth loses by radiation is no longer compensated for, and consequently
a fall of temperature takes place, which is greater according as the sky is
clearer, for clouds send towards the earth rays of greater intensity than
those which come from the celestial spaces. In some winters it has been
found that rivers have not frozen, the sky having been cloudy, although the
thermometer had been for several days below - 4° ; while in other less
severe winters the rivers freeze when the sky is clear. The emissive power
exercises a great influence on the cold produced by radiation ; the greater it
is, the greater is the cold.

In Bengal, the nocturnal cooling is used in manufacturing ice. Large
flat vessels containing water are placed on non-conductmg substances, such
as straw or dry leaves. In consequence of the radiation the water freezes,
even when the temperature of the air is 10° C. The same method can be
applied in all cases with a clear sky.

The Peruvians, in order to preserve the shoots of young plants from
freezing, light great fires in their neighbourhood, the smoke of which, pro-
ducing an artificial cloud, hinders the cooling produced by radiation.

496. Absolute zero of temperature. — As a gas is increased ^^^3 of its
volume for each degree Centigrade, it follows that at a temperature of 273^
C. the volume of any gas measured at zero is doubled. In like manner, if
the temperature of a given volume at zero were lowered through — 273°, the
contraction would be equal to the volume : that is, the volume would not
exist. At this temperature the motion of the molecules of the gas would
completely cease, and the pressure thereby occasioned. In all probability,
before reaching this temperature, gases would undergo some change.

This point on the Centigrade scale is called the absolute zero of tempera-
ture ; the temperatures reckoned from this point are called absolute tem-
peratures. They are clearly obtained by adding 273 to the temperature on
the Centigrade scale. Thus - 35° C. is 238° on the absolute scale of tem-
perature, and + 15° C. is 288^.

474 On Heat. [497

CHAPTER XII.

MECHANICAL EQUIVALENT OF HEAT.

497. Mechanical equivalent of heat. — If the various instances of the
production of heat by motion be examined, it will be found that in all cases
mechanical force is consumed. Thus in rubbing two bodies against each
other, motion is apparently destroyed by friction ; it is not, however, lost,
but appears in the form of a motion of the particles of the body ; the motion
of the mass is transformed into a motion of the molecules.

Again, if a body be allowed to fall from a height, it strikes against the
ground with a certain velocity. According to older views, its motion is de-
stroyed, vis viva is lost. This, however, is not the case ; the vis viva of
the body appears as vis viva of its molecules.

In the case, too, of chemical action, the most productive artificial source
of heat, it is not difficult to conceive that there is, in the act of combining,
an impact of the dissimilar molecules against each other, an effect analogous
to the production of heat by the impact of masses of matter against each
other (483).

In like manner, heat may be made to produce motion, as in the case of
the steam-engine, and the propulsion of shot from a gun.

Traces of a view that there is a connection between heat and motion are
to be met with in the older writers, Bacon for example ; and Locke says,
' Heat is a very brisk agitation of the insensible parts of the object, which
produces in us that sensation from whence we denominate the object hot ;
so that what in our sensation is heat, in the object is nothing but motion.'
Rumford, in explaining his great experiment of the production of heat by
friction, was unable to assign any other cause for the heat produced than
motion ; and Davy, in the explanation of his experiment of melting ice by
friction i)i vacuo., expressed similar views. Carnot, in a work on the steam-
engine, published in 1S34, also indicated a connection between heat and
work.

The views, however, which had been stated by isolated writers had little
or no influence on the progress of scientific investigation, and it is in the
year 1 842 that the modern theories may be said to have had their origin.
In that year Dr. Mayer, a physician in Heilbronn, formally stated that there
exists a connection between heat and work ; and he it was who first intro-
duced into science the expression ' mechanical equivalent of heat.' Mayer
also gave a method by which this equivalent could be calculated ; the par-
ticular results, however, are of no value, as the method, though correct in
principle, is founded on incorrect data.

In the same year too, Colding of Copenhagen published experiments on

497J

Mechanical Equivalent of Heat.

47 S

the production of heat by friction, from which he concluded that the evolu-
tion of heat was proportional to the mechanical energy expended.

About the same time as Mayer, but quite independently of him. Joule
commenced a series of experimental investigations on the relation between
heat and work. These first drew the attention of scientific men to the
subject, and were admitted as a proof that the transformation of heat into
mechanical energy, or of mechanical energy into heat, always takes place in
a definite numerical ratio.

Subsequently to Mayer and Joule, several physicists, by their theoretical
and experimental investigations, have contributed to establish the mechanical
theory of heat : namely, in this country. Sir W. Thomson and Rankine ; in
(jermany, Helmholtz, Clausius, and Holtzmann ; and in France, Clapeyron,
and Regnault. The following are some of the most important and satis-
factory of Joule's experiments.

A copper vessel, B (fig. 430), was provided with a brass paddle-wheel
(indicated by the dotted lines), which could be made to rotate about a

vertical axis. Two weights, E and F, were attached to cords which passed
over the pulleys C and D, and were connected with the axis A. These
weights in falling cause the wheel to rotate. The height of the fall, which in
Joule's experiments was about 63 feet, was indicated on the scales G and H.

The roller A was so constructed that by detaching a pin the weights could
be raised without moving the wheel. The vessel B was filled with water
and placed on a stand, and the weights allowed to sink. When they had
reached the ground, the roller was detached from the axis, and the weights
again raised, the same operations being repeated twenty times. The heat
produced was measured by ordinary calorimetric methods (447).

The work expended is measured by the product of the weight into the
height through which it falls, or pk, less the v.-ork lost by the friction of the
various parts of the apparatus. This is diminished as far as possible by the
use of friction wheels {jj), and its amount is determined by connecting C
and D without causing them to pass over A, and then determining the
weight necessary to communicate to them a uniform motion.

476 On Heat. [497

In this way it has been found that a thermal unit— that is, the quantity of
heat by which a pound of water is raised through i° C. — is generated by the
expenditure of. the same amount of work as would be required to raise 1,392
pounds through i foot, or i pound through 1,392 feet. This is expressed by
saying that the mechanical equivalent of the thermal unit is 1,392 foot-
pounds.

The friction of an iron paddle-wheel in mercury gave 1,397 foot-pounds,
and that of the friction of two iron plates gave 1,395 foot-pounds, as the
mechanical equivalent of one thermal unit.

In another series of experiments, the air in a receiver was compressed by
means of a force-pump, both being immersed in a known weight of water at
a known temperature. After 300 strokes of the piston the heat, C, was
measured which the water had gained. This heat was due to the compres-
sion of the air and to the friction of the piston. To eliminate the latter in-
fluence, the experiment was made under the same conditions, but leaving the
receiver open. The air was not compressed, and 300 strokes of the piston
developed C thermal units. Hence C — C is the heat produced by the com-
pression of the gas. Representing the foot-pounds expended in producing

this heat by W, we have ^^p^ for the value of the mechanical equivalent.

By this method Joule obtained the number 1,442.

The mean number which Joule adopted for the mechanical equivalent of
one thermal unit on the Centigrade scale is 1,390 foot-pounds ; on the
Fahrenheit scale it is 772 foot-pounds. The number is called /cw/^'j- ^^z«-
valent, and is usually designated by the symbol J.

On the metrical system 424 metres usually are taken as the height through
which a kilogramme of water must fall to raise its temperature i degree
Centigrade. This is equal to 42,400,000 ^i:^s or 4-24 10" grammes raised
through a height of a centnnetre.
^^*>- ■ Professor Rowland of Baltimore has recently made a very careful and
complete determination of the mechanical equivalent of heat, by Joule's
. ,c>j,nethod, in which he has examined and allowed for all possible sources of
error. His results give 426'9 kilogramme-metres as the mean value of this
constant for the latitude of Baltimore.

Him made the following determination of the mechanical equivalent by
means of the heat produced by the compression of lead. A large block of
sandstone, CD (fig. 431), is suspended vertically by cords ; its weight is P.
E is a piece of lead, fashioned so that its temperature may be determined by
the introduction of a thermometer. The weight of this is n, and its specific
heat c. AB is a cylinder of cast iron, whose weight is/. If this be raised to
A'B', a height of //, and allowed to fall again, it compresses the lead, E,
against the anvil, CD. It remains to measure on the one hand the work
lost, and on the other the heat gained.

The hammer AB being raised to a height //, the work of its fall is ph ;
but as, by its elasticity, it rises again to a height //,, the work \s p (//-//,).
The anvil CD, on the other hand, has been raised through a height H
to CD' and has recjuired in so doing PH units of work. The work, W,
definitely absorbed by the lead \s p (/^-/z,)- PH. On the other hand, the
lead has been heated by 6, it has gained UcO thermal units, c being the

497J

Mechanical Equivalent of Heat.

A77
specific heat of lead, and the mechanical equivalent J is equal to the c[uotient

. A series of six experiments gave 1,394 for the mechanical equivalent

as thus obtained.

\^ '■

, _^ j

g '■- ^

^^^*-;^:^

1---

The recent experiments of Cantoni and Gerosa in this direction are the
simplest. They allowed mercury to fall from a funnel through a narrow
tube into a vessel below, when its temperature was measured. In this way
the number 1,390 was obtained.

Experiments in the opposite direction have also been made, in which the
work produced by one thermal unit was determined. This was done on a
large scale by Hirn by means of a steam-engine of one hundred horse-power.
He determined the quantity of heat contained in the steam before its action,
and then the amount contained in the water after its condensation. This was
less, for some had been expended in work ; and this work as measured by
the dynamometer was equivalent to that which had disappeared, the number
13907 being thus obtained.

The following is the method which origmally Mayer employed in calcu-
lating the mechanical equivalent of heat. It is taken, with slight modifica-
tions, from Prof. Tyndall's work on Heat, who, while strictly following
Mayei-'s reasoning, has corrected his data.

Let us suppose that a rectangular vessel with a section of a square foot
contains at 0° a cubic foot of air under the ordinary atmospheric pressure ;
and let us suppose that it is inclosed by a piston without weight.

Suppose now that the cubic foot of air is heated until its volume is
doubled ; from the coefficient of expansion of air we know that this is the
case at 273° C. The gas in doubling its volume will have raised the piston
through a foot in height ; it will have lifted the atmospheric pressure through
this distance. But the atmospheric pressure on a square foot is in round
numbers 15 x 144 = 2,160 pounds. Hence a cubic foot of air in doubling its
volume has hfted a weight of 2,160 pounds through a height of a foot.

Now, a cubic foot of air at zero weighs 1-29 ounce, and the specific heat
of air under constant pressure — that is, when it can expand freely — as com-
pared with that of an equal weight of water, is 0-24 ; so that the quantity of
heat which will raise 1-29 ounce of air through 273° will only raise 0-24 x 1-29

478

On Heat.

[497-

= 0-31 oz. of water through the same temperature ; but 0*31 oz. of water raised
through 273° is equal to 5-29 pounds of water raised through 1° C.

That is, the quantity of heat which will double the volume of a cubic foot
of air, and in so doing will lift 2,160 pounds through a height of a foot, is
5-29 thermal units.

Now, in the above case the gas has been heated under constant pressure,
that is, when it could expand freely. If, however, it had been heated under
constant volume, its specific heat would have been less in the ratio : 1-414
(460), so that the quantity of heat required under these circumstances to

raise the temperature of a cubic foot of air would be 5"29 < -~ = 374.

Deducting this from 5-29, the diffei-ence 1-55 represents the weight of water
v\'hich would have been raised 1° C. by the excess of heat imparted to the
air when it could expand freely. But this excess has been consumed in the
work of raising 2,160 pounds through a foot. Dividing this by P55 we have
1 5393- Hence the heat which will raise a pound of water through 1° C. will
vaise a weight of 1,393 pounds through a height of a foot ; a numerical value
of the mechanical equivalent of heat agreeing as closely as can be expected
with that which Joule adopted as the most certain of his experimental
results.

The law of the relation of heat to mechanical energy may be thus stated : —
Heat and mechanical energy are iniitiially convertible ', ajid Jieat requires tor
rts production, and produces by its disappearance, mechanical energy in the
ratio of 1,2,^0 foot-pouitds for every thermal unit.

A variety of experiments may in like manner be adduced to show that
whenever heat disappears work is produced. For example, if in a reservoir
immersed in water the air be compressed to the extent of 10 atmospheres :
supposing that now, when the compressed air has acquired the temperature
of the water, it be allowed to act upon a piston loaded by a weight, the
weight is raised. At the same time the water becomes cooler, showing that

497J

Medianical Equivalent of Heat.

479

a certain quantity of heat had disappeared in producing the mechanical
effort of raising the weight. This may also be illustrated by the following
experiment (fig. 432), due to Prof. Tyndall : —

A strong metal box is taken, provided with a stopcock, on which can be
screwed a small condensing pump. Having compressed the air by its means
as it becomes heated by this process, the box is allowed to stand for some
tmie, until it has acquired the temperature of the surrounding medium. On
opening the stopcock the air rushes out : it is expelled by the expansive
force of the internal air ; in short, the air drives itself out. Work is there-
fore performed by the air, and there should be a disappearance of heat ; and
if the jet of air be allowed to strike against the thermopile, the galvano-
meter is deflected, and the direction of its deflection indicates a cooling
(fig. 432). The same effect is observed when, on opening a bottle of soda
water, the carbonic gas which escapes is allowed to impinge against the
thermopile.

If, on the contrary, the experiment is made with an ordinary pair of
bellows, and the current of air is allowed to strike against the pile, the
deflection of the galvanometer is in the opposite direction, indicating an

Fig. 433-

increase of temperature (fig. 433). In this case the hand of the experimenter
performs the work, which is converted into heat.

Joule placed in a calorimeter two equal copper reservoirs, which could
be connected by a tirbe. One of these contained air at 22 atmospheres, the
other was exhausted. When they were connected, they came into equi-
librium under a pressure of 11 atmospheres ; but as the gas in expanding
had done no work, there was no alteration in temperature. When, however,
the second reservoir was full of water, the air in entering was obliged to
expel it and thus perform work, and the temperature sank, owing to an
absorption of heat.

For further information the student of this subject is referred to the
following works : — Tyndall on Heat as a Mode of Motion., Maxwell on Heat.,
Wormell's Thermodynamics (Longmans), and Tait on Thermodynamics

4So On Heat [497-

(Edinondston & Douglas). A condensed, though complete and systematic
account of the dynamical theory of heat is met with in Professor Foster's
articles on ' Heat,' in Watts' Dictionary of Chemistry.

498. Dissipation of energry. — Rankine has the following interesting
observations on a remarkable consequence of the mutual convertibility which
has been shown to exist between heat and other forms of energy : — Sir W.
Thomson has pointed out the fact that there exists, at least in the present
state of the known world, a predominating tendency to the conversion of all
the other forms of physical energy into heat, and to the uniform diffusion of
heat throughout all matter. The form in which we generally find energy
originally collected is that of a store of chemical power consisting of uncom-
bined elements. The combination of these elements produces energy in the
form known by the name of electrical currents, part only of which can be
employed in analysing chemical compounds, and thus reconverted into a
store of chemical power ; the remainder is necessarily converted into heat ;
a part only of this heat can be employed in analysing compounds or in re-
producing electric currents. If the remainder of the heat be employed in
expanding an elastic substance, it may be converted entirely into visible
motion, or into a store of visible mechanical power (by raising weights, for
example), provided the elastic substance is enabled to expand until its
temperature falls to the point which corresponds to the absolute privation
of heat ; but unless this condition is fulfilled a certain proportion only of
the heat, depending on the range of temperature through which the elastic
body works, can be converted, the rest remaining in the state of heat. On
the other hand, all visible motion is of necessity ultimately converted into
heat by the agency of friction. There is, then, in the present state of the
known world, a tendency towards the conversion of all physical energy into
the sole form of heat.

Heat, moreover, tends to diffuse itself uniformly by conduction and radia-
tion, until all matter shall have acquired the same temperature. There is,
consequently, so far as we understand the present condition of the universe,
a tendency towards a state in which all physical energy will be in the state of
heat, and that heat so diffused that all matter will be at the same temperature ;
so that there will be an end of all physical phenomena.

V^ast as this speculation may seem, it appears to be soundly based on
experimental data, and to truly represent the present condition of the uni-
verse as far as we know it.

-499] Theories of Light 481

BOOK VII.

ON LIGHT.

CHAPTER I.

TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT.

499. Theories of light Light is the agent which, by its action on the

retina, excites in us the sensation of vision. That part of physics which deals
with the properties of hght is known as optics.

In order to explain the origin of light, various hypotheses have been made,
the most important of which are the emission or corpuscular theory, and the
undulatory theory.

On the emission theory it is assumed that luminous bodies emit, in all
directions, an imponderable substance, which consists of molecules of an
extreme degree of tenuity : these are propagated in right lines with an almost
infinite velocity. Penetrating into the eye they act on the retina, and deter-
mine the sensation which constitutes vision.

On the undulatory theory, all bodies, as well as the celestial spaces, are
filled by an extremely subtle elastic medium, which is called the lt(miniferoiis
ether. The luminosity of a body is due to an infinitely rapid vibratory motion
of its molecules, which, when communicated to the ether, is propagated in all
directions in the form of spherical waves, and this vibratory motion, being
thus transmitted to the retina, calls forth the sensation of vision. The
vibrations of the ether take place not in the direction of the wave, but in a
plane at right angles to it. The latter are called the transversal vibrations.
An idea of these may be formed by shaking a rope at one end. The vibra-
tions, or to and fro movements, of the particles of the rope, are at right
angles to the length of the rope, but the onward motion of the wave's form
is in the direction of the length.

On the emission theory the propagation of light is effected by a motion
or translation of particles of light thrown out from the luminous body, as a
bullet is discharged from a gun ; on the undulatory theory there is no pro-
gressive motion of the particles themselves, but only of the state of disturb-
ance which was communicated by the luminous body ; it is a motion of
oscillation., and, like the propagation of waves in water, takes place by a series
of vibrations.

The luminiferous ether penetrates all l)odies, but on account of its
extreme tenuity it is uninfluenced by gravitation ; it occupies space, and
although it presents no appreciable resistance to the motion of the denser
bodies, it is possible that it hinders the motion of the smaller comets. It has

482 On Light. [499-

been found, for example, that Encke's comet, whose period of revolution is
about 3^ years, has its period diminished by about O'li of a day at each
successive rotation, and this diminution is ascribed by some to the resistance
of the ether.

The fundamental principles of the undulatory theory were enunciated by
Huyghens, and subsequently by Euler. The emission theor)^, principally
owing to Newton's powerful support, was for long the prevalent scientific
creed. The undulatory theory was adopted and advocated by Young, who
showed how a large number of optical phenomena, particularly those of
diffraction, were to be explained by that theory. Subsequently, too, though
independently of Young, Fresnel showed that the phenomena of diffraction,
and also those of polarisation, are explicable on the same theory, which, since
his time, has been generally accepted.

The undulatory theory not only explains the phenomena of light, but it
reveals an intimate connection between these phenomena and those of heat
r429) ; it shows, also, how completely analogous the phenomena of light are
to those of sound, regard being had to the differences of the media in which
these two classes of phenomena take place.

500. Xiuminous, transparent, translucent, and opaque bodies. — Lumi-
noits bodies are those which emit light, such as the sun, and ignited bodies.
Transparent or diaphanous bodies are those which readily transmit light,
and through which objects can be distinguished : water, gases, polished glass
are of this kind. Translucent bodies transmit light, but objects cannot be
distinguished through them : ground glass, oiled paper, &c., belong to this
class. Opaque bodies do not transmit light ; for example, wood, metals, &c.
No bodies are quite opaque ; they are all more or less translucent when cut
in sufficiently thm leaves.

Foucault showed that when the object-glass of a telescope is thinly
silvered, the layer is so transparent that the sun can be viewed through it
without danger to the eyes, since the metallic surface reflects the greater
part of the heat and light.

501. Iiuminous ray and pencil. — A luminous ray is the direction of the
line in which light is propagated ; a luminous pencil is a collection of rays
from the same source ; it is said to be parallel when it is composed of
parallel rays, divergent when the rays separate from each other, and con-
vergent \\\\^r\ they tend towards the same point. Every luminous body emits
divergent rectilinear rays from all its points, and in all directions.

502. Propagation of light in a homogreneouB medium. — A medium is
any space or substance which light can traverse, such as a vacuum, air, water,
glass, &c. A medium is said to be homogeneous when its chemical compo-
sition and density are the same in all parts.

In every homogeneous medium light is propagated in a right line. For,
if an opaque body is placed in the right line which joins the eye and the
luminous body, the light is intercepted. The light which passes into a dark
room by a small aperture is visible from the light fallin- on the particles of
dust suspended in the atmosphere.

Light changes its direction on meeting an object which it cannot pene-
trate, or when it passes from one medium to another. These phenomena
will be described under the heads rejlection and refraction.

503]

Shadozv, Penumbra.

483

503. Sbadow, penumbra. — When light falls upon an opaque body it
cannot penetrate into the space immediately behind it, and this space is
called the shadow.

In determining the extent and the shape of a shadow projected by a body,
two cases are to be distinguished ; that in which the source of light is a
single point, and that in which it is a body of any given extent.

In the first case, let S (fig. 434) be the luminous point, and M a spherical
body, which causes the shadow. If an infinitely long straight line, SG,

move round the sphere M tangentially, always passing through the point S,
this line will produce a conical surface, which, beyond the sphere, separates
that portion of space which is in shadow from that which is illuminated. In
the present case, on placing a screen, PQ, behind the opacjue body the limit
of the shadow HG will be sharply defined. This is not, however, usually
the case, for luminous bodies have always a certain magnitude, and are not
merely luminous points.

Suppose that the luminous and illuminated bodies are two spheres, SL
and MN (fig. 435). If an infinite straight line, AG, moves tangentially to

both spheres, always cutting the line of the centre in the point A, it will pro-
duce a conical surface with this point for a summit, and which traces behind
the sphere MN a perfectly dark space MGHN. If a second right line, LD,
which cuts the line of centre in B, moves tangentially to the two spheres, so
as to produce a new conical surface, BDC, it will be seen that all the space
outside this surface is illuminated, but that the part between the two conical
surfaces is neither cjuite dark nor quite light. So that if a screen, PQ, is
placed behind the opaque body, the portion cQdYi of the screen is quite in
the shadow, while the space ab receives light from certain parts of the lumi-
nous body, and not from others. It is brighter than the true shadow, and

4«4

On Lis-ht

[503-

not so bright as the rest of the screen, and it is accordingly called the
pcnujitOfa.

Shadows such as these are geometrical sliadou's ; physical shadoiL's, or
those which are really seen, are by no means so sharply defined. A certain
quantity of light passes into the shadow, even when the source of light is a
mere point, and conversely the shadow influences the illuminated part. This
phenomenon, which will be afterwards described, is known by the name of
diffraction (646).

The explanation of the phenomena of eclipses follows directly from the
theory of shadows.

When the opaque disc of the moon comes according to the conditions
between the sun and the earth, the shadow cast by the moon causes a more
or less complete solar eclipse on those parts of the earth which it meets.

Let S be the sun, T the earth, and L the moon placed in a position
favourable for an eclipse (fig. 436). If we can suppose the three bodies

represented with their
7-clativc magnitudes and
distances we need only
repeat the graphical
construction of fig. 436
to determine the dimen-
sions of the cone of the
shadow, and of the pe-
numbra of the moon.
The length LI of the
cone of the shadow
varies between 57 and 59 terrestrial radii, according to the relative positions
of the earth and its satellite ; the distance of the two planets varies between
55 and 62 such radii ; hence under favourable conditions the cone of the

Fig. 436.

shadow may reach the earth, and in those points of the earth thus touched, m.
there is a total eclipse of the sun. As this area has relatively a small extent,
an eclipse which is visible by the inhabitants of this area is not so by those in
the neighbourhood. After the lapse of a time which never exceeds 3 min.

-5041

Images produced by small Apertures.

485

13 sec. the cone will have left the place ;« and will pass to w', which is not
necessarily on the same parallel of latitude. It will thus sweep over the
surface of the earth, in virtue of the special motion of the two heavenly
bodies, along a line which astronomers can determine beforehand. On all
points along- this line (fig. 437) there will successively be a total eclipse ;
for adjacent ones, which are within the cone of the penumbra, the eclipse
will h& partial.

If the cone of the shadow does not reach the earth, there will nowhere be
a total eclipse ; but on a point in' (fig. 43S) there will be no light from the
central part of the sun ; this will then appear like a black circle surrounded
by a bright ring (fig. 439) ; this is what is called an a/mtilar eclipse.

Fig. 439-

Total or partial eclipses of the moon are produced by the total or partial
immersion of the moon in the cone of the shadow cast by the earth ; for an
observer on the moon they would constitute total or partial eclipses of the
sun ; total at those parts of the moon in the shadow, partial at those in the
penumbra.

The traiisits of Venus or of Mercury over the sun are phenomena of the
same kind as eclipses, being produced by the projection on the earth of the
penumbral cones of shadow of those planets. The eclipses of the satellites
of certain planets such as Jupiter are identical with the eclipses of the moon.

504. Imagres produced by small apertures. — When luminous rays,
which pass into a dark chamber tJirougJi a small aperture, are received upon
a screen, they form images of external objects. These images are inverted,

their shape is always that of the external objects, and is independent of the
shape of the aperture.

The inversion of the images arises from the fact that the luminous rays
proceeding from external objects, and penetrating into the chamber, cross
one another in passing the aperture, as shown in fig. 440. Continuing in a
straight line, the rays from the higher parts meet the screen at the lower

486 On Light. [604-

parts ; and conversely, those which come from the lower parts meet the
higher parts of the screen. Hence the inversion of the image. In the
article Camera Obscura it will be seen that the brightness and precision of
these images are increased by means of lenses.

In order to show that the shape of the image is independent of that of
the aperture, when the latter is sufficiently small and the screen at an ade-
quate distance, imagine a triangular aperture, O (fig. 441), made in the door

of a dark chamber, and let ab be a screen on which is received the image of
a flame, AB. A divergent pencil from each point of the flame passes through
the aperture, and forms on the screen a triangular image resembling the
aperture. But the union of all these partial images produces a total image
of the same form as the luminous object. For if we conceive that an infinite
straight line moves round the aperture, with the condition that it is always
tangential to the luminous object AB, and that the aperture is very small,
the straight line describes two cones, the apex of which is the aperture,
while one of the bases is the luminous object and the other the luminous
object on the screen — that is, the image. Hence, if the screen is per-
pendicular to the right line joining the centre of the aperture and the centre
of the luminous body, the image is similar to the body ; but if the screen is
oblique, the image is elongated in the direction of its obliquity. This is
what is seen in the shadow produced by foliage ; the luminous rays passing
through the leaves produce images of the sun, which are either round or
elliptical, according as the ground is perpendicular or oblique to the solar
rays ; and this is the case whatever be the shape of the aperture through
which the light passes.

505. Velocity of ll^bt. — Light moves with such a velocity that at the
surface of the earth there is, to ordinaiy observation, no appreciable interval
between the occurrence of any luminous phenomenon and its perception by
the eye. And, accordingly, this velocity was first determined by means of
astronomical observations. Romer, a Danish astronomer, in 1675, first
deduced the velocity of light from an observation of the eclipses of Jupiter's
first satellite.

Jupiter is a planet, round which four satellites revolve, as the moon
does round the earth. This first satellite, E ^tig. 442), suflcrs occultation —
that is, jiasses into Jupiter's shadow — at equal intervals of time, which arc
42h. 28m. 36s. While the earth moves in that part of its orbit, al\ nearest
Jupiter its distance from that planet docs not materially alter, and the
intervals between two successive occultations of the satellite are approximately

-506] Apparatus for determining the Velocity of Light. 487

the same ; but, in proportion as the earth moves away in its revolution
round the sun, S, the interval between two occultations increases, and when,
at the end of six months, the earth has passed from the position T to the
position T', a total retardation of i6m. 36s. is observed between the time at
which the phenomenon is seen and that at which it is calculated to take
place. But when the earth was in the position T, the sun's light reflected
from the satellite E had to traverse the distance ET, while in the second
position the light had to traverse the distance ET'. This distance exceeds
the first by the quantity TT', for, from the great distance of the satellite E,

Fig. 442,

the rays ET and ET' may be considered parallel. Consequently, light
requires i6m. 36s. to travel the diameter TT'of the terrestrial orbit, or twice
the distance of the earth from the sun, which gives for its velocity 190,000
miles in a second.

The stars nearest the earth are separated from it by at least 206,265
times the distance of the sun. Consequently, the light which they send
requires more than 3 years to reach us. Those stars, which are only visible
by means of the telescope, are possibly at such a distance that thousands
of years would be required for their light to reach our planetaiy system.
They might have been extinguished fer ages without our knowing it.

506. Foucault's apparatus for determining: the velocity of light.—
Notwithstanding the prodigious velocity of light, Foucault succeeded in
determining it experimentally by the aid of an ingenious apparatus, based
on the use of the rotating mirror, which was adopted by Wheatstone in
measuring the velocity of electricity.

In the description of this apparatus, a knowledge of the principal pro-
perties of mirrors and of lenses is presupposed. Fig. 444 represents the
chief parts of Foucault's arrangement. The window shutter, K, of a dark
chamber is perforated by a square aperture, behind which the platinum
wire o is stretched vertically. A beam of sunlight reflected from the out-
side upon a mirror enters the dark room by the square aperture, meets the
platinum wire, and then traverses an achromatic lens, L, with a long focus,
placed at a distance from the platinum wire less than double the principal
focal distance. The image of the platinum wire, more or less magnified,
would thus be formed on the axis of the lens ; but the pencil of light,
having traversed the lens, impinges on a plane mirror, ;;?, rotating with great
velocity ; it is reflected from this, and forms in space an image of the
platinum wire, which is displaced with an angular velocity double that of the
mirror (520). This image is reflected by a concave mirror, M, whose centre

488

On Lio-ht.

[506-

of curvature coincides with the axis of rotation of the mirror tn, and with its
centre of figure. The pencil reflected from the mirror M returns upon itself,
is again reflected from the mirror ;«, traverses the lens a second time, and
forms an image of the platinum wire, which appears on the wire itself so
long as the mirror Jii turns slowly.

In order to see this image without hiding the pencil of light which enters
by the aperture in K, a mirror of unsilvered glass, V, with parallel faces, is
placed between the lens and the wire, and is inclined so that the reflected
rays fall upon a powerful eyepiece, P.

The apparatus being arranged, if the mirror in is at rest, the pencil after
meeting M is reflected to in, and from thence returns along its former path,
till it meets the glass plate V in a, and being partially reflected, forms at d —
the distance ad being equal to ao — an image of the wire, which the eye is
enabled to observe by means of the eyepiece, P. If the mirror, insteadjof
being fixed, is moving slowly round — its axis being at right angles to the

plane of the paper— there will be no sensible change in the position of the
mirror in during the brief interval elapsing while light travels from in to M
and back again, but the image will alternately disappear and reappear. If
now the velocity of Vl is increased to upwards of 30 turns per second, the
interval between the disappearance and reappearance is so short that the
impression on the eye is persistent, and the image appears perfectly steady.
Lastly, if the mirror turns with sufficient velocity, there is no appreciable
change in its position during the time which the light takes in making the
double journey from ;// to M, and from M to in ; the return ray, after its
reflection from the mirror w, takes the direction ;///', and forms its image
at / ; that is, the image has undergone a total deviation di. Speaking pre-
cisely, there is a deviation as soon as the mirror turns, even slowly ; but it is
only appreciable when it has acquired a certain magnitude, which is the case
when the velocity of rotation is sufficiently rapid, or the distance Mw suffi-
( icntly great, for the deviation necessarily increases with the time which the
light takes in returning on its own path.

-507] Experiments of Fizeau. 489

In Foucault's experiment the distance Mw was only 13^ feet ; when the
mirror rotated with a velocity of 600 to 800 turns in a second, deviations of
f^ to ^''-j of a millimetre were obtained.

Taking M;« = /, L;« = /', cL = r, and representing by n the number of
turns in a second, by S the absolute deviation di^ and by V the velocity of
light, Foucault arrived at the formula

a(/4-/')'

from which the velocity of light is calculated at 185,157 miles in a second ;
this number, which is less than that ordinarily assumed, agrees remarkably
well with the value deduced from the new determinations of the value of the
solar parallax.

The mechanism by which the mirror was turned consisted of a small
steam turbine, bearing a sort of resemblance to the syren, and, like that
instrument, giving a higher sound as the rotation is more rapid : in fact, it
is by the pitch of the note that the velocity of the rotation is determined.

In this apparatus liquids can be experimented upon. For that purpose
a tube, AB, 10 feet long, and filled with distilled water, is placed between the
turning mirror in, and a concave mirror M', identical with the mirror M.
The luminous rays reflected by the rotating mirror, in the direction ;;zM',
traverse the column of water AB twice before returning to V. But the return
ray then becomes reflected at c, and forms its image at h : the deviation is
consequently greater for rays which have traversed water than for those
which have passed through air alone ; hence the velocity of light is less in
water than in air.

This is the most important part of these experiments. For it had been
shown theoretically that on the undulator>' theory the velocity of light must
be less in the more highly refracting medium (638), while the opposite is a
necessary consequence of the emission theory. Hence Foucault's result may
be regarded as a crucial test of the validity of the undulatory theory.

507. Szperiments of Flzeau. — In 1849 Fizeau measured directly the
velocity of light, by ascertaining the time it took to travel from Suresnes to
Montmartre and back again. The apparatus employed was a toothed wheel,
capable of being turned more or less quickly, and with a velocity that could
be exactly ascertained. The teeth were made of precisely the same width
as the intervals between them. The apparatus being placed at Suresnes, a
pencil of parallel rays was transmitted through an interval between two
teeth to a mirror placed at Montmartre. The pencil, directed by a properly
arranged system of tubes and lenses, returned to the wheel. As long as the
apparatus was at rest the pencil returned exactly through the same interval
as that through which it first set out. But when the wheel was turned
sufficiently fast, a tooth was made to take the place of an interval, and the
ray was intercepted. By causing the wheel to turn more rapidly, it re-
appeared when the interval between the next two teeth had taken the place
of the former tooth at the instant of the return of the pencil.

The distance between the two stations was 28,334 feet. By means of the
data furnished by this distance, by the dimensions of the wheel, its velocity
of rotation, &c., Fizeau found the velocity of light to be 196,000 miles per

4SO On Light. [507-

second — a result agreeing with that given by astronomical observation as
closely as can be expected in a determination of this kind.

Comu recently investigated the velocity of light by Fizeau's method,
but with improvements so that the probable error did not exceed ^]- of the total
amount ; the two stations, which were 6-4 miles apart, were a pavilion of
the Ecole Polytechnique and a room in the barracks of Mont Valerien. By
means of electromagnetic arrangements the rotation of the toothed disc,
and the times of obscuration and illumination, were registered on a blackened
cylinder, on the principle of the method described in (245). Comu thus
obtained the number 185,420 miles — a result closely agreeing with that
of Foucault, and which is supported by calculations based on the results of
astronomical observations of the transit of Venus in 1874. Michelson made
a determination of the velocity of light by Foucault's method, by which he
obtained the result 186,380, with a possible error of 33 miles.

508. Xiaws of the intensity of llgbt. — The ifitensify of illumination is
the quantity of light received on the unit of surface ; it is subject to the
following laws :• —

I. T/ic intensity of illumination on a given surface is inversely as the
square of its distance from the source oj light.

II. The intensity of illumination which is received obliquely is propor-
tiojial to the cosine of the angle which the Iwninous rays make with the
normal to the illuminated surface.

In order to demonstrate the first law, let there be two circular screens,
CD and AB (fig. 445),. one placed at a certain distance from a source of

light, L, and the other at
double this distance, and
let J and S be the areas
of the two screens. If
a be the total quantity of
lig'ht which is emitted by
the source in the direc-
tion of the cone ALB.
the intensity of the light
on the screen CD— that
is, the quantity which

and the intensity on the screen AB is -.

falls on the unit of surfa

Now as the triangles ALB and CLD are similar, the diameter of AB is
double that of CD ; and as the surfaces of circles are as the squares of their

diameters, the surface S is four times j, consequently the intensity -^ is one-
fourth that of ' .
s

The same law may also be demonstrated by an experiment with the
apparatus represented in fig. 447. It is made by comparing the shadows of an
opaque rod cast upon a glass plate, in one case I)y the light of a single candle,
and in another by tliat of a lamp equalling four candles, placed at double the
distance of the first. In both cases the shadows have the same intensity.

Fig. 445 shows that it is owing to the divergence of the luminous rays

-509]

Photometers.

491

emitted from the same source that the ntensity of hght is inversely as the
square of the distance. The illumination of a surface placed in a beam of
parallel luminous rays is the same at all distances in a vacuum ; in air and
in other transparent media the intensity of light decreases, in consequence
of absorption, more rapidly than the square of the distance.

The second law of intensity corresponds to the law which we have found
to prevail for heat : it may be theoretically deduced as follows : — Let DA,
EB (fig. 446) be a pencil of parallel rays falling obliquely on a surface, AB
and let ovt be the normal to this
surface. If S is the section of the
pencil, a the total quantity of light
which falls on the surface AB, and
I that which falls on the unit of
surface — that is, the intensity of

illumination — we have I =

AB"

But

Fig. 446.

as S is only the projection of AB

on a plane perpendicular to the pencil, we know from trigonometry that

S = AB cos a, from which AB =

This value substituted in the above

equation gives I = -- cos a

a formula which demonstrates the law of the

cosine, for as a and S are constant quantities, I is proportional to cos a.

The law of the cosine applies also to rays emitted obliquely by a luminous
surface ; that is, the rays are less intense in proportion as they are more
inclined to the surface which emits them. In this respect they correspond
to the third law of the intensity of radiant heat.

509. Pbotometers. — A photometer is an apparatus for measuring the
relative intensities of dififerent sources of light.

Rumford's photometer. — This consists of a ground glass screen, in front
of which is fixed an opaque rod (fig. 447) ; the lights to be compared — for

Fig. 447.

instance, a lamp and a candle — are placed at a certain distance in such a
manner that each projects oh the screen a shadow of the rod. The shadows

492 On Light. [509-

thus projected are at first of unequal intensity, but by altering the position
of the lamp, it may be so placed that the intensity of the two shadows is the
same. Then, since the shadow thrown by the lamp is illuminated by the
candle, and that thrown by the candle Is illuminated by the lamp, the illu-
mination of the screen due to each light is the same. The intensities of the
two lights — that is, the illuminations which they would give at equal dis-
tances— are then directly proportional to the squares of their distances from
the shadows ; that is to say, if the lamp is three times the distance of the
candle, its illuminating power is nine times as great.

For if i and i' are the intensities of the lamp and the candle at the unit
of distance, and d and d' their distances from the shadows, it follows, from
the first law of the intensity of light, that the intensity of the lamp at the

distance d is -- and that of the candle — -; at the distance d'. On the screen
d- d-

these two intensities are equal ; hence -r; = '7-; or ~ = -^^j ^vhich was to be

d-d- I d-

proved.

Biinsen's photometer. — When a grease-spot is made on a piece of bibu-
lous paper, the part appears translucent. If the paper be illuminated by a
light placed in front, the spot appears darker than the surrounding space ;

Fie. 448.

if, on the contrary, it be illuminated from behind, the spot appears light on
a dark ground. If the greased part and the rest appear unchanged, the
intensity of illumination on both sides is the same. Bunsen's photometer
depends on an application of this principle. Its essential features are repre-
sented in fig. 448. A circular spot is made on a paper screen by means of a
solution of spermaceti in naphtha : on one side of this is placed a light of a
certain intensity, which serves as a standard ; in London it is a sperm
candle of six to the pound, and burning 120 grains in an hour. The light to
be tested, a petroleum lamp or a gas burner consuming a certain volume of
gas in a given time, is then moved in a right line to such a distance on the
other side of the screen that there is no difference in brightness between the
greased part and the rest of the screen. By measuring the distances of
the lights from the screen by means of the scale, their relative illuminating
powers are resj)cctively as the squares of their distances from the screen.

The difficulty of getting more carefully constructed candles to give a
li).;ht sufficiently uniform for standard purposes has led Harcourt to adopt
as unit the light formed by burning a mixture of 7 volumes pentane gas and

-510] Relative Intensities of Various Sources of LigJit. 493

20 volumes of air, at the rate of half a cubic foot in an hour, in a specially
constructed burner so as to produce a flame of a definite height. This has
been found to answer well in practice. By this kind of detemiination the
degree of accuracy which can be attained is not so great as in many physical
determinations, more especially when the lights to be compared are of dif-
ferent colours ; one, for instance, being yellow, and the other of a bluish tint.
It gives, however, results which are sufficiently accurate for practical pur-
poses, and is almost universally employed for determining the illuminating
power of coal gas and of other artificial lights.

The absolute unit of light adopted by the International Congress of
Electricians is that emitted by a square centimetre of melted platinum at the
moment of its solidification. It is equal to about fifteen standard candles.

Whcatstone's pJwtometer. — The principal part of this instrument is a
steel bead, P (fig. 449), fixed on the
edge of a disc, which rotates on a
pinion, ^, working in a larger
toothed wheel. The wheel fits in a
cylindrical brass box which is held
in one hand, while the other works
a handle, A, which turns a central
axis, the motion of which is trans-
mitted by a spoke, cz, to the pinion
0. In this way the latter turns on ^'^- ''''■ ^'^- ^5°-

itself, and at the same time revolves round the circumference of the box ;
the bead shares the double motion and consequently describes a curve in
the form of a rose (fig. 450).

Now, let M and N be the two lights whose intensities are to be com-
pared ; the photometer is placed between them and rapidly rotated. The
brilliant points produced by the reflection of the light on the two opposite
sides of the bead give rise to two luminous bands, arranged as represented
in fig. 450. If one of them is more brilliant than the other — that which pro-
ceeds from the light M, for instance— the instrument is brought nearer the
other light until the two bands exhibit the same brightness. The distance
of the photometer from each of the two lights being then measured, their
intensities are proportional to the squares of the distances.

510. Relative intensities of various sources of ligrht. — The light of the
sun is 600,000 times as powerful as that of the moon ; and 16,000,000,000
times as powerful as that of a Centauri, the third in brightness of all the
stars. The moon is thus 27,000 times as bright as this star; the sun is 5,500
million times as bright as Jupiter, and 8a billion times as bright as Neptune.
Its light is estimated to be 670,000 times that of a wax candle at a distance
of I foot. According to Fizeau and Foucault the electric light produced by
50 Bunsen's cells is about \ as strong as sunlight.

The relative luminosities of the following stars are as compared with
Vega=i; Pole Star 0-13, Afdebaran 0*30, Saturn 0-47, Arcturus 079,
Mars 2-93, Sinus 4"29i, Jupiter 8-24, Venus 38-9.

A difference in the strength of light or shadow is perceived when the
duller light is ^5 of the brightness of the other, and both are near together,
especially when the shadow is moved about.

494

On Light.

[511-

CHAPTER II.

REFLECTION OF LIGHT. MIRRORS.

511. laws of the reflection of light.— When a ray of light meets a
pohshed surface, it is reflected according to the two following laws, which,
as we have seen, also hold for heat.

I. The angle of reflection is equal to the angle of incidence.

II. The incident and the reflected ray are both in the same plane .^ which
is perpendicular to the reflecting surface.

The words are here used in the same sense as in article 417, and need

no further explanation.

First proof— The two laws may be demonstrated by the apparatus

represented in fig. 451. It consists of a graduated circle in a vertical plane.

Two brass slides move round the cir-
cumference ; on one of them there is
a piece of ground glass, P, and on the
other an opaque screen, X, in the
centre of which is a small aperture.
Fixed to the latter slide there is also
a mirror, M, which can be more or less
inclined, but always remains in a plane
perpendicular to the plane of the gra-
duated circle. Lastly, there is a small
polished metallic mirror, ;//, placed
horizontally in the centre of the circle.
In making the experiment, a pencil
of solar or any suitable artificial light,
S, is caused to fall on the mirror
M, which is so inclined that the re-
flected light passes through the aper-
ture in N, and falls on the centre of
the mirror, ;//. The luminous pencil
then experiences a second reflection
in a direction m\\ which is ascertained

Fig. 451.

by moving P until an image of the aperture is found in its centre. The
number of degrees comprised in the arc AN is then read off, and likewise
that in AP ; these being equal, it follows that the angle of reflection .\wP
is equal to the angle of incidence .X/z/M.

The second law follows from the arrangcinonl of ihc apparatus, the i)lanc
of the rays M/« and inV being parallel to the plane of the graduated circle,
and, consequently, perpendicular to the mirror ///.

-513 J Fonnation of Images by Plane Mirrors. 495

Second proof. — The law of the reflection of light may also be demon-
strated by the following experiment, which is susceptible of greater accuracy
than that just described :— In the centre of a graduated circle, M (fig. 452),
placed in a vertical position, there is a small telescope movable in a plane
parallel to the limb ; at a suitable distance there is a vessel D full of mercury,
which forms a perfectly horizontal plane mirror. Some particular star of
the first or second magnitude is viewed through the telescope in the direc-
tion AE, and the telescope is then inclined so as to receive the ray AD coming
from the star after being reflected from the brilliant surface of the mercury.

Fig. 452

In this way the two angles formed by the rays EA and DA, with the hori-
zontal AH, are found to be equal, from which it may easily be shown that
the angle of incidence E'DE is equal to the angle of reflection EDA. For
if DE is the normal to the surface of the mercuiy, it is perpendicular to AH,
and AED, ADE are the complements of the equal angles EAH, DAH ;
therefore AED, ADE are equal ; but the two rays AE and DE' may be
considered parallel, in consequence of the great distance of the star, and
therefore the angles EDE' and DEA are equal, for they are alternate angles
and, consequently, the angle E'DE is equal to the angle EDA.

REFLECTION OF LIGHT FROM PLANE SURFACES.

512. Mirrors. Xmag-es. — Mirrors are bodies with polished surfaces,
which show by reflection objects presented to them. The place at which
objects appear is their image. According to their shape, mirrors are divided
\r\io plane, concave, convex, spherical, parabolic, cofiical, &c.

513. Formation of imagres by plane mirrors. — The determination of
the position and size of images resolves itself into investigating the images
of a series of points. And first, the case of a single point, A, placed in front
of a plane mirror, MN (fig. 453), will be considered. Any ray, AB, incident
from this point on the mirror is reflected in the direction BO, making the
angle of reflection DBO equal to the angle of incidence DBA.

If, now, a perpendicular, AN, be let fall from the point A on the mirror.

496

On Lidit.

[513-

and if the ray 015 be prolonged below the mirror until it meets this perpen-
dicular in the point a, two triangles are formed, ABX and BXa, which are
equal, for they have the side BX common to both, and the angles AXB,
ABX, equal to the angles rtXB, aBX ; for the angles AXB and aXB are
right angles, and the angles ABX and aBX are each equal to the angle
OBM. From the equality of these triangles, it follows that rtX is equal to
AX ; that is, that any ray, AB, takes such a direction after being reflected,
that its prolongation below the mirror cuts the perpendicular A<z in the point
a, which is at the same distance from the mirror as the point A. This
applies also to the case of any other ray from the point A ; AC. for example.

Fi^. 453-

From this the important consequence follows, that all rays from the point
A, reflected from the mirror, follow, after reflection, the same directiQn as if
they had all proceeded from the point a. The eye is deceived, and sees the
point A at a, as if it were really situated at a. Hence in plane mirrors the
image of any point is formed behind the mirror at a distance equal to that oj
the given point, and on the perpendicular let fall from this point on the
mirror.

It is manifest that the image of any object will be obtained by construct-
ing, according to this rule, the image of each of its points, or, at least, of
those which are suflicient to determine its form. Fig. 454 shows how the
image ab of any object, AB, is formed.

It follows from this construction that in plane mirrors the image is of the
same size as the object ; for if the trapezium ABCD be applied to the trape-
zium DCab, they are seen to coincide, and the object AB agrees with its image.

A further consequence from the above construction is, that in plane
mirrors the image is symmetrical in reference to the object, and not inverted.

514. virtual and real Imagres. — There are two cases relative to the
direction of rays reflected by mirrors according as the rays after reflection
are convergent or divergent. In the first case the reflected rays do not meet,
but if they are supposed to be produced on the other side of the mirror, their
jjrolongations coincide in the same point, as shown in figs. 453 and 454.
The eye is then aftected just as if the rays proceeded from this point, and
it sees an image. But the image has no real existence, the luminous rays do
not come from the other side of the mirror : this appearance is called the
I'irtuul image. The images of real objects produced bj- plane mirrors are of
this kind.

In the second case, where the reflected rays converge, of which we shall

-516]

Multiple Images from Tiuo Plane Mirrors.

497

soon have an example in concave mirrors, the rays coincide at a point in
front of the mirror, and on the same side as the object. They form there an
image called the real image, for it can be received on a screen. The dis-
tinction may be expressed by saying that real images are those fo7-7ncd by
the reflected rays themselves, and virtual images those formed by their pro-
!o)igatio7is.

515. IVIultlple Imagres formed by g^lass mirrors. — Metal mirrors
which have but one reflecting surface give only one image ; glass mirrors
give rise to several images, which are readily ob-
served when the image of a candle is looked at
obliquely in a looking-glass. A very feeble image
IS first seen, and then a very distinct one ; behind
this there are several others, whose intensities gra-
dually decrease until they disappear.

This phenomenon arises from the looking-glass
having two reflecting surfaces. When the rays
from the point A meet the surface, fig. 456, a part is
reflected and forms an image, a, of the point A, on
the prolongation of the ray ^E, reflected by this '^' '*^ '

surface ; the other part passes into the glass (536), and is reflected at c from
the layer of metal which covers the hinder surface of the glass, and reaching
the eye in the direction dW gives the image a'. This image is distant from
the first by double the thickness of the glass. It is more distinct, because
metal reflects better than glass.

In regard to other images it will be remarked that whenever light is trans-
mitted from one medium to another — for instance, from glass to air— (536),
only some of the rays get through ; the remainder are reflected at the surface
which bounds the two media. Consequently when the pencil cd, reflected
from f, attempts to leave the glass at d, most of the rays composing it pass
into the air, but some are reflected at d, and continue within the glass.
These are again reflected by the metallic surface, and form a third image of
A ; after this reflection they come to MN, when many emerge and render
the third image visible ; but some are again reflected within the glass, and
in a similar manner give rise to a fourth, fifth,
&c., image, thereby completing the series
above described. It is manifest from the
above explanation that each image must be
much feebler than the one preceding it, and
consequently only a small number are visible
— ordinarily not more than eight or ten in
all.

This multiplicity of images is objection-
able in observations, and, accordingly, me-
tal mirrors are to be preferred in optical
instruments.

:i6. Multiple images f>om two plane

Fig- 457-

mirrors.- When an object is placed be-
tween two plane mirrors, which form an angle with each other, either right
or acute, images of the object are formed, the number of which increases

K K

498

Oft Li^ht.

[516-

with the inclination of the mirrors. If they are at right angles to each
other, three images are seen, arranged as represented in fig. 457. The rays
OC and OD from the point O, after a single reflection, give the one an
image O', and the other an image O", while the ray OA, which has under-
gone two reflections at A and B, gives the third image O'". When the
angle of the mirrors is 60°, five images are produced, and seven if it is 45°.
The number of images continues to increase in proportion as the angle
diminishes, and when it is zero — that is, when the mirrors are parallel — the
number of images is theoretically infinite. In general, if two mirrors are
inclined to each other, the number of images they produce is equal to the
number of times the angle between them is contained in 360.

The kaleidoscope, invented by .Sir D. Brewster, depends on this property
of inclined mirrors. It consists of a tube, in which are three mirrors inclined
at 60° ; one end of the tube is closed by a piece of ground glass, and the
other by a cap provided with an aperture. Small irregular pieces of coloured
glass are placed at one end between the ground glass and another glass disc,
and on looking through the aperture, the other end being held towards the
light, the objects and their images are seen arranged in beautiful symme-
trical forms ; by turning the tube, an almost endless variety of these shapes
is obtained.

517. Multiple imag-es In two plane parallel mirrors. — In this case
the number of images of an object placed between them is theoretically in-
finite. Physically the number is limited, for as the incident light is never
totally reflected, some of it being always absorbed, the images gradually
become fainter and are ultimately quite extinguished.

Fig. 457 shows how the pencil La reflected once from M gives at I the
image of the object L at a distance ml = ;«L ; then the pencil Lb reflected
once from the mirror M, and once from X, furnishes
the image I' at a distance nV = n\; in like manner
the pencil Lc, after two reflections on M, and one
on N, forms the image I" at a distance }n\" = m\\
and so on for an infinite series. The images /, i\ i"

are formed
in the same
manner by
rays of light
which, emit-
ted by the
object L, fall
first on the
mirror X.
5 I >S. Xrreg:ular reflection. Diffused llg^bt. — The
reflection from the surfaces of polished bodies, the laws
of which have just been stated, is called the rci^ular or
specular reflection ; but the quantity thus reflected is less
'^' ■*' ■ than that of the incident light. The light incident on an

opaque body separates, in fact, into three parts : one is reflected rec^ularly :
another irret^ulitrly — that is, in all directions ; while a third is extinguished,
or r^fAr^rM/ by the reflecting body. If lij^ht falls on a trans|)arcnt body, a
considerable porliim is transmittrd with rcj^ularity.

-520] Reflection of a Ray of Light in a Rotating Mirror. 499

The irregularly reflected light is called scattered light : it is that which
makes bodies visible (502). The light which is reflected regularly does not
give us the image of the reflecting surface, but that of the body from
which the light proceeds. If, for example, a beam of sunlight be incident on
a well-polished mirror in a dark room, the more perfectly the light is reflected
the less visible is the mirror in the different parts of the room. The eye
does not perceive the image of the mirror, but that of the sun. If the reflect-
ing power of the mirror be diminished by sprinkling on it a light powder, the
sun's image becomes feebler, and the mirror is visible from all parts of the
room. Perfectly smooth, polished reflecting surfaces, if such there were,
would be invisible. The beam of light itself is only seen in the room owing
to irregular reflections from the particles of dust, and the like, which are
floating in the air. Tyndall has shown that when this floating matter in the
air in an inclosed space is completely removed, the beam of sunlight or the
electric light is quite invisible. The atmosphere diffuses the light which
falls on it from the sun in all directions, so that it is light in places which
do not receive the direct rays of the sun. Thus, the upper layers of the air
diffuse the light which they receive before sunrise and after sunset, and ac-
cordingly give rise to the phenomena of tiuilight.

519. Intensity of reflected llgrlit.— The intensity of reflected light is
always less than that of the incident light, for some of the original vibrations
are converted into vibrations of the reflecting surfaces. The intensity
increases with the obliquity of the incident ray. For instance, if a sheet
of white paper be placed before a candle, and be looked at very obliquely,
an image of the flame is seen by reflection, which is not the case if the eye
receives less oblique rays.

The intensity of the reflection varies with different bodies, even when
the degree of polish and the angle of incidence are the same. Thus with a
perpendicular incidence the reflected light is | of the incident in the case
of that reflected from a metal mirror, | from mercury, ^-^ from glass, and i
from water. It also varies with the nature of the medium which the ray is
traversing before and after reflection. Polished glass immersed in water
loses a great part of its reflecting power.

In the case of scattered reflection the actual lustre or brightness of a
luminous surface is only a fraction of the light
which falls upon it, and depends on the nature of
the surface. If we call the incident light 100,
we have for the brightness of freshly fallen snow
78, white paper 70, white sandstone 24, porphyrj'
II, and ordinar)- earth 8.

520. Reflection of a ray of llgrbt in a ro-
tating mirror. — When a horizontal ray of light
falls on a plane mirror which can rotate about
a vertical axis, if the mirror is turned through an
angle a, the reflected ray is turned through
double the angle.

Let 7im (fig. 459) be the first position of the mirror, n'lii' its position after
it has been turned through the angle a ; and let OD be the fixed incident
ray. If from the centre of rotation C, with any radius we describe the

500 On Light. [520-

circumference 0;««, and from the point O, where it cuts the incident ray,
chords 00' and OO" are drawn perpendicular respectively to mn and w/';/' ;
the points O' and O" are the images of the point O in the two positions of
the mirror, and the angles CO'D and CO"I)' are each equal to COD. The
lines O'D and 0"D'thus making equal angles with O'C and 0"C, the angle
between the two former lines is equal to that between the two latter ; that
is, it will be equal to O'CO", and will be measured by the arc O'O".
The rotations of the reflected ray and of the mirror are thus measured by
the two arcs O'O" and ;«/;/' respectively.

Now, the two angles O'OO" and wCw' are equal, for they have their
sides perpendicular each to each ; but the angle O'OO", which is an angle
at the circumference, is measured by half the arc O'O", and the angle wCw'
by the whole arc vim' ; hence O'O" is the double of ;«;«', which shows that
when the mirror has turned through an angle a, the reflected ray has turned
through 2f.

521. Radley's reflecting- sextant. — The principal features of this in-
strument, which is used to measure the angular distance of any two distant
objects, are represented in fig. 460. It consists of a metal sector, the arc, cd.

of which is graduated. About
the centre of the sector, an
index arm, ab, turns ; this is
provided with a vernier and
a micrometer screw, by which
the index may be accurately
adjusted and also clamped.
.A. mirror at a is fixed perpen-
dicularly to the arm afy, and
therefore moves with it. A
telescope de is permanently
fixed to the arm at% and oppo-
site to it is a second mirror
in, also permanently fixed :
the lower half of this is
silvered, and the axis of the
telescope just traverses the
boundary of the silvered and
unsilvered part of the mirror.
In making an observation,
the sextant is held so that its plane may pass through both the objects whose
angular distance is to Ije measured. The index arm is at the zero of the
graduation, which indicates the parallelism of the two mirrors. One of the
objects is then viewed in the direction onu through the telescope, and the
unsilvered part of the mirror w. The index arm is then moved until the
eye sees simultaneously with this the image of another object g, which
reaches the eye after successive reflections from the mirror a, and from the
silvered part of the mirror w ; that is, l)y the path i^^anicdo. The angle
ni/ia which the two mirrors now form is measured by the graduation of the
sector cd,Mu\ is half the angle gout. For when the two mirrors were parallel
the angular deflection of the ray^rt, after two reflections, would be zero, and

■/i

Fis. 4^0.

-523] Malice's Heliograph. 501

its deflection is now the angle ^r>/« ; whence, by the last article, the mirror a
must have turned through half that angle, the mirror j/i having been fixed in
position throughout.

522. Measurement of small angles by reflection from a mirror

An important application of the laws of reflection in measuring small
angles of deflection in

magnetic and other ob- ^q

servations was first
made by Gauss. The
principle of this method
will be understood from
fig. 461, in which AO
represents a telescope,
underneath which, and
at right angles to its
axis, is fixed a gradu-
ated scale ss ; the cen-
tre of which, the zero,
corresponds to the axis
of the telescope. "*' '^^'"

Let XS be the object whose angular deflection is to be measured, a mag-
net for instance, and let nuii represent a small perfectly plane mirror fixed
rigidly at right angles to the axis of the magnet. If now, at the beginning
of the observation, the telescope is adjusted so that the image of the zero
appears behind the cross wires, its axis is perpendicular to the mirror. Now
when the mirror is turned, by whatever cause, through an angle a, the eye
will see, through the telescope, the image of another division of the scale, a
for instance, the ray proceeding from which makes with the line cOA. the
angle 2a.

From the distance of this division 0^ from the zero of the scale and the

distance O^ from the mirror we have tan 2a= -^. Thus, for instance, if Oa
is 12 millimetres and Of 5,000 millimetres, then tan 2a =

5,000

2a = Z' 15". As a practised eye can easily read y^„ of a millimetre, it is pos-
sible by such an arrangement to read off an angular deflection of two seconds.

523. Mance's heliograph. — The reflection of light from mirrors has
been applied by Sir H. Alance in signalling at great distances by means of
the sun's light.

The apparatus consists essentially of a mirror about 4 inches in diameter
mounted on a tripod, and provided with suitable adjustments, so that the
sun's light can be received upon it and reflected to a distant station. An
observer then can see through a telescope the reflection of the sun's rays as
a spot of light. The mirror has an adjustment by which it can be made to
follow the sun in its apparent motion. There is also a lever key by which
the signaller can deflect the mirror through a very small angle either to the
right or left, and thus the observer at the distant station sees correspondmg
flashes to the right or left. Under the subject of Telegraphy it will be seen
.how these alternate motions can be used to form an alphabet.

502

On Liq-ht.

[523

The heliograph proved of essential service in the campaigns in Africa
and Afghanistan. Instead of any special form of apparatus, an ordinary
shaving mirror or handglass is frequently used ; and the proper inclination
having been given so as to send the sun's rays to the distant station, which
is very easily effected, the signals are produced by obscuring the mirror by
sliding a piece of paper over it for varying lengths of time. In this way
longer or shorter flashes of light are produced, which, properly combined,
form the alphabet.

Of course this mode of signalling can only be used where the sun's light
is available, but it has the advantage of being cheap, simple, and portable.
Signals have been sent at the rate of 12 words a minute, through distances,
in very fine weather, of 40 miles.

REFLECTION OF LIGHT FROM CURVED SURF.-VCES.

524. Spherical mirrors. — It has been already stated (512) that there
are several kinds of curved mirrors ; those most frequently employed are
spherical and parabolic mirrors.

Spherical mirrors are those whose curvature is that of a sphere ; their
surface may be supposed to be formed by the revolution of an arc MX (fig.
462) about the radius CA, which unites the middle of the arc to the centre
of the circle of which it is a part. According as the reflection takes place

from the internal or from
the e.xternal face of the
mirror, it is said to be
concave or convex. C, the
centre of the hollow sphere
of which the mirror forms
part, is called the centre of
curiuiiure, or geometrical
!'■'?• 462. centre : the point A is the

centre of the figure. The infinite right line AL, which passes through A and
C, is \\\(t principal axis of the mirror; any right line which simply passes
through the centre C, and not through the point A, is a secondary axis.
The angle MCN, formed by joining the centre and extremities of the
mirror, is the aperture. A principal or meridional section is the section
made by a plane through its principal axis. In speaking of mirrors those
lines alone will be considered which lie in the same principal section.

The theory of the reflection of light from curved mirrors is easily deduced
from the laws of reflection from plane mirrors, by considering the surface of
the former as made up of an infinitude of extremely small plane surfaces,
which are its elements. The nornial to the cur\ed surface at a given point is
the perpendicular to the corresponding element, or, what is the same thing,
to its corresponding tangent plane. It is shown in geometry that in spheres
all the normals pass through the centre of curvature, so that the normal may
readily be drawn to any point of a spherical mirror.

525. Focus of a spherical concave mirror. — In a curved mirror the
J\hus is a point in which the reflected rays meet or tend to meet, if produced

either backwards or forwards ; there may either be a real focus or a virtual
focus.

-525] Focus of a Spherical Concave Mirror. 503

Real focus. — We shall first consider the case in which the rays of light
are parallel to the principal axis, which presupposes that the luminous body
is at an infinite distance. Let GD (fig. 462) be such a ray.

From the hypothesis that curved mirrors are composed of a number of
infinitely small plane elements, this ray would be reflected from the element
corresponding to the point D, according to the laws of the reflection from
plane mirrors (513); that is, that CD being the normal at the point of
incidence D, the angle of reflection CDF is equal to the angle of incidence
GDC, and is in the same plane. It follows from this, that the point F, where
the reflected ray cuts the principal axis, divides the radius of curvature AC
very nearly into two equal parts. For in the triangle DFC the angle DCF
is equal to the angle CDG, for they are alternate and opposite angles ; likewise
the angle CDF is equal to the angle CDG, from the laws of reflection ; there-
fore the angle FDC is equal to the angle FCD, and the sides FC and FD
are equal as being opposite to equal angles. Now the smaller the arc AD,
the more nearly does DF equal AF ; and when the arc is only a small number
of degrees, the right lines AF and FC may be taken as approximately equal,
and the point F may be taken as the middle of AC. So long as the aperture
of the mirror does not exceed 8 to 10 degrees, any other ray HB will, after
reflection, pass very nearly through the point F. Hence, for practical pur-
poses, we may say that when a pencil of rays parallel to the axis falls on a
concave mirror the rays intersect after reflection in the same point, which is
at an equal distance from the centre of curvature, and from the mirror. This
point is called the principal focus of the mirror, and the distance AF is the
principal focal distance.

All rays parallel to the axis meet in the point F ; and, conversely, if a
luminous point be placed at F, the rays emitted by this point will after
reflection take the directions
DG, BH, parallel to the
principal axis ; for in this
case the angles of incidence
and reflection have changed
places ; but these angles
always remain equal.

The case is now to be
considered in which the rays
are emitted from a luminous

point, L (fig. 463), placed on the principal axis, but at such a distance that
they are not parallel, but divergent. The angle LKC, which the incident
ray LK forms with the normal KC, is smaller than the angle SKC, which
the ray SK, parallel to the axis, forms with the same normal ; and, conse-
quently, the angle of reflection corresponding to the ray LK must be smaller
than the angle CKF, corresponding to the ray SK. And therefore the ray
LK will meet the axis after reflection in the point /, between the centre C
and the principal focus F. So long as the aperture of the mirror does not
exceed a small number of degrees, all the rays from the point L will inter-
sect after reflection in the point /. This point is called the conjugate focus ;
for there is this connection between the points L and /, that if the luminous
point were transferred to /, its conjugate focus would be at L, IK being the
incident and KL the reflected ray.

504

On Light.

[525-

On considering the figure 463 it will be seen that when the point L is
brought near to or removed from the centre C, its conjugate focus approaches
or recedes in a corresponding manner, for the angles of incidence and re-
flection increase or decrease together.

If the point L coincides with the centre C, the angle of incidence is
null, and as the angle of reflection must be the same, the ray is reflected on
itself, and the focus coincides with the luminous point. When the luminous
point is between the centre C and the principal focus, the conjugate focus in
turn is on the other side of the centre, and is further from the centre accord-
ing as the luminous point is nearer the principal focus. If the luminous point
coincides with the principal focus, the reflected rays, being parallel to the
axis, will not meet, and there is, consequently, no focus.

Virtual focus. — There is, lastly, the case in which the point is placed at
L, between the principal focus and the mirror (fig. 464). Any ray LM,
omitted from the point L, makes with the normal CM an angle of incidence
LMC, greater than FMC ; the angle of reflection must be greater than C.MS,
and therefore the reflected ray ME diverges from the axis AK. This is also
the case with all rays from the point L, and hence these rays do not intersect,

and, consecjuently, form no conjugate focus ; but if they are conceived to be
prolonged on the other side of the mirror, their prolongations will intersect
in the same point, /, on the axis, and the eye experiences the same impression
as if the rays were directly emitted from the point /. Hence a virtual focus
is formed cjuite analogous to those formed by plane mirrors (514).

In all these cases it is seen that the position of the principal focus is
constant, while that of the conjugate foci and of the virtual foci varies. The
principal and the conjugate foci are always on the same side of the mirror as
the luminous point, while the 7>irtual focus is always on the other side of the
mirror.

Hitherto the luminous point has always been supposed to be placed on
the princi])al axis itself, and then the focus is formed on this axis. In the
case in whi( h the luminous point is situate on a seconilary axis, LB (fig. 465),
by applying to this axis the same reasoning as in the preceding case, it will
be seen that the focus of the point L is formed at a point / on the secondary
axis, and that, according to the distance of the point L, the focus may be
either principal, conjugate, or virtual.

526. Pod of convex mirrors. — In convex mirrors there are only virtual
foci. Let SI, TK . . . dig. 466) be rays jiarallcl to the principal axis of a
convex mirror. These rays, after reflection, take the ili\crging directions
IM, KH, which, when continued, meet in a point I", which is ihc principal

527] Determination of tJie Principal Focus of a Mirror. 505

virtual focus of the mirror. By means of the triangle CKF, it may be shown,
in the same manner as with concave mirrors, that the point F is approxi-
mately the centre of the radius of curvature, CA.

Fig. 4C6.

If the incident luminous rays, instead of being parallel to the axis, pro-
ceed from a point L, situated on the axis at a finite distance, it is at once
seen that a virtual focus will be formed at a point /, between the principal
focus F and the mirror.

527. determination of tbe principal focus of a mirror. — In the appli-
cations of concave and convex mirrois it is often necessary to know the
radius of curvature. This is tantamount to finding the principal focus ; for
being situated at the middle of the radius, it is simply necessary to double
the focal distance.

To find this focus with a concave mirror, it is exposed to the sun's rays,
so that its principal axis is parallel to them, and then with a small screen of
ground glass the point is sought at which the image is formed with the
greatest intensity ; this is the principal focus. The radius of the mirror is
double this distance.

If the mirror is convex, it is covered with paper; but two small portions,
H and I, are left exposed at
equal distances from the
centre of the figure A, and on
the same principal section
(fig. 467). A screen MN, in
the centre of which is an
opening larger than the dis-
tance HI, is placed before
the mirror. If a pencil of
solar rays, SH, ST, parallel
to the axis, fall on the mirror, the light is reflected at H and I, on the parts
where the mirror is left exposed, and forms on the screen two brilliant images
at h and i. By moving the screen MN nearer to or farther from the mirror,
a position is found at which the distance hi is double that of HI. The
distance AD from the screen to the mirror then equals the principal focal
distance. For the arc HAI does not sensibly differ from its chord ; and

because the triangles FHI and Yhi are similar,

HI FA

, but HI is half of

hi FD'
hi, and therefore also FA is the half of FD, and therefore AD is equal to

5o6

On Li Hit.

[527-

AF. Further, FA is the principal focal distance ; for the rays SH and S'l
are parallel to the axis ; consequently also twice the distance AD equals the
radius of curvature of the mirror.

528. rormatlon of imagres in concave mirrors. — Hitherto it has been
supposed that the luminous or illuminated object placed in front of the
mirror was simply a point ; but if this object has a certain magnitude,
we can conceive a secondary axis drawn through each of its points, and
thus a series of real or virtual foci could be detennined the collection of
which composes the image of the object. By the aid of the construc-
tions which have served for determining the foci, we shall investigate
the position and magnitude of these images in concave and in convex
mirrors.

Real image. — We shall first take the case in which the mirror is concave,
and the object AB (fig. 468) is on the other side of the centre. To obtain

the image or the focus of any point A, a secondary axis, AE, is drawn from
this point, and then drawing from the point A an incident ray AD, the
normal to this point, CD, is taken, and the angle of reflection CDa is made
equal to the angle of incidence ADC. The point a, where the reflected ray
cuts the secondary axis AE, is the conjugate focus of the pomt A, because
every other ray drawn from this point passes through a. Similarly if a
secondary axis, BI, be drawn from the point B, the rays from this point
meet after reflection in b, and form the conjugate focus of B. And as the
images of all the points of the object are formed between a and b, ab is the
complete image of AB. From what has been said about foci (525), it
follows that this image is real, inverted, smaller tJuin the object, and phucd
between the centre of curvature and the principal focus. This image may be

seen in two ways : by placing
the eye in the continuation of
the reflected rays, and then it is
an aiirial image which is seen ;
or the rays are collected on a
screen, on which the image ap-
pears to be depicted.

If the luminous or illuminated
^''^' ■''"^' object is ])laccd at ab, between

the ])rincipal focus and the centre, its image is formed at AB. It is then a
real but inverted image ; it is larger than the object, and the larger as the
object, ab, is nearer the focus.

-530]

Fornmlcs for Spherical Mirrors.

507

Fis. 470.

If the object is placed in the principal focus itself, no image is produced^
for then the rays emitted from each point form, after reflection, as many
pencils respectively parallel to the secondary axis, which is drawn through
the point from which they are emitted (524), and hence neither foci nor
images are formed.

When all points of the object AB are above the principal axis (fig. 469),
by repeating the preceding construction, it is readily seen that the image of
the object is formed at ab.

Vi7-tual image. — The case remains in which the object is placed between
the principal focus and the mirror. Let AB be this object (fig. 470) ; the
incident rays after reflection
take the directions DI and KH,
and their prolongations form a
virtual image, a, of the point A,
on the secondary axis. Simi-
larly, an image of B is formed
at b ; consequently the eye sees
at ab the imiage of AB. This
image is virtual, erect, and
larger than the object.

From what has been stated,
it is seen that, according to the
distance of the object, concave mirrors produce two kinds of images, or none
at all ; a person notices this by placing himself in front of a concave mirror.
At a certain distance he sees an image of himself inverted and smaller ; this
is the real image ; at a less distance the image becomes confused, and dis-
appears when he is at the focus ; still nearer the image appears erect, but
larger — it is then a virtual image.

529. Formation of imaeres in convex mirrors. — Let AB (fig. 471) be
an object placed in front of a mirror at any given distance. AC and BC are
secondary axes, and it follows,
from what has been already
stated, that all the rays from A
are divergent after reflection,
and that their prolongations pass
through a point a, which is the
virtual image of the point A.
Similarly the rays from B form
a virtual image of it in the point Fig. 471.

b. The eye which receives the

divergent rays DE, KH . . . sees in ab an image of AB. Hence, whatever
the position of an object in front of a convex mirror, the image is always
7<irtual, erect, and smaller than the object.

530. Formulae for spberlcal mirrors. — The relation between the
position of an object and that of its image in spherical mirrors may be
expressed by a very simple formula. In the case of concave mirrors, let
R be its radius of curvature, j?^ the distance LA of the object L (fig. 472),
and/' the distance /A of the image from the mirror. In the triangle LM/,
the perpendicular MC divides the angle LM/ into two equal parts, and from.

5o8 On Light. [530-

geometry it follows that the two segments LC, C/ are to each other as the
two sides containing the angle ; that is,

C/ _ /M . therefore CL x LM = C/x /M.
CL"LM

If the arc AM does not exceed 5 or 6 degrees, the lines AIL and M/ are

approximately equal to AL and A/ ;
that is, to/ and/'.
Further, C/ = CA - A/ = R -/',
and also CL = AL-AC --^p — K.

The value substituted in the
preceding equations gives
'"''■'''• {K-p')p = {p-K)P'.

From which transposing and reducing we have

\<p+\lp'=2pp'.

If the terms of this equation be all divided by//'R, we ol)tain

(I)
(2)

(3)

ivhich is the usual form of the equation.
From the equation (i) we get

P' = -^ . .

which gives the distance of the image from the mirror, in terms of the
distance of the object, and of the radius of curvature.

531. Discussion of the formulae for mirrors. — We shall now in-
vestigate the different values of /', according to the values of/ in the
formula (3).

i. Let the object be placed at an infmite distance on the axis, in which
case the incident rays are parallel. To obtain the value of p', both terms
of the fraction (3) must be divided by/, which gives

R_
/

; that is, th

/' =

• (4)
nage is formed

as / is infinite, is zero, and we have/' :
/

in the principal focus, as ought to be the case, for the incitlent rays are
parallel to the axis.

ii. If the object approaches the mirror,/ decreases, and as the denomi-
nator of the formula (4) diminishes, the value of/' increases ; consequently
the image approaches the centre at the same time as the object, but it is
always between the principal focus and the centre, for so long as

/ is > R, we have - ^ .,> ^ ami < R.

"'/
iii. When the object coincides with the centre, /= R, anil, consei|ucntly,
/' - R ; that is, the image coincides with the object.

-532] Calculation of the Magnitude of Images. 509

iv. When the luminous object is between the centre and the principal
focus, p < R, and hence from the formula (4), /' > R ; that is, the image is
formed on the other side of the centre. When the object is in the focus,

R R

p = ^ which gives /' = -;- = CO ; that is, tlie image is at an infinite distance,

for the reflected rays are parallel to the axis.

V. Lastly, if the object is between the principal focus and the mirror, we

get j^ < ^ ; p' \'i then negative, because the denominator of the formula (4)

is negative. Therefore, the distance p' of the mirror from the image must
be calculated on the axis in a direction opposite to /. The image is then
virtual, and is on the other side of the mirror.

Making p' negative in the formula (2), it becomes -- ^ = — ; in this

p P' "K
form It comprehends all cases of virtual images in concave mirrors.

In the case of convex mirrors the image is always virtual (526) ; p' and
R are of the same sign, since the image and the centre are on the same side
of the mirror, while the object being on the opposite side, / is of the contrary
sign ; hence in the formula (2) we get

'p-rk • • • • (5)

as the formula for convex mirrors. It may also be found directly by the
same geometrical considerations as those which have led to the formula (2)
for concave mirrors.

It must be obser^'ed that the preceding formuhc are not rigorously true,
inasmuch as they depend upon the assumption that the lines LM and /M
(fig. 472) are equal to LA and A/: although this is not true, the error
diminishes without limit with the angle MCA ; and when this angle does
not exceed a few degrees, the error is so small that it may, in practice, be
neglected.

532. Calculation of the mag^nltude of imagres.— By means of the above
formula' the magnitude of an image may Ise calculated when the distance
of the object, its magnitude,
and the radius of the mirror
are given. For if BD be
the object (fig. 473), bd its
image, and if the distance
A and the radius AC be
known, Ac can be calculated
by means of formula (3) of
article 530. Ac known, oZ

can be calculated. But as the triangles BCD and d<Zb are similar, their
bases and heights are in the proportion bd: BD = Cc : CK, or

Length of the image : length of the object
= distance from image to centre : distance from the object to the centre.

The brightness of an image formed by a concave mirror is nearly pro-
portional to its surface, and to the coefiicient of reflection ; and is inversely
as the square of the focal distance.

510 On Light. [533-

533. Spberlcal aberration. Caustics. — In the foregoing explanation
•of the formation of foci and images of spherical mirrors, it has already been
observed that the reflected rays only pass through a single point when the
aperture of the mirror does not exceed 8 or 10 degrees (525). With a larger
aperture the rays reflected near the edges meet the axis nearer the mirror
than those that are reflected at a small distance from the neighbourhood
of the centre of the mirror. Hence arises a want of sharpness in these
images, which is called spherical aberration by re/lcctio/i, to distinguish it
from the spherical aberratio}t by refraction, which occurs in the case of
lenses.

Every reflected ray cuts the one next to it (fig. 474), and their points of
intersection form in space a cun-ed surface which is called the caustic by

rejection. The curve FM repre-
sents one of the branches of a
section of this surface made by the
plane of the paper. When the
light of a candle is reflected from
the inside of a tea-cup or a glass
tumbler, a section of the caustic
surface can be seen by partly filling
'"■ ■*''^' the cup or tumbler with milk.

534. Applications of mirrors. Hellostat. — The applications of plane
mirrors in domestic economy are well known. Mirrors are also frequently
used in physical apparatus for sending light in a certain direction. We
have already seen an application of this in the heliograph (523). The light
of the sun can only be sent in a constant direction by making the mirror
movable. It must have a motion which compensates for the continual change
in the direction of the sun's rays produced by the apparent diurnal motion
of the sun. This result is obtained by means of a clockwork motion, to
which the mirror is fixed, and which causes it to follow the course of the
sun. Such an apparatus is called a heliostat. The reflection of light is also
used to measure the angles of crystals by means of the instruments known
as reflecting gonio)iieters.

Concave spherical mirrors are also often used. They are applied for
magnifying mirrors, as in the older forms of shaving mirrors. They have
been employed for burning mirrors, and are still used in telescopes. They
also serve as reflectors, for conveying light to great distances, by placing
a luminous object in their principal focus. For this purpose, however,
parabolic mirrors are preferable.

The images of objects seen in concave or convex mirrors appear smaller
or larger, but otherwise similar geometrically, except in the case where
some parts of a body are nearer the mirror than others. The distor-
tion of features observed on looking into a spherical garden mirror is more
marked the nearer we are to the glass. Objects seen in cylindrical or
conical mirrors appear ludicrously distorted. From the laws of reflection
the shape of such a distorted figure can be geometrically constructed. In
like manner distorted images of objects can be constructctl which, seen in
such mirrors, appear in their normal proportions. They aif called anamor-
phoses.

-535]

Parabolic Mirrors.

511

535. Parabolic mirrors. — Parabolic mirrors are concave mirrors whose
surface is generated by the revolution of the arc of a parabola, AM, about
its axis AX (fig. 475)-

It has been already stated that in spherical mirrors the rays parallel to
the axis converge only approximately to the principal focus ; and reciprocally,
when a source of light is placed in
the principal focus of these mirrors,
the reflected rays are not exactly
parallel to the axis. Parabolic
mirrors are free from this defect ;
they are more difficult to construct,
but are better for reflectors. It is
a property of a parabola that the
right line FM, drawn from the
focus F to any point M of the
curve, and the line ML, parallel to
the axis AF, make equal angles
with the tangent TT' at this point.
Hence all rays parallel to the axis after reflec-
tion meet in the focus of the mirror F ; and
conversely, when a source of light is placed
in the focus, the rays incident on the mirror
are reflected exactly parallel to the axis.
The light thus reflected tends to maintain its
intensity even at a great distance, for it has
been seen (508) that it is the divergence of the
luminous rays which principally weakens the
intensity of light.

From this property parabolic mirrors are
used in carriage lamps, and in the lamps placed
in front of and behind railway trains. These re-
flectors were formerly used for lighthouses, but
have been replaced by lenticular glasses.

When two equal parabolic mirrors are cut
by a plane perpendicular to the axis passing
through the focus, and are then united at their
intersections as shown in fig. 476, so that their foe
of reflectors is obtained with which a single lamp

Fig. 476.

coincide, a system
illuminates in two

directions at once,
passages.

This arrangement is used in lighting staircases and

512

On Ltzht.

[536

CHAPTER III.

SINGLE REFRACTION. LENSES.

536. .Phenomenon of refraction. — Refraction is the deflection or bending
which the rays of Hght experience in passing obliquely from one medium to
another : for instance, from air into water (fig. 478). We say obHquely
because if the incident ray is perpendicular to the surface separating the two
media, it is not bent, but continues its course in a right hne (fig. 477).

The incident ray being represented by SO (fig. 479), the refracted ray is

Fig. 477-

IH^H

/^"^SSB^Mt^^^^

ji!i^

'Bh

■

"j'J- 1 ■

■

the direction OH which
Hght takes in the second
medium ; and of the
angles SOA and HOB,
which these rays form
with the line AB, at
right angles to the sur-
face which separates the
two media, the first is
the angle of incidence,
and the other the angle
of refraction. Accord-
ing as the refracted ray
approaches or deviates
from the normal, the
second medium is said
to be more or less re-
fringent or refracting
than the first.

All the liijht which

falls on a refracting surface does not completely pass into it ; one part is
reflected and scattered (518), while another penetrates into the medium.

Mathematical analysis shows that the direction of refraction depends on
the relative velocity of light in the two media. On the undulatory theory

-538]

Index of Refraction.

513

the more highly refracting medium is that in which the velocity of propaga-
tion is least.

In uncrystallised media, such as air, licjuids, ordinary glass, the luminous
ray is singly refracted ; but in certain crystallised bodies, such as Iceland
spar, selenite, &c., the incident ray gives rise to two refracted rays. The
latter phenomenon is called double refraction., and will be discussed in another
part of the book. We shall here deal e\clusi\-ely with single refraction.

537. Xiaws of single refraction. — When a luminous ray is refracted in
passing from one medium into another of a different refractive power, the
following laws prevail : —

I, Whatever the obliquity of the incide?it ray, the ratio which the sine of
the incident angle bears to the sine of the angle of refraction is constant for
the same two media, but varies with different media.

II. The incide7it and the refracted ray are i?i the same plane, ivhich is
perpendicular to the surface separating the two media.

These have been known as Descartes' s law ; they are, however, really
due to W'illibrod Snell, who discovered them in 1620; they are demon-
strated by the same apparatus as that used for the laws of reflection (511).
The plane mirror in the centre of the graduated circle is replaced by a
semi-cylindrical glass vessel, filled with water to such a height that its
level is exactly the height of the centre (fig. 480). If the mirror, M, be
then so inclined that a reflected ray, MO, is directed towards the centre, it
is refracted on passing into the water, but it passes out without refraction,
because its direction is then at right angles to the curved sides of the
vessel. In order to observe the course
of the refracted ray, it is received on a
screen, P, which is moved until the
image of the aperture in the screen N
is formed at its centre. In all positions
of the screens N and P, the sines of
the angles of incidence and refraction
are measured by means of two graduated
rules, movable so as to be always hori-
zontal, and hence perpendicular to the
diameter AD.

On reading off the length of the sines
of the angles MOA and DO P in the .
scales I and R, the numbers are found
to vary with the position of the screens,
but their ratio is constant ; that is, if
the sine of incidence becomes twice or
three times as large, the sine of refrac-
tion increases in the same ratio, which
demonstrates the first law. The second
law follows from the arrangement of the
apparatus, for the plane of the graduated 1
of the liquid in the semi-cylindrical vessel

538. Index of refraction. — The ratio between the sines of the incident

Fig. 480.

imb is perpendicular to the surface

and refracted angle is called index of refraction, or refractive index.

L L

514

On LioJit.

[638-

vanes with the media ; for example, from air to water it is *, and from air to
glass it is 'i.

If the media are considered in an inverse order — -that is, if light passes
from water to air, or from glass to air — it follows the same course, but in a
contrary direction, PO becoming the incident and OM the refracted ray.
Consequently the index of refraction is reversed ; from water to air it is then
I, and from glass to air \.

539. Effects produced by refraction. — In consequence of refraction,
bodies immersed in a medium more highly refracting than air, appear nearer
the surface of this medium, but they appear to be more distant if immersed
in a less refracting medium. Let L (fig. 481) be an object immersed in a
mass of water. In passing thence into air, the rays LA, LB . . . diverge
from the normal to the point of incidence, and take the direction AC, BD
. . . , the prolongations of which intersect approximately in the point L',
placed on the perpendicular L'K. The eye receiving these rays sees the
object L at L'. The greater the obhquity of the rays LA, LB . . . the higher
the object appears.

It is for the same reason that a stick plunged obliquely into water appears
bent (fig. 482), the immersed part appearing raised.

An experimental illustration of the effect of refraction is the following : —
A coin is placed in an empty porcelain basin, and the position of the eye is
so adjusted that it is just not visible. If now, the position of the eye re-
maining unaltered, water be poured into the basin, the coin becomes visible.
A consideration of fig. 481 will suggest the explanation of this phenomenon.

Owing to an effect of refraction, stars are visible to us even when they
are below the horizon. For as the layers of the atmosphere are denser in

I .-. 4::]. I'U. 4S:i. I'.-- .( 3.

l)roportion as they are nearer the earth, and as the refractive power of a gas
increases with its density (550), it follows that on entering the atmosphere
the luminous rays become Ijcnt, as seen in fig. 4S3, descril)ing a curve before
reaching the eye, so that we can see the star at S' along the tangent of this
curve instead of at S. In our climate the atmospheric refraction does not
raise the stars when on the horizon more than half a degree.

The effect of refraction is that objects at a distance appear higher than
ihcy are in reality; our horizon is thereby widened. When individual layers
of air refract more strongly than usual, objects may thercl)y become visible
which arc usually below the horizon. Thus, from Hastings, the coast of
France, which is at a distance of 56 miles, is not unfrequcntly seen.

-541]

Miraze.

515

Fig. 435-

540. Total reflection. Critical angrle. — When a ray of light passes
from one medium into another which is less refracting, as from water into
air, it has been
seen that the
angle of inci-
dence is less
than the angle
of refraction.
Hence, when
light is propa-
gated in a mass
of water from S
to O (fig. 484),
there is always

a value of the angle of incidence SOB, such that the angle of refraction AOR
is a right angle, in which case the refracted ray emerges parallel to the
surface of the water.

This angle, SOB, is called the ciitical cutgle, since for any greater angle,
POB, the incident ray cannot emerge, but undergoes an internal reflection,
which is called total reflection because the incident light is entirely reflected.
From water to air the critical angle is 48° 35' : from glass to air, 41° 48'.

The occurrence of this internal reflection may be observed by the follow-
ing experiment :— An object. A, is placed before a glass vessel filled with
water (fig. 485) ; the surface of the liquid is then looked at as shown in the
figure, and an image of the object A is seen at a, formed by the rays reflected
at 7)1, in the ordinary manner of a mirror.

Similar effects of the total reflection of the images of objects contained
in aquaria are frequently observed, and add much to the interest of their
appearance.

In total reflection there is no loss of light from absorption or transmission,
and accordingly it produces the greatest brilliancy. If an empty test-tube
be placed in a slanting position in water, its surface, when looked at from
above, shines as brilliantly as pure mercury ; those rays which fall obliquely
on the side cannot pass into the water, and are, therefore, totally reflected
upwards. If a little water be passed into the tube, that portion of it loses its
lustre. Bubbles, again, in water glisten like pearls, and cracks in transparent
bodies like strips of silver, for the oblique rays are totally reflected. The
lustre of transparent bodies bounded by plane surfaces, such as the lustre of
chandeliers, arises mainly from total reflection. This lustre is the more
frequent and the more brilliant the smaller the limiting angle ; the lustre
of diamond, therefore, is the most brilliant.

541. Mirage. — The mirage is an optical illusion by which inverted images
of distant objects are seen as if below the ground or in the atmosphere. This
phenomenon is of most frequent occurrence in hot climates, and more espe-
cially on the sandy plains of Egypt. The ground there has often the aspect of
a tranquil lake, on which are reflected trees and the surrounding villages.
Monge, who accompanied Napoleon's expedition to Egypt, was the first to
give an explanation of the phenomenon.

It is a phenomenon of refraction, which results from the unequal density

L L 2

5i6 On Light. [541-

of the different layers of the air when they are expanded by contact with the
heated soil. The least dense layers are then the lowest, and the pencil of light
from an elevated object, A (fig. 486), traverses layers which are gradually less
refracting ; for, as will be shown presently (550), the refracting power of a
gas diminishes with lessened density. The angle of incidence accordingly
increases from one layer to the other, and ultimately reaches the critical
angle, beyond which internal reflection succeeds to refraction (540). The
pencil then rises, as seen in the figure, and undergoes a series of successive
refractions, but in the direction contrary to the first, for it now passes
through layers which are gradually more refracting. The pencil then reaches

Fis. 4S6.

the eye with the same direction as if it had proceeded rom a point below
the ground, and hence it gives an inverted image of the object, just as if it
had been reflected at the point O, from the surface of a tranquil lake.

The effect of the mirage may be illustrated artificially, though feebly, as
Dr. WoUaston showed, by looking along the side of a red-hot poker at a word
or object ten or twelve feet distant. At a distance less than three-eighths of
an inch from the line of the poker, an inverted image was seen, and within
and without that an erect image. A better arrangement than a red-hot
poker is a flat sheet-iron box, about 3 feet in length by 5 to 7 inches in
height and breadth (fig. 487) ; it is filled with red hot charcoal and held at a

p^ -Im

Fig. 487.

about the level of the eye. Looking over the litl of the box in the direction
pin a ^/>ri/, and in the direction /;«' an //;7vvYtv/ image of a distant point,/;/,
is seen. The same phenomenon is observed by looking along the sides.

Mariners sometimes sec inverted images in the air of ships and distant
objects which arc still under the horizon ; this is due to the same cause as
the mirage, but is in a contrary direction. The lower layers of the air licing

-543] Prisms. 5 1 7

in contact with the water are cold and dense. The rays of an ol)ject, a ship
for instance, bent in an upward direction are more and more bent away from
the vertical as they are continually passing into gradually less dense layers,
and ultimately fall so obliciuely on an upper attenuated layer that they are
totally reflected downwards, and can thus reach the eye of an observer on the
sea or on the shore. Scoresby observed several such cases in the Polar
seas.

The twinkling or scintillation of the fixed stars is also to be accounted
for by alterations in the direction of the motion of their light due to refrac-
tion.

TRANSMISSION OF LIGHT THROUGH TRANSPARENT MEDIA.

542. ivxedia wltb parallel faces. — When light traverses a medium with
parallel faces, the cinc>-gcnt rays are parallel to the incident rays.

Let MN (fig. 488) be a glass plate with parallel faces, let SA be the
incident and DB the emergent ray, i and r the angles of incidence and of
refraction at the entrance of the ray, and, lastly, i' and r' the same angles
at its emergence. At A the light undergoes

a first refraction, the index of which is

sm /
sin r
(537)- At D it is refracted a second time,

and the index is then— ^ — ,. But we have
smr

seen that the index of refraction of glass to

air is the reciprocal of its refraction from air

, 1 sin i' sm r

to glass ; hence— ^ = . — :.

smr sm z

But as the two normals AG and DE are
parallel, the angles r and i' are equal, as being alternate interior angles. As
the numerators in the above equation are equal, the denominators must also
be equal ; the angles ;-' and / are therefore equal, and hence DB is parallel
to SA.

543. Prism. — In optics a prism is any transparent medium comprised
between two plane faces inclined to each other. The intersection of these
two faces is the edge of the prism, and their inclination is its refracting angle.
Every section perpendicular to the edge is called a. ptincipal section.

The prisms used
for experiments are
generally right trian-
gular prisms of glass,
as shown in fig. 489,
and their principal sec-
tion is a triangle (fig.
490). In this section
the point A is called
the sunimit of the
prism, and the right line BC is called the base : these expressions have
reference to the triangle ABC, and not to the prism.

Fig. 489.

Fi^. 490.

5i8

On Light.

[544-

544. Path of rays In prism. Angle of deviation. — When the laws
of refraction are known, the path of the rays in a prism is readily determined.
Let O be a luminous point (fig. 490) in the same plane as the principal sec-
tion ABC of a prism, and let OD be an incident ray. This ray is refracted
at D, and approaches the normal, because it passes into a more highly
refracting medium. At K it experiences a second refraction, but it then
deviates from the normal, for it passes into air, which is less refractive than
glass. The light is thus refracted twice in the same direction, so that the ray
is dcjiected towards the base, and consequently the eye which receives the
emergent ray KH sees the object O at O' ; that is, objects seen through a
prism appear deflected towards its suvunit. The angle OEO', which the
incident and emergent rays form with each other, expresses the deviation of
light caused by the prism, and is called tlie angle of dc7'iation.

Besides this, objects seen through a prism appear in all the colours of
the rainbow : this phenomenon, known as dispersion, will be afterwards
described (564).

This angle increases with the refractive index of the material of the prism,
and also with its refracting angle. It also varies with the angle under which

Fig. 491

Fig. 492.

the luminous ray enters the prism. The angle of deviation increases up to
a certain limit, which is determined by calculation, knowing the angle of
incidence of the ray, and the refracting angle of the prism.

That the angle of deviation increases with the refractive index may be
shown by means of the polyp) is)n. This name is given to a prism formed
of several prisms of the same angle connected at their ends (fig. 491). These
prisms are made of substances unequally refringcnt, such as flint glass, rock
crystal, or crown glass. If any object— a line, for instance — be looked at
through the polyprism, its different parts are seen at unequal heights. The
highest portion is that seen through the flint glass, the refractive index of

-546] Coiiditio7is of. Emergence in Prisms. 519

which is greatest ; then the rock crystal ; and so on in the order of the
decreasing refractive indices.

The piisin with variable atigle (fig. 492) is used for showing that the
angle of deviation increases with the refracting angle of the prism. It con-
sists of two parallel brass plates, B and C, fixed on a support. Between
these are two glass plates, moving on a hinge, with some friction against the
plates, so as to close it. When water is poured into the vessel the angle
may be varied at will. If a ray of light, S, be allowed to fall upon one of
them, by inclining the other more the angle of the prism increases, and the
deviation of the ray is seen to increase.

545- Application of rigbt-angrled prisms in reflectors. — Prisms whose
principal section is an isosceles right-angled triangle afford an important
application of total reflection (540). For let
ABC (fig. 493) be the principal section of
such a prism, O a luminous point, and OH
a ray at right angles to the face BC. This
ray enters the glass without being refracted,
and makes with the face AB an angle
equal to B — that is, to 45 degrees — and
therefore greater than the limiting angle of
glass, which is 41° 48' (540). The ray OH f"'s- 493-

undergoes, therefore, at H total reflection, which imparts to it a direction
HI perpendicular to the second face AC. Thus the hypotenuse surface of
this prism produces the effect of the most perfect plane mirror, and an eye
placed at I sees O', the image of the point O. This property of right-angle
prisms is frequently used in optical instruments such as the camera lucida
(603) and the prismatic compass (697) instead of metal reflectors, which so
readily tarnish. The newer lighthouse lenses are made up of such prisms.

546. Conditions of emergrence in prisms. — In order that any luminous
rays refracted at the first face of a prism may emerge from the second, it
is necessary that the refractive angle of the prism be less than twice the
critical angle of the substance of which the prism is composed. For if LI
(fig. 494) be the ray incident on the first face, IE the refracted ray, PI and
PE the normals, the ray IE can only emerge from the second face when
the incident angle lEP is less than
the critical angle (540). But as the
incident angle LIN increases, the
angle EIP also increases, while lEP
diminishes. Hence, according as the
direction of the ray LI tends to be-
come parallel with the face AB, does
this ray tend to emerge at the second
face.

Let LI be now parallel to AB, the
angle r is then equal to the critical
angle / of the prism, because it has its
maximum value. Further, the angle
EPK, the exterior angle of the triangle IPE, is equal to ? +/'; but the
angles EPK and A are ecjual, because their sides are perpendicular, and

Fig. 494.

520 On Light. [546-

therefore A = r + /' ; therefore also P^ = l + i\ for in this case r = l. Hence, if
A = 2/ or is >2/, we shall have i' = / or >/, and therefore the ray would not
emerge at the second face, but would be parallel to AC or would undergo
internal reflection, and emerge at a third face, BC. This would be much
more the case with rays whose incident angle is less than BIN, because we
have already seen that i' would continually increase. Thus in the case in
which the refracting angle of a prism is equal to 2/ or is greater, no luminous
ray could pass through the faces of the refracting angle.

As the critical angle of glass is 41° 48', twice this angle is less than 90°,
and, accordingly, objects cannot be seen through a glass prism whose re-
fracting angle is a right angle. As the critical angle of water is 48^ 35',
light could pass through a hollow rectangular prism formed of three glass
plates and filled with water.

If we suppose A to be greater than / and less than 2/, then of rays inci-
dent at I, some within the angle NIB will emerge from AC, others will not
emerge, nor will any emerge that are incident within the angle NIA. If we
suppose A to have any magnitude less than /, all rays incident at I within

the angle NIB will
emerge from AC,
as also will some of
those incident with-
in the angle NIA.

547. Mlniinuin
deviation.- — \\'hen
a pencil of sunlight
passes through an
aperture A, in the
side of a dark cham-
I''s-4U5. ber (fig. 495), the

pencil is projected in a straight line AC, on a distant screen. But if a ver-
tical prism be interposed between the aperture and the screen, the pencil is
deviated towards the base of the prism, and the image is projected at D, at
some distance from the point C. If the prism be turned so that the incident
angle decreases, the disc of light approaches the point C up to a certain
position, E, from which it reverts to its original position even when the prism
is rotated in the same direction. Hence there is a deviation, EBC, less than
any other. It may be demonstrated mathematically that this mittimum
deviation takes place when the angles of incidence and of emergence are
equal.

The angle of minimum deviation may be calculated when the incident
angle and the refracting angle of the prism are known. For when the
deviation is a minimum, then since the angle of emergence ;•' is equal to the
incident angle /(fig. 494), r must et|ual/'. But it has been shown above (546)
that A = r + /■' ; consequently

A = 2;- (I)

angle of deviation LI)/ be called </, this angle being ex-
c DIE, we readily obtain the ctiuation

(t = i ~r+r' — i' = li - 2r,

If the minunui
terior to the trianjj

-550] Measurement of tJie Rcfractii'c Index of Liquids. 521

whence d=2i — A. (2)

which gives the angle d, when i and A are known.

From the formulas (i) and (2) a third may be obtained, which serves to
calculate the index of refraction of a prism when its refracting angle and the
minimum of deviation are known. The index of refraction, ?i, is the ratio

of the sines of the angles of incidence and refraction ; hence n = filLi ; re-

sm r
placing i atid r from their values in the above equations (i) and (2) we get

/A + (/x

(3)

548. AXeasurement of tlie refractive Index of solids. — By means of
the preceding formula (3) the refractive index of a solid may be calculated
when the angles A and d are known.

In order to determine the angle A, the substance is cut in the form of a
triangle prism, and the angle measured by means of a goniometer (534).

The angle d \s measured in the following manner ;— A ray, LI, emitted
from a distant object (fig. 496), is received on the prism, which is turned
in order to obtain the
minimum deviation
EDL'. By means of
a telescope with a
graduated circle the
angle EDL' is read
off, which the re-
fracted ray DE makes
with the ray DL',
coming directly from
the object ; now this is the angle of minimum deviation, assuming that the
object is so distant that the two rays LI and L'D are approximately parallel.
These values then only need to be substituted in the equation (3) to give the
value of n.

549. Measurement of the refractive index of liquids. — Biot applied
Newton's method to determining the refractive index of liquids. For this
purpose a cylmdrical cavity O, of about 075
in diameter, is perforated in a glass prism,
PQ (fig. 497), from the incident face to the
face of emergence. This cavity is closed by
two plates of thin glass which are cemented
on the sides of this prism. Liquids are
introduced through a small stoppered aper-
ture, B. The refracting angle and the
minimum deviation of the liquid prism in
the cavity O having been determined, their
values are introduced into the formula (3), which gives the index.

550. Measurement of the retractive index of gases.— A method for
this purpose, founded on that of Newton, was devised by Biot and Arago.

fig- 497-

522

On Light

[550-

The apparatus which they used consists of a glass tube (fig. 498), bevelled at
its two ends, and closed by glass plates, which are at an angle of 143°.
This tube is connected with a bell-jar, H, in which there is a siphon barometer,
and with a stopcock by means of which the apparatus can be exhausted, and
different gases introduced. After having ex-
hausted the tube AB, a ray of light, SA, is trans-
mitted, which is bent away from the normal
through an angle r = z at the first incidence, and
towards it through an angle /' - r' at the second.
These two deviations being added, the total
deviation d is r — i-^i' — r'. In the case of a
minimum deviation, i = r' and r = i\ whence
</= A - 2/, since r -t- z = A (547). The index from

vacuum to air, which

is evidently-^"-,

sm I

has

therefore the value

(^)

(4)

Hence, in order to deduce the refractive
'^' "^^ ■ index n from vacuum into air, which is the

absolute index or principal itidex, it is merely necessary to know the re-
fracting angle A, and the angle of minimum deviation d. To obtain the
absolute index of any other gas, after having produced a vacuum, this gas is
mtroduced ; the angles A and d having been measured, the above formula
gives the index of refraction from gas to air. Dividing the index of refrac-
tion from vacuum to air by the index of refraction from the gas to air, we
obtain the index of refraction from vacuum to the gas ; that is, its absolute
index.

The square of the refractive index of a substance, less unity, that is «' — i,
measures what is called the refractive action. On the undulatory theory ti-
is the density of the ether in the medium, when i is the density of the ether
in a vacuum. The refractive action is therefore a measure of the excess of
the density of the ether in the refracting medium. The refractive action

divided by the density or

is called the absolute refractive po^i'er.

Table of refractive indices.

Diamond .

2-470 to 2750

Plate glass, St. Gobin

• 1-587

Rutile

. 2-6i6

Rock crystal .

• 1-548

Phosphorus

. 2-224

Rock salt

• 1-545

.Sulphur

• 2-215

Turpentine

• I 471

Ruby .

• 1779

Alcohol .

• I -363

Flint glass .

. 1-702

Albumen

. 1-360

bisulphide of

carbon . . 1-678

Ether .

• 1-358

Iceland spar,

ordinary ray . 1-654

Crystalline lens

. 1384

-551]

Different Kinds of Lenses.

Iceland spar, extraordinary Vitreous lens

ray i'483 Aqueous „ .

Crown glass . . . i-6o8 Water .

Oil of cassia . . . i-6oo Ice

1-339
1-357
1-336
1-310

Vacuum

Hydrogen

Oxygen .

Air

Nitrogen

Ammonia

Refractive indices of gases.
I -000000 Carbonic acid

1-000138
1-000272
I -000294
I -000300
1-000385

Hydrochloric acid
Nitrous oxide .
Sulphurous acid
Olefiant gas
Chlorine .

I -000449
I -000449
1-000503
I -000665
I -000678
1-000772

LENSES. THEIR EFFECTS.

551. Different kinds Of lenses. — Lettscs are transparent media which,
from the curvature of their surfaces, have the property of causing the luminous
rays which traverse them either to converge or to diverge. According to
their curvature they are either spherical, cylindrical, elliptical, or parabolic.
Those used in optics are always exclusively spherical. They are commonly
made either of croiun glass, which is free from lead, or of flint glass, which
contains lead, and is more refractive than crown glass.

The combination of spherical surfaces, either with each other or with
plane surfaces, gives rise to six kinds of lenses, sections of which are repre-
sented in fig. 499 ; four are formed by two spherical surfaces, and two by a
plane and a spherical surface.

M is a double convex, N is a plano-convex, O is a converging concavo-
convex, P is a double concave, Q is a plano-concave, and R is a diverging
concavo-coftvex. The lenses O and R are also called meniscus lenses, from
their resemblance to the crescent-shaped moon.

The first three, which are thicker at the centre than at the borders, are
convergijtg ; the others, which are thinner in the centre, are diverging. In
the first group the double convex lens only need be considered, and in the

Fig. 499.

second the double concave, as the properties of each of these lenses apply
to all those of the same group.

In lenses whose two surfaces are spherical, the centres for these surfaces
are called cetitres of curvature, and the right line which passes through

524

On Li ill It.

[551-

these two centres is i\\t f)ritjcipal axis. In a plano-concave or plano-convex
lens the principal axis is the perpendicular let fall from the centre of the

spherical face on the plane face.

In order to compare the path of
a luminous ray in a lens with that
in a prism, the same hypothesis is
made as for curved mirrors (525) ;
that is, the surfaces of these lenses
are supposed to be formed of an
infinity of small plane surfaces or
elements (fig. 500) : the normal at
any point is then the perpendicular
to the plane of the corresponding
element. It is a geometrical principle
that all the normals to the same
spherical surface pass through its
centre. On the above hypothesis
we can always concei\e two plane
surfaces at the points of incidence
and emergence, which are inclined
to each other, and thus produce
the efilect of a prism. Pursuing
this comparison, the three lenses
M, N, and O may be compared to
a succession of prisms having their
summits outwards, and the lenses
P, Q, and R to a series having
their summits inwards : from this
we see that the first ought to con-
dense the rays, and the latter to
disperse them, for we have already
seen that when a luminous ray traverses a prism it is deflected towards the
base (544).

552. VocX in double convex lenses. — The focus of a lens is the pomt
where the refracted rays, or their prolongations, meet. Double convex

lenses have both real
and virtual foci, like con-
cave mirrors.

Real /od.—W'e shall
first consider the case
m which the luminous
rays which fall on the
lens are parallel to its
l)rincipal axis, as shown
in fig 501. In this case,
any incident ray, LI5, in
approaching the normal ot the point of incidence B, and in diverging from
it at the point of emergence D, is twice refracted towards the axis, which it
cuts at F. As all rays parallel to the axis are refracted in the same manner.

Fig. 5"

I'ig. 501.

-552]

Foci in Double Convex Lenses.

525

it can be shown by calculation that they all pass very nearly through the
point F, so long as the arc DE does not exceed 10° to 12°. This point is
called the principal focus, and the distance FA is xhe pri?tcipal focal dis-
tatice. It is constant in the same lens, but varies with the radii of curvature
and the index of refraction. In ordinary lenses, which are of crown glass,
and in which the radii of the two surfaces are nearly equal, the principal
focus coincides very closely with the centre of curvature.

We shall now consider the case in which the point of light is outside the
principal focus,
but so near that
all incident rays
form a divergent
pencil, as shown
in fig. 502. The
point of light
being at L, by
comparing the
path of a di-
verging ray, LB,

with that of a ray, SB, parallel to the axis, the former is found to make with
the normal an angle, LB;/, greater than the angle SB« ; consequently, after
traversing the lens, the ray cuts the axis at a point, /, which is more distant
than the principal

focus F. As all

rays from the point

L intersect approxi-
mately in the same

point /, this latter

is the conjugate
focus of the point

L ; this term has

the same meaning

here as in the case

of mirrors, and expresses the relation existing between the two points L

and /, which is of such a nature that, if the luminous point is moved to /,

the focus passes to L.

According as the point of light comes nearer the lens, the convergence

of the emergent rays decreases, and the focus / becomes more distant ;

when the point L coin-
cides with the principal

focus, the emergent rays

on the other side are

parallel to the axis, and

there is no focus, or, what

is the same thing, it is

infinitely distant. As the

refracted rays are parallel
in this case, the intensity
of light only decreases slowly and a simple lamp can illuminate great dis-

Fig.

526

On Light.

[552

tances. It is merely necessarj^ to place it in the focus of a double convex
lens, as shown in fig. 504.

Virtual foci. — A double convex lens has a virtual focus when the luminous
object is placed between the lens and the principal focus, as shown in fig. 504.
In this case the incident rays make with the normal greater angles than those
made with the rays FI from the principal focus ; hence, when the fonner
rays emerge, they move farther from the axis than the latter, and fomi a
diverging pencil, HK, GM. These rays cannot produce a real focus, but
their prolongations intersect in some point, /, on the axis, and this point is
the virtual focus of the point L (514).

553. Poci In double concave lenses. — In double concave lenses there
are only virtual foci, whatever the distance of the object. Let SS' be any
pencil of rays parallel to the axis (fig. 505) ; any ray SI is refracted at the

point of incidence I, and approaches the normal CI. At the point of emer-
gence it is also refracted, but diverges from the normal GC', so that it is
twice refracted in a direction which moves it from the axis CC'. As the
same thing takes place for every other ray, S'KMN, it follows that the rays,
after traversing the lens, form a diverging pencil, GHMN. Hence there is
no real focus, but the prolongations of these rays cut one another in a point
F, which is the principal virtual focus.

In the case in which the rays proceed from a point, L (fig. 506), on the
axis, it is found by the same construction that a virtual focus is formed at /,
which is between the principal focus and the lens.

554. Experimental determination of the principal focus offenses. —
To determine the principal focus of a convex lens, it may be exposed to
the sun's rays so that they are parallel to its axis. The emergent pencil
being received on a ground glass screen, the point to which the rays con-
verge is readily seen ; it is the principal focus.

Or an image of an object is
formed on a screen, their respective
distances from which are then mea-
sured, and from these distances the
focus is calculated from the dioptric
formula (561).

With a double concave lens, the
lace (xb (fig. 507) is covered with an
opaque substance, such as lamp-
black, two small apertures a and b
being left in the same principal section, and at an equal distance from the
axis ; a pencil of sunlight is then received on the other face, and the

-655] Optical Centre, Secondary Axis. 527

screen P, which receives the emergent rays, is moved nearer to or farllier
from the lens, until A and B, the spots of light from the small apertures a
and h, are distant from each other by twice ab. The distance DI is then
equal to the focal distance FD, because the triangles Yab and FAB are
similar. Another method of determinmg the focus of a concave lens is
given in article 560.

555. Optical centre, secondary axis. — In every lens there is a point
called the optical centre, which is situate on the axis, and which has the
property that any luminous ray passing through it experiences no angular
deviation ; that is, that the emergent ray is parallel to the incident ray.
The existence of this point may be demonstrated in the following manner : —
Let two parallel radii of cur%^ature, CA and C'A' (fig. 508), be drawn to the

two surfaces of a double convex lens. Since the two plane elements of the
lens A and A' are parallel, as being perpendicular to two parallel right lines,
it will be granted that the refracted ray AA' is propagated in a medium
with parallel faces. Hence a ray KA, which reaches A at such an inclination
that after refraction it takes the direction AA', will emerge parallel to its first
direction (542); the point O, at which the right line cuts the axis, is there-
fore the optical centre. The position of this point may be determined for
the case in which the curvature of the two faces is the same, which is the
usual condition, by observing that the triangles COA and C'OA' are equal,
and therefore that OC = OC, which gives the point O. If the curvatures are
unequal, the triangles COA and COA' are similar, and either CO or CO may
be found, and therefore also the point O.

In double concave or concavo-convex lenses the optical centre may be
determined by the same construction. In lenses with a plane face this point
is at the intersection of the axis by the curved face.

Every right line PP' (fig. 509), which passes through the optical centre
without passing through the centres of cur\-ature, is a secondary axis. From
this property of the optical centre, every secondary axis represents a luminous
rectilinear ray passing through this point : for, from the slight thickness of
the lenses, it may be assumed that rays passing through the optical centre
are in a right line ; that is, that the small deviation may be neglected which
rays experience in traversing a medium with parallel faces (fig. 508).

So long as the secondary axes only make a small angle with the principal
axis, all that has hitherto been said about the principal axis is applicable to
them ; that is, that rays emitted from a point P (fig. 509) on the secondaiy
axis PP' nearly converge to a certain point of the axis P', and according as
the distance from the point P to the lens is greater or less than the principal

528 On Light. [555-

focal distance, the focus thus formed will be conjugate or virtual. This
principle is the basis of what follows as to the formation of images.

556. Formation of imag-es In double convex lenses. — In lenses, as well
as in mirrors, the image of an object is the collection of the foci of its several
points ; hence the images furnished by lenses are real or virtual in the same

case as the foci, and
their construction
resolves itself into
determining the
position of a series
of points, as was
the case with mir-
rors (528).

i. Real image.
Fig. 510. Let AB (fig. 510)

be placed beyond
the principal focus. It a secondary axis, A«, be drawn from the outside
point A, any ray AC, from this point, will be twice refracted at C and
D, and both times in the same direction approaching the secondary axis,
which it cuts at a. From what has been said in the last paragraph, the
other rays from the point A will intersect in the point «, which is accordingly
the conjugate focus of the point A. If the secondary axis be drawn from
the point B, it will be seen, in like manner, that the rays from this point
intersect in the point b ; and as the points between A and B have their
foci between a and b, a real but inverted image of AB will be formed at ab.
To see this image, it may be received on a white screen, on which it will
be depicted, or the eye may be placed in the path of the rays emerging
from it.

Conversely, if ab were the luminous or illuminated object, its image
would be formed at AB. Two consequences important for the theory
of optical instruments follow from this : that, ist, if aft object, even a very
large one, is at a sufficient distance from a double convex lens, the real and
inverted image wJnch is obtained of it is very sfnall — // is near the prin-
cipal focus, but somewhat fartlicr from the lens titan this is ; 2nd, if a very
small object be placed near the principal focus, but a little in front of it, the
image which is formed is at a great distance — it is much larger, and that in
propo7-tion as the object is tiear the principal focus. In all cases the object
and the image are in the same proportion as their distances from the lens.

These two principles are experimentally confirmed by receiving on a
screen the image of a lighted candle, placed successively at various distances
from a doable convex lens.

ii. Virtual image. There is another case in which the object .\B (fig. 511)
is placed between the lens and its principal focus. If a secondary axis On
be drawn from the point A, every ray AC, after having been twice refracted,
diverges from this axis on emerging, since the point A is at a less distance
than the principal focal distance (552). This ray, continued in an opposite
direction, will cut the axis Oa in the point a, which is the virtual focus of the
point A. Tracing the secondary axis of the point B, it will be found,
in the same manner, that the virtual focus of this point is formed at b.

Caustics. 529

This is a virtual image ; it is

proportion as the lens is more

- 558] SpJierical A ber ration.

There is, therefore, an image of Al) at ab.
erect., and larger than the object.

The magnifying power is greater
convex, and the
object nearer
the principal
focus. We shall
presently show-
how the magni-
fying power may
be calculated
by means of the
formula? relating
to lenses (561).
Double convex

lenses, used in this manner as magnifying glasses, are called simple micro-
scopes.

557. Formation of imag-es in double concave lenses. — Double con-
cave lenses, like convex mirrors, only give virtual images, whatever the
distance of the object.

Let AB (fig. 512) be an object placed in front of such a lens. If the
secondary axis AO be drawn from
the point A, all rays, AC, AI, from
this point are twice refracted in the
same direction, diverging from the
axis AO ; so that the eye, receiving
the emergent rays DE and GH,
supposes them to proceed from the
point where their prolongations cut
the secondary axis AO in the point
a. In like manner, drawing a
secondary axis from the point B,
the rays from this point form a pen-
cil of divergent rays, the directions of which, prolonged, intersect in b. Hence
the eye sees at ab a virtual image of AB, which is always erect., and smaller
than the object.

558. Spherical aberration. Caustics. — In speaking about foci, and
about the images formed by different kinds of spherical lenses, it has been
hitherto assumed that the rays emitted from a single point intersect also
after refraction in a single point. This is virtually the case with a lens whose
aperture— 'CciTi.X. is, the angle obtained by joining the edges to the principal
focus — does not exceed 10° or 12°.

Where, however, the aperture is larger, the rays which traverse the lens
near the edge are refracted to a point F nearer the lens than the point G,
which is the focus of the rays which pass near the axis. The phenomenon
thus produced is named spherical aberration by refraction ; it is analogous
to the spherical aberration produced by reflection (533). The luminous sur-
faces fonned by the intersection of the refracted rays are termed caustics by
refraction.

M M

Fig. 512.

530

On Light.

[558-

Spherical aberration is prejudicial to the sharpness and definition of an
image. If a ground glass screen be placed exactly in the focus of a lens,

the image of an ob-
ject will be sharply-
defined in the
centre, but indis-
tinct at the edges ;
and, vice versa, if
the image is sharp
at the edges, it will
be indistinct in the
centre. This defect
is very objection-
able, more espe-
cially in lenses used
for photography. It

Fig. 513

is partially obviated by placing in front of the lenses diaphragms provided
with a central aperture, called stops, which admit the rays passing near the
centre, but cut off those which pass near the edges. The image thereby
becomes sharper and more distinct, though the illumination is less.

If a screen be held between the light and an ordinary double convex
lens which quite covers the lens, but has two concentric series of holes,
two images are obtained, and may be received on a sheet of paper. By
closing one or the other series of holes by a flat paper ring it can be
easily ascertained which image arises from the central, and which from
the marginal rays. When the paper is at a small distance the marginal rays
produce the image in a point, and the central ones in a ring ; the former are
converged to a point, and the latter not. At a somewhat greater distance
the marginal rays produce a ring, and the central ones a point. It is thus
shown that the focus of the marginal rays is nearer the lens than that of the
central rays.

Mathematical investigation shows that convex lenses whose radii of cur-
vature stand in the ratio expressed by the formula
r _4-2«^-H«

are most free from spherical aberration, and are called lenses of best form :
in this formula r is the radius of curvature of the foci turned to the parallel
rays, and r, that of the other face, while n is the refractive index. Thus,

with a glass whose refractive index is "^j r, = 6r. Spherical aberration is

also destroyed by substituting for a lens of short focus two lenses of double
focal length, which are placed at a little distance apart." Greater length of
focus has the result that for the same diameter the aperture and also the
aberration arc less ; and as it is not necessary to stop a great part of the
lens there is a gain in luminosity, which is not purchased by indistinctness
of the images, while the combination of the two lenses has the same focus
as that of the single lens (560). Lenses which are free from spherical aber-
ration are called aplanatic.

-559] Fornmlce relating to Lenses. 531

559. Formulae relating: to lenses. — In all lenses the relations between
the distances of the image and object, the radii of curvature, and the refrac-
tive index may be expressed by a formula. In the case of a double convex
lens, let P be a luminous point situate on the axis (fig. 514), let PI be an in-
cident ray, IE its direction within the lens, EP' the emergent ray, so that P'
is the conjugate focus of P. Further, let CI and CE be the normals to the

points of incidence and emergence, and I PA be put equal to a, EP'A' = /3
ECA' = y, IC'A = S, NIP = z, EIO = r, IEO = z', N'EP' = r.

Because the angle i is the exterior angle of the triangle PIC, and the
angle r' the exterior angle of the triangle CEP', therefore z = a-t-S, and
r' = 7 + /3, whence

z+r' = a-i-8 + y-l-S ^l)

But at the point I, sin i = 7i sin r, and at the point E, sin r' = n sin i (538), n
being the refractive index of the lens. Now if the arc AI is only a small
number of degrees, these sines may be considered as proportional to the
angles z, r, z' and r' ; whence, m the above formula we may replace the sines
by their angles, which gives i^nr and r' = m', from which i + r' = n {r^-i').
Further, because the two triangles lOE and COC have a common equal
angle O, therefore r + i' = y + b, from which z-t-r' = 7z {y+b). Introducing
this value into the equation (i) we obtain

/z (y -(• S) = a -(• jS H- y -I- S, from which (;z - I ) (y -I- S) = a + /3 . (2)

Let CA' be denoted by R, CA by R', PA by^, and P'A' hy p'. Then
with centre P and radius PA describe the arc A^, and with centre P' and
radius P'A' describe the arc A'«. Now when an angle at the centre of a
circle subtends a certain arc of the circumference, the quotient of the arc
divided by the radius measures the angle ; consequently
A^ ^^ Ad „ k-'n A'E ^. . AI
'' = AP°'^^''^ = >-'^= R'^^^^^-R'-
Therefore by substitution in (2), («-i) f^'^+^h = — +— •

V K YL / p p'

Now since the thickness of the lens is very small, the angles are also small,
and A</, AI, A'E, A'« differ but little from coincident straight lines, and are
therefore virtually equal. Hence the above equation becomes

(«-')(^R>)%-%-' (3)

532 On Light. [559-

This is the formula for double convex lenses ; if/ be = :/o — that is, if the
rays are parallel— we have

/' being the principal focal distance. Calling this/ we get

("-)(i-R.)V ..... (4)

from which the value of/ is easily deduced. Considered in reference to
equation (4), the equation (3) assumes the form

'*■,=;. (5)

P P J

which is that in which it is usually employed. When the image is virtual,
p' changes its sign, and formula (5) takes the form

'-' ^\ (6)

P P' f ^ ^

In double concave lenses /'and / retain the same sign, but that of/
changes ; the equation (5) becomes then

III , ,

rj'-f ■■■•■■ (7)

The equation (7) may be obtained by the same reasonings as the other.

560, Combination of lenses. — If parallel rays fall on a conve.x lens A,
which has the focal distance/ and then on a similar lens B with the focal
distance/', at a distance d from A, the distajice from the lens B at which
the image is formed at F is

V f J-d
If the lenses are close together, so that d=o, then

¥ f f

If the lenses have the same curvature, that is /"=/', then „- = ^ ; that is to

say, the focal distance of the combination is half that of a single lens.

If the second lens is a dispersing one of the focal distance /', then

L = ^ _ ' ; and if the lenses are close together, then ^ =^ - } ^.

This formula can be used to determine the focal distance of a concave
lens, by combining it with a convex lens of longer focus, and then deter-
mining the focal distance of the combination.

561. Relative masroltudes of Imasre and object. Determination of
focus. — From the similarity of the triangles AOB, aOb (fig. 510), we get

for the relative magnitudes of image and object the proportion =P ;

lib p'

whence =-^ , where AB = 0 is the magnitude of the object, and ab = \
O /

-563 J Laryngoscope. 533

that of the image; while/ and/' are their respective distances from the

lens. Replacing/' by its value from the equation -+- = i where the

P P'

image is real, or from the equation — — = — where it is virtual, we shall

P P' f

obtain the different values of the ratio — for various positions of the object.
In the first case we have - ^ ^^•

Thus if p>2f I>0

/ = 2/ 1 = 0
/<2/ I>0

In the second case when the image is virtual we shall have

- = / . so that in all cases I >0.
O /-/

By using the above formula we may easily deduce the focal length of a
convex lens where direct sunlight is not available For if it be placed in
front of a scale, and if a screen be placed on the other side, then by altering
the relative positions of the lens and the screen, a position may be found by
trial, such that an image of the object is formed on the screen of exactly the
same size. Dividing now by 4 the total distance between the object and
the screen, we get the focal distance of the lens.

Another method is to place on one side of the lens, and a little beyond
its principal focus, a brightly illuminated scale, which is best of glass, on which
a strong light falls ; on the other side a screen is placed at such a distance
as to produce a greatly magnified distinct image of the scale Then if/ and
L are the lengths of the scale and its image respectively, and d the distance
of the screen from the lens,

562. Determination of the refractive index of a liquid. — By measure-
ments of focal distance the refractive index of a liquid may be ascertained in
cases in which only small quantities of liquid are available.
One face of a double convex lens of known focal distance yj
and known curvature r, is pressed against a drop of the liquid
in question on a plate glass (fig. 515). The liquid forms
thereby a plano-concave lens whose radius of curvature is r.
The focal distance F of the whole system is then determined
experimentally ; this gives the focal length of the liquid lens

/' from the formula Fig. 515.

I _ i_ I

while from the formula - = («— i) we get the value of n.

f r

563. Karyng-oscope. — As an application of lenses may be adduced the
laryngoscope, which is an instrument invented to facilitate the investigation

534

On Lio-ht.

[563-

of the larynx and the other cavities of the mouth. It consists of a plano-
convex lens L, and a concave reflector M, both fixed to a ring which can be
adjusted to any convenient lamp (fig. 516). The flame of a lamp is in the
principal focus of the lens, and at the same time is at the centre of curvature
of the reflector. Hence the divergent pencil proceeding from the lamp to

Fig. 516.

the lens is changed after emerging into a parallel pencil. Moreover, the
pencil from the lamp, impinging upon the mirror, is reflected to the focus ot
the lens, and traverses the lens, forming a second parallel pencil which is
superposed on the first. This being directed into the mouth of a patient,
its condition may be readily observed.

564]

535

CHAPTER IV.

DISPERSION AND ACHROMATISM.

564. Becomposltlon of wblte Ugrht. Solar spectrum. — The pheno-
menon of refraction is by no means so simple as we have hitherto assumed
When -vhite Hght, or that which reaches us from the sun, passes from one
medium into another, it is decomposed into several kinds of light, a pheno-
menon to which the name dispersion is given.

In order to show that white light is decomposed by refraction, a pencil of
the sun's rays SA (fig. 517) is allowed to pass through a small aperture in the
window shutter of a
dark chamber. This
pencil tends to form a
round and colourless
image of the sun at
K ; but if a flint glass
prism arranged hori-
zontally be interposed
in its path, the beam,
on emerging from the
prism, becomes re-
fracted towards its
base, and produces
on a distant screen a
vertical band rounded '^' ^'^'

at the ends, coloured in all the tints of the rainbow, which is called the solar
spectriun (see Plate I.). In this spectrum there is, in reality, an infinity of diffe-
rent tints, which imperceptibly merge into each other, but it is customary to
distinguish seven principal colours. These are violet, indigo, blue, green,
yellow, orange, red ; they are arranged in this order in the spectrum, the
violet being the most refrangible, and the red the least so. They do not all
occupy an equal extent in the spectrum, violet having the greatest extent,
and orange the least.

With transparent prisms of different substances, or with hollow glass
prisms filled with various liquids, spectra are obtained formed of the same
colours, and in the same order ; but when the deviation produced is the
same, the length of the spectrum varies with the substance of which the
prism is made. The angle of separation of two selected rays (say in the red
and the violet) produced by a prism is called the dispersion, and the ratio of

536 On Light. [564-

this angle to the mean deviation of the two rays is called the dispersive power.
This ratio is constant for the same substance so long as the refracting angle
of the prism is small. For the deviation of the two rays is proportional to
the refracting angle ; their difference and their mean vary in the same
manner, and therefore the ratio of their difference to their mean is constant.
For flint glass this is 0-043 J for crown glass it is 0-0246, since the dispersive
power of flint is almost double that of crown glass.

The spectra which are formed by artificial lights rarely contain all the
colours of the solar spectrum ; but their colours are found in the solar
spectrum, and in the same order. Their relative intensity is also modified.
The shade of colour which predominates in the flame predominates also in
the spectrum ; yellow, red, and green flames produce spectra in which the
dominant tint is yellow, red, or green.

565. Production of a pure solar spectrum. — In the above experiment,
when the light is admitted through a wide slit, the spectrum formed is built
up of a series of overlapping spectra, and the colours are confused and indis-
tinct. In order to obtain a pure spectrum, the slit, in the shutter of the dark
room through which light enters, should be from 15 to 25 mm. in height and
from I to 2 mm. in breadth. The sun's rays are directed upon the slit by a
mirror, or still better by a heliostat (534). An achromatic double convex
lens is placed at a distance from the slit of double its own focal length,
which should be about a metre, and a screen is placed at the same distance
from the lens. An image of the slit of exactly the same size is thus formed
on the screen (561). If now there is placed near the lens, between it and
the screen, a prism with an angle of about 60°, and with its refracting edge
parallel to the slit, a very beautiful, sharp, and pure spectrum is formed on
the screen. The prism should be free from strias, and should be placed so
that it produces the minimum deviation.

566. The colours of tbe spectrum are simple, and unequally refran-
gible.— If one of the colours of the spectrum be isolated by intercepting the
others by means of a screen E, as shown in fig. 518, and if the light thus

isolated be allowed to
p:iss through a second
])rism, B, a refraction
will be observed, but
the light remains un-
changed ; that is, the
image received on the

screen H is violet if the

violet pencil has been
'*'■ ^' ■ allowed to pass, blue

if the blue pencil, and so on. Mence the colours of the spectrum ?i.ic simple ;
that is, they cannot be further decomposed by the prism.

Moreover, the colours of the spectrum are unequally refrangible ; that
is, they possess different refractive indices. The elongated shape of the
spectrum would be sufficient to prove the unequal rcfrangibility of the simple
colours, for it is clear that the violet, which is most deflected towards the
base of the prism, is also most refrangible ; and that red, which is least de-
flected, is least refrangible. Hut the unequal rcfrangibility of simple colours

-566]

The Colours of the Spectrum.

537

may be shown by numerous experiments, of which the two following may be
adduced : —

i. Two narrow strips of coloured paper, one rctl and the other violet, are
fastened close to each other on a sheet of black paper. On looking at them
through a prism, they are seen to be unequally displaced, the red band to a
less extent than the violet ; hence the red rays are less refrangible than the
violet.

ii. The same conclusion may be drawn from Newton's experiment with
crossed prisms. On a prism A (fig. 519), in a horizontal jjosition, a pencil

Fijj. 519.

of white light, S, is received, which, if it had merely traversed the prism A,
would form the spectrum r?', on a distant screen. But if a second prism, B,
be placed in a vertical position behind the first, in such a manner that the
refracted pencil passes through it, the spectrum rv becomes deflected towards
the base of the vertical prism ; but, instead of being deflected in a direction
parallel to itself, as would be the case if the colours of the spectrum were
equally refracted, it is obliquely refracted in the direction r'v\ proving that
from red to violet the colours are more and more refrangible.

These different experiments show that the refractive index differs in
different colours ; even rays which arc to j)erception undistinguishablc have
not the same refractive index. In the rcil hand, for instance, the rays at the

extremity of the spectrum are less refracted than those which are nearer the
orange zone. In determining indices of refraction (538), it is usual to take,
as the index of any particular substance, the refrangibility of the yellow ray
in a prism formed of that substance.

S38

On Light.

[567-

567. Recomposition of wbite ligrbt. — Not merely can white light be
resolved into lights of various colours, but by combining the different pencils
separated by the prism white light can be reproduced. This maybe effected
in various ways.

\. If the spectrum produced by one prism be allowed to fall upon a second
prism of the same material and the same refracting angle as the first, but
inverted, as shown in fig. 521, the latter reunites the different colours of
the spectrum, and it is seen that the emer-
gent pencil E, which is parallel to the pencil
S, is colourless.

ii. If the spectrum falls upon a double

convex lens (fig. 520), a white image of the

sun will be formed on a white screen placed

in the focus of the lens ; a glass globe filled

j.,j^ _^ with water produces the same effect as the

lens.

iii. When the spectrum falls upon a concave mirror, a white image is

formed on a screen of ground glass placed in its focus (fig. 522),

iv. Light may be recomposed by means of a pretty experiment, which
consists in receiving the seven colours of the spectrum on seven small glass

I'ig- 523-

mirrors with plane faces, and which can be so inclined in all positions that
the reflected light may be transmitted in any given direction (fig. 523\
When these mirrors are suitably arranged, the seven reflected pencils may
be caused to fall on the ceiling, in such a manner as to form seven distinct
images — red, orange, yellow, &c. When the mirrors are moved so that the
separate images become superposed, a single image is obtained, which is
white.

V. By means oi Newton's disc (fig. 524) it may be shown that the seven
colours of the spectrum form white. This is a cardboard disc of about a
foot in diameter ; the centre and the edges are covered with black paper,
while in the space between there arc pasted strii)s of paper of the colours of
the spectrum. They proceed from the centre to the circumference, and their

-568] Neivton's Tlieory of the Compositio7i of LigJit. 539

relative dimensions and tints are such as to represent five spectra (fig. 525).
When this disc is rapidly rotated, the effect is the same as if the retina
received simultaneously the impression of the seven colours.

vi. If by a mechanical arrangement a prism, on which the sun's light
falls, is made to oscillate rapidly, so that the spectrum also oscillates, the
middle of the spectrum appears white.

These latter phenomena depend on the physiological fact that sensation
always lasts a little longer than the impression from which it results (625).
If a new impression is allowed to act, before the sensation arising from the
former one has ceased, a sensation is obtained consisting of two impressions.
And by choosing the time short enough, three, four, or more impressions
may be mixed with each other. With a rapid rotation the disc (fig. 524)

Fig. S24.

is nearly white. It is not quite so, for the colours cannot be exactly arranged
in the same proportions as those in which they exist in the spectrum, and
moxe.Q\&r pigtne?it colours are not pure (571).

568. Newton's theory of the composition of light. — Newton was the
first to decompose white light by the prism, and to recompose it. From the
various experiments which we have described, he concluded that white light
was not homogeneous, but formed of seven lights unequally refrangible,
which he called simple or primitive lights. Owing to the difference in
refrangibility they become separated in traversing the prism.

The designation of the various colours of the spectrum is to a very great
extent arbitrary ; for, in strict accuracy, the spectrum is made up of an in-
finite number of simple colours, which pass into one another by imperceptible
graduations of colour and refrangibility.

540 On Light. [569-

569. Colour of bodies. — The natural colour of bodies results from the
fact that one portion of the coloured rays contained in white light is
absorbed at the surface of the body. If the unabsorbed portion traverses
the body, it is coloured and transparent ; if, on the contrary, it is reflected,
it is coloured and opaque. In both cases the colour results from the
constituents which have not been absorbed. Those which reflect or
transmit all colours in the proportion in which they exist in the spectrum
are white : those which reflect or transmit none are black. Between these
two Imiits there are infinite tints according to the greater or less extent to
which bodies reflect or transmit some colours and absorb others. Thus a
body appears yellow because it absorbs all colours with the exception of
yellow. In like manner, a solution of ammoniacal oxide of copper absorbs
preferably the red and yellow rays, transmits the blue rays almost completely,
the green and violet less so ; hence the light seen through it is blue.

Accordingly bodies have no colour of their own ; the colour of the body
changes with the nature of the incident light. Thus, if a white body in a
dark room be successively illuminated by each of the colours of the spectrum,
it has no special colour, but appears red, orange, green, &c., according to the
position m which it is placed. If homogeneous light falls upon a body, it
appears brighter in the colour of this light, if it does not absorb this colour ;
but black if it does absorb it. In the light of a lamp fed by spirit in which
some common salt is dissolved, everything white and yellow seems bright,
while other colours, such as vermilion, ultramarine, and malachite, are
black. This is well seen in the case of a stick of red sealing-wax viewed in
such a light. In the light of lamps and of candles, which from the want of
blue rays appear yellow, yellow and white appear the same, and blue seems
like green. In bright twilight or in moonshine the light of gas has a reddish
tint.

570. Mixed colours. Complementary colours. — By mixed colours we
understand the impression of colour which results from the coincident action
of two or more colours on the same position of the retina. This new im-
pression is single ; it cannot be resolved into
its components ; in this respect it differs from
a complex sound, in which the ear, by practice,
can learn to distinguish the constituents. Mixed
colours may be produced by Lamherfs method,
which consists in lookmg in an oblique direction
through a vertical glass plate P (fig. 526) at a
coloured wafer b, while, at the same time, a wafer

J,.. , of another colour g sends its light by reflection

towards the observer's eye ; if ^ is placed in a
proper position, which is easily found by trial, its image exactly coincides
with that of b. The method of the colour disc (567) affords another means
of producing mixed colours.

.•\ very convenient way of investigating the phenomena of mixed colours
is that o{ Maxiueirs colour-discs. These consist of discs of cardboard with
an aperture in the centre, by which they can be fastened on the spindle of the
turning-table (fig. 527). Each disc is painted with a separate colour, and,
having a radial slit, tlicy may be slid over each other so as to overlap to any

-570]

Mixed Colours. Complementary Colours.

541

desired extent (figs. 528 and 529) ; and thus, when in this way two such discs
are rotated, we get the efifect due to this mixture of these two colours. It is
clear also that the eftect of three colours may be investigated in the same way.

Fig. 529.

If in any of the methods by which the impression of mixed spectral
colours is produced, one or more colours be suppressed, the residue corre-
sponds to one of the tints of the spectrum ; and the mixture of the colours
taken away produces the impression of another spectral colour. Thus, if in
fig. 526 the red rays are cut off from the lens L, the light on the focus is no
longer white, but greenish blue. In like manner, if the violet, indigo, and
blue of the colour disc be suppressed, the rest seems yellow, while the mixture
of that which has been taken out is a bluish violet. Hence white can always
be compounded of two tints ; and two tints which together give white are
called complementary colours. Thus of spectral tints red zxvdi greenish yellow
are complementary, so are oraftge and Prussian blue ; yellow and indigo
blue ; greenis/i yellozu and violet.

The method by which Helmholtz investigated the mixture of spectral
colours is as follows : — Two very narrow slits, A and B (fig. 530), at right

angles to each other, are made in the shutter of a dark room ; at a distance
from this is placed a powerfully dispersing prism with its refracting edge
vertical. When this is viewed through a telescope, the slit B gives the
oblique spectrum LM, while the sHt A gives the spectrum ST. These two
spectra partially overlap, and when this is the case two homogeneous spectral
colours mix. Thus at i the red of one spectrum coincides with the green of
the other ; at 3, indigo and yellow coincide ; and so forth.

When the experiment is made with suitable precautions, the colours ob-
tained by mixing the spectral colours are given in the table on the next page,
where the fundamental spectra to be mixed are given in the first horizontal
and vertical column, and the resultant colours where these cross.

The mixture of mixed colours gives rise to no new colours. Only the
same colours are obtained as a mixture of the primitive spectral colours would
yield, except that they are less saturated, as it is called ; that is, more mixed
with white.

542 On Light. [571-

571. Spectral colours and plerment colours. — A distinction must be
made between spectral colours and pig!?ie?it colours. Thus a mixture of
pigment yellow and pigment blue produces green, and not white, as is the
case when the blue and yellow of the spectrum are mixed. The reason of
this is that in the mixture of pigments we have a case of subtraction of
colours, and not of addition. For the pigment blue in the mixture absorbs
almost entirely the yellow and red light ; and the pigment yellow absorbs
the blue and violet light, so that only the green remains.

In the above series are two spectral colours veiy remote in the spectrum,
which have nearly the same complementary tints ; these are red, the com-
plementary colour to which is greenish blue ; and violet, whose complementary
colour is greenish yellow. Now when two pairs of complementary colours
are mixed together they must produce white, just as if only two comple-
mentary colours were mixed. But a mixture of greenish blue and of greenish
yellow is green. Hence it follows that from a mixture of red, green, and
violet, white must be formed. This may easily be ascertained to be the case
by means of a colour disc on which are these three colours in suitable pro-
portions.

Violet

Blue Green Yellow Red

Red

Yellow
Green

Purple

Rose

X Orange

Red

Rose

White

^^- Ye„ow

Pale blue

Bluish
green

Green

Blue

Indigo

Blue

Violet

From the above facts it follows that from a mixture of red, green, and
violet all possible colours may be constructed, and hence these three spectral
colours are called the fundamental colours. It must be remarked that the
tints resulting from the mixture of these three have never the saturation of
the individual spectral colours.

We have to discriminate three points in regard to colour. In the first
place, the /////, or colour proper, by which we mean that special property
which is due to a definite refrang^ibility of the rays producing it ; secondly,
the saturation,\s\\\c\\ depends on the greater or less admixture of white light
with the colours of the spectrum, these being colours which are fully satu-
rated ; and thirdly, there is the intensity, which depends on the amplitude of
vibration.

-573] Properties of tJie Spectrum. 543

572. Homogreneous llgrbt. — The light emitted from luminous bodies is
seldom or never quite pure ; on being examined by the prism it will be found
to contain more than one colour. In optical researches it is frequently of
great importance to procure homogeneous or monochromatic light. Common
salt in the flame of a Bunsen's lamp gives a yellow of great purity. For red
light, ordinary light is transmitted through glass coloured with suboxide of
copper, which absorbs nearly all the rays excepting the red. A very pure
blue is obtained by transmitting ordinary light through a glass trough con-
taining an ammoniacal solution of sulphate of copper, and a nearly pure red
by transmitting it through a solution of sulphocyanide of iron.

573. Properties of tbe spectrum.— Besides its luminous properties, the
spectrum is found to produce calorific and chemical effects.

Luminous properties. It appears from the experiments of Fraunhofer
and of Herschel, that the light in the yellow part of the spectrum has the
greatest intensity, and that in the violet the least.

Heating effects. It was long known that the various parts of the spectrum
differed in their calorific effects. Leslie found that a thermometer placed in
different parts of the spectrum indicated a higher temperature as it moved
from violet towards red. Herschel fixed the maximum intensity of the
heating effects just outside the red ; Berard in the red itself Seebeck
showed that those different effects depend on the nature of a prism ; with a
prism of water the greatest calorific effect is produced in the yellow ; with
one of alcohol it is in the orange-yellow ; and with a prism of crown glass it
is in the middle of the red.

Melloni, by using prisms and lenses of rock salt, and by availing himself
of the extreme delicacy of the thermo-electric apparatus, first made a com-
plete investigation of the calorific properties of the thermal spectrum. This
result led, as we have seen, to the confirmation and extension of Seebeck's
observations.

Chemical properties. In numerous phenomena, light exerts a chemical
action. For instance, chloride of silver blackens under the influence of light ;
transparent phosphorus becomes opaque ; vegetable colouring matters fade -
hydrogen and chlorine gases, when mixed, combine slowly in diffused light,^
and with explosive violence when exposed to direct sunlight. The chemical
action differs in different parts of the spectrum. Scheele found that when
chloride of silver was placed in the violet, the action was more energetic
than in any other part. Wollaston observed that the action extended beyond
the violet, and concluded that, besides the visible rays, there are some in-
visible and more highly refrangible rays. These are the chemical or actinic
rays.

The most remarkable chemical action which light exerts is in the growth
of plant life. The vast masses of carbon and hydrogen accumulated in the
vegetable world owe their origin to the carbonic acid and aqueous vapour
present in the atmosphere. The light which is absorbed by the green parts
of plants acts as a reducing agent. The reduction does not extend to the
complete isolation of carbon and hydrogen, and the individual stages of the
process are unknown to us ; but the general result is, undoubtedly, that under
the influence of the sun's rays the chemical attraction which holds together
the carbon and oxygen is overcome ; the carbon, which is set free, assimilates

544 On Light. [573-

at that moment the elements of water, forming cellulose or woody fibre,
while the oxygen returns to the atmosphere in the form of gas. The
equivalent of the sunlight which has been absorbed is to be sought in the
chemical energy of the separated constituents. When we burn petroleum
or coal, we reproduce, in some sense, the light which the sun has expended
in former ages in the production of a primeval vegetable growth.

The researches of Bunsen and Roscoe show that whenever chemical
action is induced by light, an absorption of light takes place, preferably of
the more refrangible parts of the spectrum. Thus, when chlorine and
hydrogen unite, under the action of light, to form hydrochloric acid, light is
absorbed, and the quantity of chemically active rays consumed is directly
proportional to the amount of chemical action.

There is a curious difference in the action of the different spectral rays.
Moser placed an engraving on an iodised silver plate, and exposed it to the
light until an action had commenced, and then placed it under a violet glass
in the sunlight. After a few minutes a picture was seen with great distinct-
ness, while when placed under a red or yellow glass it required a very long
time, and was very indistinct. When, however, the iodised silver plate was
first exposed in a camera obscura to blue light for two minutes, and was then
brought under a red or yellow glass, an image quickly appeared, but not
when placed under a green glass. It appears as if there are vibrations of a
certain velocity which could commence an action, and that there are others
which are devoid of the property of commencing, but can continue and
complete an action when once set up. Becquerel, who discovered these
properties in luminous rays, called the former exciting rays and the latter
continuing or phosp/wrogenic rays. The phosphorogenic rays, for instance,
have the property of rendering certain objects self-luminous in the dark
after they have been exposed for some time to the light. Becquerel found
that the phosphorogenic spectrum extended from indigo to beyond the
violet.

574. Dark lines of the spectrum. — The colours of the solar spectrum
are not continuous. For se\'eral grades of refrangibility rays are wanting,
and, in consequence, throughout the whole extent of the spectrum there are a
great number of very narrow dark lines. To observe them, a pencil of solar
rays is admitted into a darkened room, through a narrow slit. At a distance
of three or four yards we look at this slit through a prism of flint glass,
which must be very free from flaws, taking care to hold its edge parallel to
the slit. We then observe a great number of very delicate dark lines parallel
to the edge of the prism, and at very unequal intervals.

The existence of the dark lines was first observed by Wollaston in 1802 ;
but PVaunhofer, a celel)rated optician of Munich, first studied and gave a
detailed description of them. Fraunhofer mapped the lines, and indicated
the most marked of them by the letters A, a, li, C, 1), E, b, F, G, H ; they
are therefore generally known as Fraun/io/cr's tines.

The dark line A (see fig. 2 of Plate I.) is at the middle and B halfway
between this and the end of the red ray ; C at the boundary of the red and
orange ray ; D is in the yellow ray ; E, in the green ; F, in the blue ; G, in
the indigo ; H, in the violet. There are certain other noticcalile dark lines,
such as a in the red and /' in the green. In the case of sunlight the positions

-576] Spectroscope. 545

of the dark lines are fixed and definite ; on this account they are used for
obtaining an exact determination of the refractive index (538) of each colour ;
for example, the refractive index of the blue ray is, strictly speaking, that of
the dark line F. In the spectra of artificial lights, and of the stars, the
relative positions of the dark lines are changed. In the electric light the
dark lines are replaced by brilliant lines. In coloured flames — that is to
say, flames in which certain chemical substances undergo evaporation — the
dark lines are replaced by very brilliant lines of light, which differ for dif-
ferent substances. Lastly, some of the dark lines are constant in position
and distinctness, such as Fraunhofei-'s lines ; but some of the lines only
appear as the sun nears the horizon, and others are strengthened. They are
also influenced by the state of the atmosphere. The fixed lines are due to
the sun ; the variable lines have been proved by Jannsen and Secchi to be
due to the aqueous \apour in the air, and are called atmospheric or telluric
lines.

Fraunhofer counted in the spectrum more than 600 dark lines, more or
less distinct, distributed irregularly from the extreme red to the extreme
violet ray. Brewster counted 2,000. By causing the refracted rays to pass
successively through several analysing prisms (576), not merely has the
existence of 3,000 dark lines been ascertained, but several which had been
supposed to be single have been shown to be compound.

575. Applications of Fraunbofer's lines. — Subsequently to Fraunhofer,
several physicists studied the dark lines of the spectrum. In 1822 Sir J.
Herschel remarked that by volatilising substances in a flame a very delicate
means is afforded of detecting certain ingredients by the colours they impart
to certain of the dark lines of the spectrum ; and Fox Talbot in 1834 sug-
gested optical analysis as probably the most delicate means of detecting
minute portions of a substance. To Kirchhoff" and Bunsen, however, is
really due the merit of basing a method of analysis on the observation of the
lines of the spectrum. They ascertained that the salts of the same metal,
when introduced into a flame, always produced lines identical in colour and
position, but that lines different in colour, position, or number were produced
by different metals ; and finally, that an exceedingly small quantity of a
metal suffices to disclose its existence. Hence has arisen a new and power-
ful method of analysis, known by the name of spectrum analysis.

576. Spectroscope. — The name of spectroscope has been given to the
apparatus employed by Kirchhoff" and Bunsen for the study of the spectrum.
One of the forms of this apparatus is represented in fig. 531. It is composed
of three telescopes mounted on a common foot, and whose axes converge
towards a prism, P, of flint glass. The telescope A is the only one which
can turn round the prism. It is fixed in any required position by a clamping
screw 71. The screw-head m is used io focus the eyepiece. The screw-head
71 serves to change the inclination of the axis.

To explain the use of the telescopes B and C we must refer to fig. 532,
which shows the passage of the light through the apparatus. The rays
emitted by the flame G fall on the lens a, and are caused to converge to a
point b, which is the principal focus of a second lens c. . Consequently the
pencil, on leaving the telescope B, is formed of parallel rays (552). This pencil
enters the prism P. On leaving the prism the light is decomposed, and in

N N

546 On Light. [576-

this state falls on the lens x. By this lens x a real and reversed image of
the spectrum is formed at i. This image is seen by the observer through a
magnifying glass, which forms at ss' a virtual image of the spectrum magni-
fied about eight times.

V'lg. 531-

The telescope C serves to measure the relative distances of the lines
of the spectrum. For this purpose a micrometer is placed at ;«, divided

Fig. 532-

A micrometer is formed thus : — A scale of 250 milli-
metres is divided with great exactness into 25 equal parts. A photographic

taken, reduced to 11; millimetres. The

into 25 equal parts,
metres is divided w
negative on glass of this scale

-576 J

Spectroscope.

547

•"■'g- 533-

negative is taken because then the scale is light on a dark ground. The
scale is then placed at m in the principal focus of the lens e ; conse-
quently, when the scale is lighted by the candle F, the rays emitted from it
leave the lens e in parallel pencils ; a portion of these, being reflected from
a face of the prism, passes through a
lens x% and forms a perfectly distinct
image of the micrometer at /, thereby
furnishing the means of measuring
exactly the relative distances of the
different spectral lines.

The micrometric telescope C (fig.
531) is furnished with several adjusting
screws, /, 0, r ; of these, / adjusts the
focus ; o displaces the micrometer in
the direction of the spectrum laterally ;
r raises or lowers the micrometer,
which it does by giving different incli-
nations to the telescope.

The opening whereby the light of the flame G enters the telescope B
consists of a narrow vertical slit, which can be opened more or less by
causing the movable piece a to advance or recede by means of the screw v
(fig. 533). When, for purposes of comparison, the spectra of two flames
are to be examined simultaneously, a small prism, whose refracting angle
is 60°, is placed over the upper part of the slit. Rays from one of the
flames, H, fall at right angles on one face of the prism ; they then experience
total reflection on a second face, and leave the prism by the third face, and
in a direction at right angles to that face. By this means they pass into the
telescope in a direction parallel to its axis, without in any degree mixing with
the rays which proceed from the second flame, G. Consequently the two
pencils of rays traverse the prism P (fig. 532), and form two horizontal spectra,
which are viewed simultaneously through the telescope A. In the flames G
and H are platinum wires, e, e'. These wires have been dipped beforehand
into solutions of the salts of the metals on which experiment is to be made ;
and by the vaporisation of these salts the metals modify the transmitted
light, and give rise to definite lines.

Each of the flames G and H is a jet of ordinary gas. The apparatus
through which the gas is supplied is known as a Buf2se?i's burner. The gas
comes through the hollow stem k (fig. 531). At the lower part of this there
is a lateral orifice which admits air to support the combustion of the gas.
This orifice can be more or less closed by a small diaphragm, which acts as
a regulator. If we allow a moderate amount of air to enter, the gas burns
with a luminous flame, and the lines are obscured. But if a strong and
steady current of air enters, the carbon is rapidly oxidised, the flame loses its
brightness, and burns with a pale blue light, but with an intense heat. In
this state it no longer yields a spectrum. If, however, a metallic salt is in-
troduced either in a solid state or in a state of solution, the spectrum of the
metal makes its appearance, and in a fit state for observation.

There are three chief types of spectra : the continuous spectra, or
those furnished by ignited solids and liquids (fig. i, Plate I.) ; X\i& band

N N 2

S48

On LicrJit.

[576-

or litic spectrum, consisting of a number of bright lines, and produced by-
ignited gases or vapours ; and absorption spectra, or those furnished by the
sun or fixed stars. For an explanation of these see art. 579. Bodies at a
red heat give only a short spectrum, extending at most to the orange ; as
the temperature gradually rises, yellow, green, blue, and violet successively
appear, while the intensity of the lower colours increases.

Instead of the prism very pure spectra may also be obtained by means of
a grating (647). For more detailed investigations of the spectral lines a train

oj prisms is used. Fig. 534 repre-
sents one with nine prisms. The
light issuing from the collimeter A
passes in succession through each
of the prisms. As the successive
deviations add themselves the dis-
persion is very much increased, and
a spectrum of great extent is ob-
tained. It is, however, feebly lumi-
nous, owing partly to its extension,.
and partly to the loss of light which
is observed through the telescope B,
which it undergoes in traversing all
these refracting surfaces. In the
case of ten prisms the loss of
light has been found to amount to
ninety-nine per cent.

Christie has used with advan-
tage a semi-prism obtained by cut-
ting an isosceles prism by a plane
at right angles to the base. These
semi-prisms have the advantage that they produce as much dispersion as
with several prisms without any appreciable loss in the sharpness of the
images ; and without that absorption of light which in the case of a number
of prisms is so very considerable.

577. Direct vision spectroscope. — Prisms may oe combined so as to
get rid of the dispersion without entirely destroying the refraction (584) ;

they may, conversely,
be combined so that
tlie light is not re-
fracted, but is decom-
posed and produces a
J,. spectrum. Combina-

tions of prisms of this
kind are used in what are called direct vision spectroscopes. Fig. 535 repre-
sents the section of such an instrument in about \ the natural size. A system
of two flint and three crown-glass prisms is placed in a tube which moves in
a second one; at the end of this is an aperture o, and inside it a slit the
width of which can by a special arrangement be regulated by simply turning
a ring r. A small achromatic lens is introduced at aa, the focus of which is
at the slit, so that the rays pass parallel through the tram of prisms, and the
spectrum is viewed at c.

^'ig- 534-

-578 J Experiments ivith the Spectroscope. 549

The reversion spectroscope contains two equal systems of direct vision
prisms arranged close to each other, but reversed, so that two spectra are
obtained with the colours in opposite order. By suitable micrometric move-
ment of a split lens, the position of the two spectra may^be moved apart or
nearer each other. Hence it is possible to bring any two identical lines so
.that they are in the same vertical line. If now the position of these lines in
the spectrum is altered, the displacement will take place in the opposite
direction in the two spectra, and will therefore be twice as distinct.

578. Experiments with the spectroscope. — The coloured plate at the
■beginning shows certain spectra observed by means of the spectroscope.
No. I represents the continuous spectrum.

No. 2 shows the spectrum of sodium. The spectrum contains neither
red, orange, green, blue, nor violet. It is marked by a very brilliant yellow
ray in exactly the same position as Fraunhofer's dark line D. Of all metals
sodium is that which possesses the greatest spectral sensibility. In fact, it
has been ascertained that one two-hundred-millionth of a grain of sodium
is enough to cause the appearance of the yellow line. Consequently it is very
difficult to avoid the appearance of this line. A very little dust produced in
the apartment is enough to produce it — a circumstance which shows how
abundantly sodium is distributed.

No. 3 is the spectrum of lithium. It is characterised by a well-marked
line in the red called Lia, and by the feebler orange line Li/:i.

Nos. 4 and 5 show the spectra of ccesimn and ritbidiwn, metals discovered
by Bunsen and Kirchhofif by means of spectrum analysis. The former is
distinguished by two blue lines, Csa and Cs/3 ; the latter by two very brilliant
dark red lines, Rby and RbS, and by two less intense violet lines, Rba and
Bb/^. A third metal, thallium, has been discovered by the same method
by Mr. Crookes in England, and independently by M. Lamy in France.
Thallium is characterised by a single green line. Subsequently to this
Richter and Reich discovered a new metal associated with zinc, and which
they call indium from a couple of characteristic lines which it forms in the
indigo ; and quite recently Boisbaudran has discovered a new metal which
he calls gallium existing in zinc in very minute quantities.

The extreme delicacy of the spectrum reactions, and the ease with v/hich
they are produced, constitute them a most valuable help in the qualitative
analysis of the alkalies and alkaline earths. It is sufficient to place a small
portion of the substance under examination on platinum wire as represented
in fig. 533, and compare the spectrum thus obtained either directly with that
■of another substance or with the charts in which the positions of the lines
produced by the various metals are laid down.

With other metals the production of their spectra is more difficult, es-
pecially in the case of some of their compounds. The heat of a Bunsen's
burner is insufficient to vaporise the metals, and a more intense tempera-
ture must be used. This is effected by taking electric sparks between
wires consisting of the metal whose spectrum is required, and the electric
sparks are most conveniently obtained by means of Ruhmkorff's coil.
Thus all the metals may be brought within the sphere of spectrum obser-
•ivation.

The power of the apparatus has great influence on the nature of the

550 On Light. [578-

spectrum ; while an apparatus with one prism only gives in a sodium flame
the well-known yellow line, an apparatus with more prisms resolves it into
two or three lines.

It has been observed that the character of the spectrum changes with the
temperature ; thus chloride of lithium in the flame of a Bunsen's burner gives
a single intense peach-coloured line ; in a hotter flame, as that of hydrogen,
it gives an additional orange line ; while in the oxyhydrogen jet or the
voltaic arc a broad brilliant blue band comes out in addition. The sodium
spectrum produced by a Bunsen's burner consists of a single yellow line ;
if, by the addition of oxygen, the heat be gradually increased, more bright
lines appear ; and with the aid of the oxyhydrogen flame the spectrum is
continuous. Sometimes also, in addition to the appearance of new lines, an
increase in temperature resolves those bands which exist into a number of
fine lines, which in some cases are more and in some less refrangible than the
bands from which they are formed. It may be supposed that the glowing
vapour formed at the low temperature consists of the oxide of some difficultly
reducible metal, whereas at the enormously high temperature of the spark
these compounds are decomposed, and the true bright lines of the metal are
formed.

The delicacy of the reaction increases very considerably with the tem-
perature. With the exception of the alkalies, it is from 40 to 400 times
greater at the temperature of the electric spark than at that of Bunsen's
burner.

The spectra of the permanent gases are best obtained by taking the
electric spark of a Ruhmkorff's coil, or Holtz's machine, through glass
tubes of a special construction, provided with electrodes of platinum and
filled with the gas in question in a state of great attenuation, known as
Geissler's tubes ; if the spark be passed through hydrogen, the light emitted
is bright red, and its spectrum consists of one red, two blue lines, >io. 7, the
first two of which appear to coincide with Fraunhofer's lines C and F, and
the third with a line between F and G. No. 6 represents the spectrum of
oxygen. No. 8 is the spectrum of nitrogen. The light of this gas in a
Geissler's tube is purple, and the spectrum very complicated.

If the electric discharge takes place through a compound gas or vapour,
the spectra are those of the elementary constituents of the gas. It seems as
if, at very intense temperatures, chemical combination were impossible, and
oxygen and hydrogen, chlorine and the metals, could coexist in a separate
form, as though mechanically mixed with each other.

The nature of the spectra of the elementary gases is very materially in-
fluenced by alterations of temperature and pressure. \Vi.iH,ner made a series
of very accurate observations on the gases oxygen, hydrogen, and nitrogen.
He not only used gases in closed tubes, which by various electrical means
he raised to different temperatures ; but in one and the same series of ex-
periments, in which a small inductorium was used, he employed pressures
varying from 100 millimetres to a fraction of a millimetre ; while in another
series in which a larger apparatus was used, he extended the pressure to
2,000 millimetres. At the lowest pressure of less than one millimetre, the
spectrum of hydrogcii was found to be green, and consisting of six splendid
groups of lines, whu h at a higher pressure than i millimetre changed to

-579] Explanation of the Dark Lines of the Soiar Spectrum. 551

continuous bands ; at 2 to 3 millimetres the spectrum consisted of the often-
mentioned three lines, which did not disappear under a higher pressure, but
gradually became less brilliant as the continuous spectrum increased in extent
and lustre. From this point the light, and therefore the spectrum, became
feebler. Using the larger apparatus, the band spectrum appeared only under
a higher pressure ; at the highest pressure of 2,000 millimetres it gave place
to the continuous spectrum, since the bright lines continually extended and
ultimately merged into each other.

579. Explanation of tbe dark lines of the solar spectrum. — It has
been already seen that incandescent sodium vapour gives a bright yellow
line corresponding to the dark line D of the solar spectrum. Kirchhoft'
found that, when the brilliant light produced by incandescent lime passes
through a flame coloured by sodium in the usual manner, a spectrum is pro-
duced in which is a dark line coinciding with the dark line D of the solar
spectrum ; what would have been a bright yellow line becomes a dark line
when formed on the background of the limelight. By allowing in a similar
manner the limelight to traverse vapours of potassium, barium, strontium,
&c., the bright lines which they would have formed were found to be con-
verted into dark lines : such spectra are called absorption spectra.

It appears, then, that the vapour of sodium has the power of absorbing
rays of the same refrangibility as that which it emits. And the same is true
of the vapours of potassium, barium, strontium, &c. This absorptive power
is by no means an isolated phenomenon. These substances share it, for ex-
ample, with the vapour of nitrous acid, which Brewster found to possess the
following property : — when a tube filled with this vapour is placed in the path
of the light either of the sun or of a gas flame, and the light is subsequently
decomposed by a prism, a spectrum is produced which is full of dark lines
(No. 9, Plate I.) ; and Miller showed that iodine and bromine vapour pro-
duced analogous effects.

Hence the origin of the above phenomenon is, doubtless, the absorption
by the sodium vapour of rays of the same kind — that is, having the same
refrangibility — as those which it has itself the power of emitting. Other rays
it allows to pass unchanged, but these it either totally or in great part sup-
presses. Thus the particular lines in the spectrum to which these rays
would converge are illuminated only by the feebly luminous sodium flame,
and accordingly appear dark by contrast with the other portions of the
spectrum which receive light from the powerful flame behind.

By replacing one of the flames G and H (fig. 533) by a pencil of solar light
reflected from a heliostat, Kirchhoft" ascertained by direct comparison that
the bright lines which characterise iron correspond to dark lines m tlie solar
spectrum. He also found the same to be the case with sodium, magnesium,
calcium, nickel, and some other metals.

This reversal of the sodium light may be produced even without a prism
by an apparatus devised by Bunsen, and shown in fig. 536. It consists of a
Woolfs bottle in which a small quantity of zinc, dilute sulphuric acid, and
common salt are placed so that hydrogen is slowly liberated, charged with
particles of sodium chloride. Through the india-rubber tube L ordinarj'
coal gas is admitted, and issues through the tubes R and R'. On each of
these tubes is a metal burner. The gas burns at the top A with a broad flat

552 On Light. [579-

flame, C ; the burner B is cylindrical, and over it is placed a conical mantle
closed at the top with wire gauze. In this way a small yellow flame is pro-
duced. On looking through this against the wide flame, the former appears
dark, as if smoky on a light background. The light of the posterior and far
brighter flame is absorbed by the front and
cooler one, and replaced by light of lesser in-
tensity, which thus appears dark by contrast.

From such observations we may draw im-
portant conclusions with respect to the consti-
tution of the sun. Since the solar spectrum has
dark lines where sodium, iron, &c., give bright
ones (No. ii, Plate I.), it is probable that
around the solid, or more probably liquid, body
of the sun which throws out the light, there
exists a vaporous envelope which, like the
sodium flame in the experiment described above,
absorbs certain rays ; namely, those which the
envelope itself emits. Hence those parts of the
spectrum which, but for this absorption, would
have been illuminated by these particular rays,
appear feebly luminous in comparison with the
other parts, since they are illuminated only by
the light emitted by the envelope, and not by
the solar nucleus ; and we are at the same time
led to conclude that in this vapour there exist
the metals sodium, iron, &c.

Huggins and Miller applied spectrum ana-
lysis to the investigation of the heavenly bodies.
The spectra of the moon and planets, whose
light is reflected from the sun, give the same
lines as those of the sun. Uranus proves an
exception to this, and is probably still in a self-
luminous condition. The spectra of the fixed
stars contain, however, dark lines differing from the solar lines, and from
one another. Four distinct types of spectra were distinguished by Secchi.
The first embraces the white stars, and includes the well-known Sirius and
a Lyra.'. Their spectra (No. 12, Plate I.) usually contain a number of very
fine lines, and always contain four broad dark lines which coincide with
the bright lines of hydrogen. Out of 346 stars 164 were found to belong to
this group. The second group embraces those having spectra intersected
by numerous fine lines like those of our sun. About 140 stars, among them
Pollux, Capclla, (\) Aquil.i?, belong to this group. The third group embraces
the red and orange stars, such as a Orionis, ii Pegasi ; the spectra of these
(Nos. 13, 14, Plate I.) are divided into eight or ten parallel columnar clusters
of dark and bright bands increasing in intensity to the red. (".roup four is
made up of small red stars with spectra, and is constructed of three bright
zones increasing in intensity towards the violet. It would thus appear that
these fixed stars, while differing from one another in the matter of which
they are composed, are constructed on the same general plan as our sun.

-579J Explanaiion of the Dark Lines of the Solar Spectrum. 553

Huggins has observed a striking difference in the spectra of the nebulas ;
where they can at all be observed they are found to consist generally of
bright lines, like the spectra of the ignited gases, instead of, like the spectra
of the sun and stars, consisting of a bright ground intersected by dark lines.
It is hence probable that the nebuk^ are 'masses of glowing gas, and do not
consist, like the sun and stars, of a photosphere surrounded by a gaseous
atmosphere.

We can apply the reasoning of Doppler's principle (233) to the case of
light, and assume provisionally that the motion of light is analogous to that
of sound. When a source of light is approaching the earth, the eye receives
a greater number of waves in a given time, the waves are shorter ; as it
moves away the opposite is the case, the waves are longer. Hence, on the
approach of yellow light, for instance, the bright band D will seem displaced
towards the violet end of the spectrum, and in receding, towards the red
end. This will also be the case with the corresponding dark line, proving
that the whole medium is moved at the same time. Accordingly, by observ-
ing the displacement of particular lines, conclusions may be drawn as to the
relative motions of what are called the fixed stars. Thus, from careful ob-
servation of the displacement of the F line in Sirius, Huggins has inferred
that it is moving away from the earth with a velocity of 42 miles per second.

One of the most interesting triumphs of spectrum analysis has been the
discovery of the true nature of the proticberances, which appear during a
solar eclipse as mountains or cloud-shaped luminous objects varying in size,
and surrounding the moon's disc.

During the eclipse of 1868 it had been ascertained by Jannsen that pro-
tuberances emitted certain bright lines coinciding with those of hydrogen.
They have, however, been fully understood only since Lockyer and Jannsen
have discovered a method of investigating them at any time. The principle
of this method is as follows :— When a line of light admitted through a slit
is decomposed by a prism, the length of the spectrum may be increased by
passing it through two or more prisms ; as the quantity of light is the same,
it is clear that the intensity of the spectrum will be diminished. This is the
case with the ordinary sources of light, such as the sun ; if the light be
homogeneous, it will be merely deviated, and not reduced in intensity, by
dispersion. And if the source of light emit light of both kinds, the image
of the slit of light of a definite refrangibility, which the mixture maycontam,
will stand out, by its superior intensity, on the weaker ground of the con-
tinuous spectrum. This is the case with the spectrum of the protuberances.
Viewed through an ordinary spectroscope, the light they emit is overshadowed
by that of the sun ; but by using prisms of great dispersive power the sun's
light becomes weakened, and the spectrum of the protuberances may be
observed. Lockyer's researches leave no doubt that they are ignited gas
masses, principally of hydrogen. By altering the position of the slit a series
of sections of the prominences is obtained, by collating which the form of
the prominence may be inferred. They are thus found to enclose the sun
usually to a depth of about 5,000 miles, but sometimes in enormous local
accumulations, which reach the height of 70,000 miles. Lockyer has not
merely examined these phenomena right on the edge of the sun, but he has
been able to observe them on the disc itself. He has shown that some of

554 On Light. [579-

these protuberances are the results of sudden outbursts or storms, which
move with the enormous velocity of 120 miles in a second ; and, by reasoning
as above, the direction of this motion has been determined.

For a fuller account of this branch of physics, which is incompatible with
the limits of this work, the reader is referred to Sir H. Roscoe's ' Lectures on
Spectrum Analysis,' and to the same writers articles, and those of Schuster,
in Watts's ' Dictionary of Chemistry,' or to Schellen's ' Spectrum Analysis,'
translated by Lassell, or to Lockyer ' On the Spectroscope.'

580. Vses of the spectroscope. — When a liquid placed in a glass tube
or m a suitable glass cell is interposed between a source of light and the
slit of the spectroscope, the spectrum observed on looking through the
telescope will in many cases be found to be traversed by dark bands.
No. 10, Plate I., represents the appearance of the spectrum when a solution
oi chlorophyl, the green colouring matter of plants, is thus interposed. In
the red, the yellow, and the violet parts, dark bands are formed, and the
blue gives way to a reddish shimmer. If, instead of chlorophyl, arterial
blood greatly diluted be used, the red of the spectrum appears brighter, but
green and violet are nearly extinguished. As these bands thus differ in
different liquids as regards position, breadth, and intensity, in many cases
they afford the most suitable means of identifying bodies. Sorby and
Browning have devised a combination of the microscope and spectroscope
called the microspectroscope^ which renders it possible to examine even very
minute traces of substances.

This application of the spectroscope has been very useful in investigating
substances which have special importance in physiology and pathology ;
thus in examining normal and diseased blood, and in ascertaining the rate
at which certain substances pass into the various fluids of the system. The
characteristic absorption bands with certain liquids, such as wine, beer, &c.,
present in their normal state, compared with those yielded by adulterated
substances, furnish a delicate and certain means of detecting the latter.

Thus the adulteration of claret with the juice of elderberries is detected
by the appearance of faint bands near line D , which are not seen with pure
red wine. The colouring matter of malt and 'hops is quite distinct from
that of many other substances with which it is
alleged to be adulterated. An alkaline solution
of blood to which ammonium sulphide is added>
_ gives two very powerful absorption bands between

. ra f ,7j D and E, and between K and b ; this is the most

I^W "I \aluable test for toxicological cases. Blood charged

with carbonic oxide is unchanged on the addition
Kig. 537. of ammonium sulphide, and thus the poisoning

by carbonic oxide can be detected. So, too, the
appearance of the characteristic bands of gall in blood, and of albumen in
urine, arc indications of jaundice and of Bright's disease respectively.

Suppose the slit of the spectroscope be divided into two halves, s, and s,_.
(fig. 537), the aperture of each of which can be varied to any measured extent
by means of micromclric screws. If then a layer of a substance of known
thickness be placed in front of the slit .s,, for instance, and the spectrum of
a particular portion be observed, there will be a difference between the

-582J Fluorescence. 555

luminosity of the two parts of the spectrum ; but by regulating the width
of the slit they may be made the same; The luminosities will then be in-
versely as the width of the slit. Thus, if the widths of each were originally i,
and the uncovered slit had to be narrowed to 0-4, the intensity of the light
transmitted through the screen would only be 0-4 of the incident. Vierordt
has based on this a method of quantitative spectrum analysis ; thus if the
absorption produced by a definite thickness of known strength be known,
the relative concentration of any other solution of the same substance for
the same thickness may be determined.

581. Abnormal dispersion. — A remarkable exception to the ordinarj^
law of dispersion was discovered by Christiansen, and subsequently confirmed
and extended by Soret and Kundt — that the solutions of certain substances,
such as indigo and permanganate of potassium, give spectra in which the
07-der of the colours is not the same as in the prismatic spectrum. Thus, when
a hollow glass prism is filled with an alcoholic solution of fuchsine, the order
of the colours in the spectrum which it yields is as follows. Violet is least
refracted, then red, and then yellow, which is most refracted. If we imagine
that the central green of an ordinary spectrum is removed, and then the
position of the rest is interchanged, we get an idea of the abnormal spectrum
of fuchsine. Kundt examined a great number of substances in this direc-
tion, mostly the colours derived from aniline, and found that the abnormal
dispersion is exhibited by all substances with surface colour. These bodies
have the peculiarity that when viewed in diffused light they exhibit a different
colour from that which they transmit. Thus a thin flake of fuchsine appears
green in diffused, but red in transmitted light.

The substances in solution are examined by placing them in hollow glass
prisms ; if the solutions are weak, the abnormal dispersion of the substance
is concealed by that of the solvent, while stronger solutions absorb so much
light as to be almost opaque, and prisms of veiy small refracting angle have
to be used. Soret gets rid of this difficulty by immersing the prism contain-
ing the solution in glass vessels with parallel sides filled with the solvent.
The dispersion due to the solvent is thereby eliminated, and only that of the
substance comes into play. Cyanine gives a well-marked abnormal spec-
trum, the order of the colours being the following : green, light blue, dark
blue, a dark space, red, and traces of orange, the green being the colour
which is least diffused.

The same explanation cannot be given of this as of the ordinaiy colour
of bodies (569), but must be ascribed to the fact that the bodies in question
totally reflect light of certain wave-lengths (637) at almost all incidences,
and that these colours are reflected on the surface. Hence it follows that
the colour of these bodies in diffused light must be almost complementary
to the transmitted light— a prevision which experiment confirms.

582. Fluorescence. — Stokes made the remarkable discoveiy that under
certain circumstances the rays of light are capable of undergoing a change
of refrangibility. The discovery originated in the study of a phenomenon
observed by Brewster, and by Herschel, that some varieties of fluorspar,
and also the solutions of certain substances, when looked at by trans-
mitted light appear colourless, but when viewed in reflected light present a
bluish appearance. Stokes has found that this property, which he calls

556

On Light.
been obscned in fluorspar,

[582-

is characteristic of a

fluorescence from havinj

large number of bodies.

If by means of a lens of long focus, preferably of quartz, a line of the

sun's rays be focussed on a solution of sulphate of quinine contained in a

glass trough, a beautiful cerulean blue cone of light (fig. 538) is formed, which

is much the brightest on the surface and the intensity of which rapidly

diminishes as it penetrates in the licjuid.

It thus appears that fluorescence is due to an absorption of certain rays;

rays of light which have passed through a sufficient thickness of a fluorescent
substance lose thereby the power of exciting
fluorescence when they are passed through a
second layer of the same substance ; thus a test
tube containing a fluorescent liquid is brightly
luminous when exposed to the sun's rays, but
loses this lustre at once when it is dipped in a
trough of the same liquid, on the front of which
the sun's rays fall. This also results from a
c(nnparison of the absorption spectrum of a
flut>rescent substance with the appearance pre-
sented by this substance when the spectrum
falls on it. When the fluorescence begins there
also begins the absorption, and to a maximum
of absorption corresponds a maximum of fluor-
escence.

The phenomenon is seen when a solution of
ined in a trough with parallel sides, is placed in
solar spectrum. No change is observed in the

sulphate of (.[uinine, conta
ditibrcnt positions in the
upper part of the spectrum, but from about the middle of the lines G and H
(coloured Plate) to some distance beyond the extreme range of the violet,
rays of a beautiful sky-blue colour are seen to proceed. These invisible
ultra-violet rays also become visible when the spectrum is allowed to fall on
paper impregnated with a solution of icsculinc (a substance extracted from
horse-chestnut), an alcoholic solution of stramonium, or a plate of canary
glass (which is coloured by means of uranium). If light be allowed to fall
on paper impregnated with platmanganideof barium, a beautiful green fluor-
escence is observed.

If a few drops of a strong solution of fluorcsceine in soila tall into a large
beaker of water on the front of which the sun's rays fall, beautiful fluorescent
clouds are first produced, and on shaking the "liquid the whole vessel
fluoresces with a bright green light.

This change arises from a diminution in the refrangibility of those rays
outside the violet, which are ordinarily too refrangible to aftect the eye.

Cilass appears to absorb many of these more refrangible rays, which is
not the case nearly to the same extent with tjuartz. When a prism and
trough formed of plates of quartz are used, and the spectrum is received
on a sheet of paper on which a wash of solution of sulphate of cpiinine has
been made, two juxtaposed spectra can be obtained. That which is on
ihe part coated with sulphate of quinine extends beyond the line H
to an extent eipial to that of the visible spectrum. In the spectrum, thus

-683] Chromatic Aberration. 557

made visiI)lo, dark lines may be seen analogous to those in the ordinary
spectrum.

The phenomena may be (observed without the use of a prism. When an
aperture in a dark room is closed l)y means of a piece of bhie glass, and the
light is allowed to fall upon a piece of canary glass, it instantly aj)pcars self-
luminous from the emission of the altered rays. If a test tube be half filled
with a solution of sulphate of quinine, and on it be poured a freshly prepared
solution of chlorophyl in ether, the respective layers appear colourless and
green in transmitted, and sky-blue and blood-red in reflected light.

In most cases it is the violet and ultra-violet rays which undergo an
alteration of refrangibility, but the phenomenon is not confined to them. A
decoction of madder in alum gives yellow and violet light from about the
line I) to beyond the violet ; an alcoholic solution of chlorophyl gives red
light from the line B to the limit of the spectrum. In these cases the
yellow, the green, and the blue rays experience diminution of refrangibility ;
the change produces more highly refrangible rays. An exception to this rule
is met with in the case of Magdala red. If on a solution of this substance
contained in a rectangular glass vessel a solar spectrum be allowed to fall,,
an orange-yellow fluorescence is found even in the red part of the spectrum.

The electric light gives a very remarkable spectrum. With quartz
apparatus Stokes obtained a spectrum six or eight times as long as the
ordinary one. Several flames of no great illuminating power emit very
peculiar light. Characters traced on paper with solution of stramonium,,
which are almost invisible in daylight, appear instantaneously when illu-
minated by the flame of burning sulphur or of bisulphide of carbon.
Robinson has found that the light of the aurora is peculiarly rich in rays of
high refrangibility.

583. Cbromatic aberration. —The various lenses hitherto described
(551) possess the inconvenience that, when at a certain distance from the
eye, they give images with
coloured edges. This defect,
which is most observable in
condensing lenses, is due to
the unequal refrangibilty of the
simple colours (564), and is
called chromatic aberration.

Vox, since a lens may be
compared to a series of prisms
with infinitely small faces, and

united at their bases (551), it not only refracts light, but also decomposes it
like a prism. On account of this dispersion, therefore, lenses have really a
distinct focus for each colour. In condensing lenses, for example, the red
rays, which are the least refrangible, form their focus at a point R on the
axis of the lens (fig. 539) ; while the violet rays, which are most refrangible,
coincide in the nearer point V. The foci of the orange, yellow, green, blue,
and indigo are between these points. The chromatic aberration is more
perceptible in proportion as the lenses are more convex, and as the point
at which the rays are incident is farther from the axis ; for then the devia-
tion, and therefore the dispersion, are increased.

558

On Light.

[583-

Fig. 540.

If a pencil of rays which has passed through a condensing lens be
received on a screen placed at mm within the focal distance, a bright spot is
seen with a red border ; if it is placed at i-j, the bright spot has a violet
border.

The inequality in the refraction of the blue and red rays may be demon-
strated by closing a small aperture, half with red and half with blue glass
(fig. 540) ; on each half a black arrow is painted, and
a lamp is placed behind it. By means of a lens of
60 cm. focus an image is formed on a screen at a dis-
tance of about 2 metres. If the screen be placed so
that a sharp image is obtained of the black object on the
blue ground, the outlines of the other are confused. To
get a sharp image of the arrow on the red ground the
screen must be moved farther away.

584. Acbromatism By combining prisms which

have different refracting angles (544), and are formed of substances of un-
equal dispersive powers (564), white light may be refracted without being
dispersed. The same result is obtained by combining lenses of different
substances, the curvatures of which are suitably combined. The images of
objects viewed through such lenses do not appear coloured, and they are
accordingly called achromatic lenses ; achromatisi?i being the term applied
to the phenomenon of the refractipn of light without decomposition.

By observing the phenomenon of the dispersion of colours in prisms ot
water, of oil of turpentine, and of crown glass, Newton was led to suppose
that dispersion was proportional to refraction. He concluded that there
could be no refraction without dispersion, and, therefore, that achromatism
was impossible. Almost half a century elapsed before this was found to be
incorrect. Hall, an English philosopher, in 1733, was the first to construct
achromatic lenses, but he did not publish his discovery. It is to Dollond,
an optician in London, that we owe the greatest improvement which has
been made in optical instruments. He showed in 1757 that by combining
two lenses — one a double convex crown glass lens, the other a concavo-
convex lens of flint glass (fig. 542) — a lens is
obtained which is virtually achromatic.

To explain this result, let two prisms, BFC
and CDF, be joined and turned in a contrary
direction, as shown in fig. 541. Let us suppose in
the first case, that both prisms are of the same
material, but that the refracting angle of the
second, CDF", is less than the refracting angle
of the first ; the two prisms will produce the
' "'' ''''' same effect as a single prism, BAF ; that is to

say, that white light which traverses it will not only be refracted, but also
decomposed. If, on the contrary', the first prism BCF were of crown glass,
and the other CKD of flint glass, the dispersion might be destroyed without
destroying the refraction. For, as flint glass is more dispersive than crown,
and as the dispersion produced by a prism diminishes with its refracting
angle (564), it follows that by suitably lessening the refracting angle of the
Hint glass prism CFD, as compared with the refracting angle of the crown

-584]

Achromatisui.

559

glass prism BCP', the dispersive power of these prisms may be equahscd ;
and as, from their position, the dispersion takes place in a contrary direc-
tion, it is neutralised ; that is, the emergent rays EO are parallel, and
therefore give white light. Nevertheless, the ratio of the angles BCF and
CFD, which is suitable for the parallelism of the red rays and violet
rays, is not so for the intermediate rays, and, consequently, only two of
the rays of the spectrum can be exactly combined, and the achromatism is
not quite perfect. To obtain perfect achromatism, several prisms would be
necessary, of unequally dispersive materials, and the angles of which were
suitably combined.

The refraction is not destroyed at the same time as the dispersion ; that
could only happen if the refracting power of a body varied in the same ratio
as its dispersive power, which is not the case. Consequently,
the emergent ray EO is not exactly parallel to the incident ray,
and there is a refraction without appreciable decomposition.

Achromatic lenses are made of two lenses of unequal dis-
persive materials : one, A, of flint glass, is a diverging concavo-
convex (fig. 542) ; the other, B, of crown glass, is double convex,
and one of its faces may exactly coincide with the concave face
of the first. As with prisms, several lenses would be necessary
to obtain perfect achromatism ; but for optical instruments two
are sufficient, their curvatures being such as to combine not the
extreme red and violet, but the blue and orange rays, while at the same time
regard is had to the correction for spherical aberration.

V\%. 542-

S6o

On Li I' hi.

.OSft

CKAI'IKK V.
Ol'l ((A I, INSIKl/MKNT-..

^K^. TtiM dittorent. klndM ol optical IniitruinuntR. liy the U\\\\\ f>/>/i( nf
itislriiiiinit y. inr-anl ;iriy < omNin.ilidti of lfii',c-%, or of lenses and niirrorn.
(^plie.il in;tiiiiiH-nt'. may he divided inl') llirro f lasses, arcordinji; to the
ends lliey arc; inlended to answer, viz. : i. Microscopes, whir h arc de-signcd
to obtain a inajniifKul iina^'e of any ohjcrl whf)He real diniensionH arc too
small to admit of its bein^ seen distinf lly by the naked eye, ii. TclescopeSy
by whidi very distant objects, whether (celestial or terrestrial, may be
oljserved. iii. [nstrtniicnts desi^nied to projec I on a sf reen a maj^iified or
diminished ima)MM)f any objctr I which can tlnrrc-by b(! eillic-r clcpic tc-d oi
rendered visible to a crowd c»f spcv lalor', ; mic h as the (ttiiu'ni Itiiida,
the catnmi oliscurd, piiotof^ropliii nfi/inni/m, the iiuiyji lantern, the solar
microsco/ie, ihc. plioloelerlrii vticrosrope^i^i. i'lic- two former (lasses yield
virtual ima^jcts ; the la', I, widi the cxc ciilion of Ihc niinrni Imiiln, yield real
imajjes.

MIC I'O.c C)M ..

5X/). Th« Hlinplo tnloroNoopn. The- \iiiifilr iiiii ros, <<fic, or in<ij^tn'/yini;
^liis.s, is merely a (c>nvex lens cif short focal len>;tli, by means of which we
betweiMi the lens and its princ ijjal foe ns. I.el Ali
I lo I)c oil , CI veil, |.l;i. cd be! ween the lens and its
|»iiMc i|)al focus, I''.
i»iaw the sccond-
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look at objects place

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',M/. OiiiMlllloiiN Of (llRlliinliinHii of ilin iiiiMK<i«. In .ml. i lli.il nli|.'. I .
Inol.i .1 al lliioii):li a mi. i.i'<. .ipr '.lioiit.l lie '...'n Willi dr, Inn In. , ., llif\ niii'.l
liavr a t.lioii^; IihIiI iIiiowii iip.iii lliriii, liiil lliii i'. Ity mi iiiramt rn.Mi|;li, Il
Il iirtr'i'taiy lli.il llw im.i).;r lir I.n mr.l :il a drirrminillr di'.lain r lioiii llir
ryr In la, t, lliiir it l.ii cin li piTLni a iil\fiiHii' of itii'st ih\fiihf riMoti a
dr. I. III. r, lli.il I . lo '.ay, al wlm li .m t,l,|i', i mini he pla. cl liom .m ,.lr.. i\. r>,

5^2

On Li ^ J it.

[587-

eye in order to be seen with greatest distinctness. This distance is different
for different observers, but ordinarily is between lo and 12 inches. It is,
therefore, at this distance from the eye that the image ought to be formed.
Moreover, this is why each observer has io focus the instrument ; that is, to
adapt the microscope to his own distance of most distinct vision. This is
effected by slightly vaiying the distance from the lens to the object, for we
have seen above that a slight displacement of the object causes a great dis-
placement of the image. With a common magnifying glass, such as is held
in the hand, the adjustment is effected by merely moving it nearer to or
farther from the object. In the microscope the adjustment is effected by
means of a rack and pinion, which in the case of the instrument shown in
fig. 544 moves the eyepiece, but moves the object in the case of the
instrument depicted in fig. 545. What has been said about focussing the
microscope applies equally to telescopes. In the latter instrument the eye-
piece is generally adjusted with respect to the image formed in the focus of
the object-glass.

In respect of the distinctness of the miage the general rules for convex
lenses apply

In order to lessen dispersion, lenses have been constructed of diamond,
of ruby, and of other precious stones, which for a small amount of dispersion
have a great degree of refrangibility. A drop of water or of Canada balsam
in a small hole in a thin piece of wood or of metal, acts as a microscope.

588. Apparent mag-nitude of an object. — The apparent magnitude
or apparent diameter of a body is the angle it subtends at the eye of the

Fig. 547-

observer. Thus, if AB is the object, and O the observer's eye (figs. 546, 547),
the apparent magnitude of the object is the angle AOB contained by two
visual rays drawn from the centre of the pupil to the extremities of the object.
In the case of objects seen through optical instruments, the angles
which they subtend are so small that the arcs which measure the angles do
not differ sensiljly from their tangents. The ratio of two such angles is
therefore the same as that of their tangents. Hence we deduce the two
following principles :

-589] Measure of Magnification. 563

i. IVJien the same object ts seen at tmeqiial distances, the apparent diatneter
varies inversely as the distance from the observer's eye.

ii. In the case of two objects seen at the sa?ne distance, the ratio oj the
apparent diameters is the same as that of their absolute magnitudes.

These principles may be proved as follows : — i. In fig. 546^ let AB be the
object in its first position, and ab the same object in its second position.
For the sake of distinctness these are represented in such positions that the
line OC passes at right angles through their middle points C and c respec-
tively. It is, however, sufficient that ab and AB should be the bases of
isosceles triangles having a common verte.x at O. Now, by what has been
said above, AB is virtually an arc of a circle described with centre O and
radius OC ; likewise ab is virtually an arc of a circle whose centre is O and
radius Oc. Therefore,

A0B:.^0^ = ^5:/;^= L : _l.
OC Oc OC Oc

Therefore, AOB varies inversely as OC.

ii. Let AB and A'B' be two objects placed at the same perpendicular
distance, OC, from the eye, O, of the observer (fig. 547). Then they are
virtually arcs of a circle whose centre is O and radius OC. Therefore,

AOB :A'OB' = ^^ :^' = AB: A'B'.

a proportion which expresses the second principle.

589. Measure of magnification. — In the simple microscope the measure
of the magnification produced is the ratio of the apparent diameter of the

image to that of the

object, both being at
the distance of most
distinct vision. The
same rule holds good
for other microscopes.
It is, however, impor-
tant to obtain an ex-
pression for the magni-
fication depending on
data that are of easier
determination.

In fig. 548 let AB ^-ig. ^^g.

be the object, and A'B'

its image formed at the distance of most distinct vision. Let a'b' be the

projection of AB on A'B'. Then, since the eye is very near the glass, the

A'OB' A'B' A'B'

magnification equals ^-, or - - ; that is, - „. But since the triangles

a Oo a b AB °

A'OB' and AOB are similar, A'B' : AB = DO : CO. Now DO is the dis-
tance of most distinct vision, and CO is very nearly equal to FO, the focal
length of the lens. Therefore, the magnification equals the ratio of the dis-
tance of most distinct vision to the focal length of the lens. Hence we con-
clude that the magnification is greater, ist, as the focal length of the lens is

002

564 On Light. [589-

smaller — in other words, as the lens is more convergent ; 2ndly, as the
observer's distance of most distinct vision is greater.

A simpler and more general definition of the measure of magnification
may be stated thus : — Let a be the angular magnitude of the object as seen
by the naked eye, /S the angular magnitude of the image, whether real or
virtual, actually present to the eye, then the magnification is/3-=-a. T^is
rule applies to telescopes.

By changing the lens the magnification can be increased, but only within
certain limits if we wish to obtain a distinct image. By means of a simple
microscope distinct magnification may be obtained up to 120 diameters.

The magnification we have here considered is linear magnification.
Superficial magnification equals the square of the linear magnification ; for
instance, the former will be 1,600 when the latter is 40.

590. Principle of the compound microscope.^ — The compound micro-
scope in its simplest form consists of two condensing lenses : one, with a
short focus, is called the object-glass, or obJcctive,he.ca.nse. it is turned towards
the object ; the other is less condensing, and is called the eyepiece, ox power,
because it is close to the observer's eye.

Fig. 549 represents the path of the luminous rays and the formation of
the image in the simplest form of a compound microscope. An object AB

being placed very
^^ ~^;»^^^^^i^ near the principal
VB W^^^^^H focus of the object-
'■ ^^ ^^^BfiH glass M, but a little
farther from the
glass, a real image
ab, inverted and
somewhat magni-
fied, is formed on the other side of the object-glass (556). Now the distance
of the two lenses M and N is such that the position of the image ab is
between the eyepiece N and its focus F. From this it follows that for the
eye at E, looking at the image through the eyepiece, this glass produces the
same effect as a simple microscope, and instead of this image ab, another
image, a'b', is seen, which is virtual, and still more magnified. This second
image, although erect as regards the first, is inverted in reference to the
object. It may thus be said that the compound microscope is in effect a
simple microscope applied not to the object but to its image already magni-
fied by the first lens.

591. Compound microscope. — The princi]ilc of the compound micro-
scope has been already (590) explained ; the ))rincipal accessories to the
instrument remain to be described.

Fig. 550 represents a perspective view, and fig. 551a section of a com-
pound microsco])c. The body of the microscope consists of a series of brass
tubes, 1)D', H, and I ; in H is fitted the cyciMcce D, and in the lower part
of DD' the object-glass 0. The tube I moves with gentle friction in the tube
DD', which in turn can also be uioved in a larger tube fixed in the ring E.
This latter is fixed to a piece BB', which, by means of a very fine screw
worked by the milled head 'i', can be moved up and down an inner rod, c,
not represented in the figure. The whole body of the microscope is raised

-591]

Compound Microscope.

565

and lowered with the piece BB', so that it can be placed near or far
from the object to be examined. Moreover, the rod c, and all the other
pieces of the apparatus, rest on a horizontal axis A, with which they turn
under so much friction as to remain fixed in any position in which they may
be placed.

The object to be observed is placed between two glass plates, V, on a
stagc^ R. This is perforated in the centre, so that light can be reflected upon
the object by a concave reflecting glass mirror, M. The mirror is mounted

Fig. 550.

on a jointed support so that it can be placed in any position whatever, so
as to reflect to the object either the diffused light of the atmosphere, or that
from a candle or lamp. Between the reflector and the stage is a diaphragm
or stop, K, perforated by four holes of different sizes, any one of which can
be placed over the perforation in the stage, and thus the light falling on the
object may be regulated ; the light can, moreover, be regulated by raising,
by a lever n, the diaphragm K, which is movable in a slide. Above the
diaphragm is a piece, w, to which can be attached either a very small stop,
so that only very little light can reach the object, or a condensing lens,

566 On Light. [591-

which illuminates it strongly, or an oblique prism, represented at X. The
rays from the reflector undergo two total reflections in this prism, and
emerge by a lenticular face that concentrates them on the object, but in an
oblique direction, which in some microscopic observations is an advantage.
Objects are generally so transparent that they can be lighted from below ;
but where, owing to their opacity, this is not possible, they are lighted from
above by means of a condensing lens mounted on a jointed support, and so
placed that they receive the diffused light of the atmosphere.

Fig. 551 shows the arrangement of the lenses and the path of the rays
in the microscope. At 0 is the object-glass, consisting of three small con-
densing lenses, represented on a larger scale at L, on the right of the figure.
The effect of these lenses being added to each other is that they act like a
single very powerful condensing lens. The object being placed at /, a very
little beyond the principal focus of the system, the emerging rays fall upon a
fourth condensing lens, n, the use of which will be seen presently (592, 593).
Having become more convergent, owing to their passage through the lens
«, the rays form at aa' a real and amplified image of the object /. This
image is between a fifth condensing lens, O, and the principal focus of this
lens. Hence, on looking through this, it acts as a magnifier (556), and gives
at AA' a virtual and highly magnified image of aa\ and therefore of the
object. The two glasses 71 and O constitute the eyepiece, in the same
manner as the three glasses 0 constitute the object-glass.

The first image, aa', must not merely be formed between the glass O
and its principal focus, but at such a distance from this glass that the second
image, AA', is formed at the observer's distance of distinct vision. This
result is obtained in moving, by the hand, the body DH of the microscope
in the larger tube fixed to the ring E, until a tolerably distinct image is
obtained ; then turning the milled head T in one direction or the other,
the piece BB', and with it the whole microscope, are moved until the image
AA' attains its greatest distinctness, which is the case when the image aa'
is formed at the distance of distinct vision : a distance which can always be
ultimately obtained, for as the object-glass approaches or recedes from the
object, the image aa' recedes from or approaches the eyepiece, and at the
same time the image AA'.

This operation is called the focussitig. In the microscope, where the
distance from the object-glass to the eyepiece is constant, it is effected by
altering their distance from the object. In telescopes, where the objects
are inaccessible, the focussing is effected by varying the distance of the eye-
piece and the object-glass.

The microscope possesses numerous eyepieces and object-glasses, by
means of which a great variety of magnifying power is obtained. A small
magnifying power is also obtained by removing one or two of the lenses of
the object-glass.

The above contains the essential features of the microscope ; it is made
in a great variety of forms, which differ mainly in the construction of the
stand, the arrangement of the lenses, and in the illumination. For descrip-
tions of these the student is referred to special works on the microscope.

592. Acbromatlsiu of tbe microscope. Campanl's eyepiece. — When
a compound microscope consists of two single lenses, as in fig. 549, not only

-592] AcJirouiatisni of the Microscope. 567

is the spherical aberration uncorrected, but also the chromatic aberration,
the latter defect causing the images to be surrounded by fringes of the
prismatic colours, these fringes being larger as the magnification is greater.
It is with a view to correcting these aberrations that the object-glass (see
fig- 550 is composed of three achromatic lenses, and the eyepiece of two
lenses, n and O ;for the first of these, «, would be enough to produce colour
unless the magnifying power were low.

The efifect of this eyepiece in correcting the colour may be explained
as follows : — It will be borne in mind that with respect to red rays the focal
length of a lens is greater than the focal length of the same lens with refer-
ence to the violet rays.

■D

In fact, if in the equation (4) (559) we write R' = oo, we obtain /= .

n— I

which gives the focal length of a plano-convex lens whose refractive index

is n. Now, in flint glass, and for the red ray, n - 1 equals 0-63, and for the

violet ray n — 1 equals o'Gj.

Let ai be the object, O the object-glass, which is corrected for colour.

Consequently, a pencil (fig. 552) of rays falling from a on O would converge

Fig. 552.
to the focus A without any separation of colours ; but falling on the fietd-
glass C, the red rays would converge to r, the violet rays to v, and inter-
mediate colours to intermediate points. In like manner the rays from b,
after passing through the field-glass, would converge to r', or v', and inter-
mediate points. So that on the whole there would be formed a succession
of coloured images oi ab ; viz. a red image at rr', a violet image at vv\ and
between them images of intermediate colours. Let d be the point of the
object which is situated on the axis. The rays from d will converge to R,
V, and intermediate points. Now suppose the eye-glass O' to be placed in
such a manner that R is the principal focus of O' for the red rays, then V
will be its principal focus for the violet rays. Consequently, the red rays,
after emerging from O, will be parallel to the axis, and so will the violet
rays coming from V, and so of any other colour. Accordingly, the colours
of d, which are separated by C, are again combined by O'. The same is
very nearly true of r and v, and of r' and v' Hence a combination of lenses
C and O' corrects the chromatic aberration that would be produced by the
use of a single eye-glass. Moreover, by drawing the rays towards the axis,
it diminishes the spherical aberration, and, as we shall see in the next article,
enlarges the field of view.

In all eyepieces consisting of two lenses the lens to which the eye is
applied is called the eye-lens ; the one towards the object-glass is called the
field-lens. The eyepiece above described was invented by Huyghens, who
was not, however, aware of its property of achromatism. He designed it
for use with the telescope. It was applied to the microscope by Campani.

568

On Li^ht.

[592-

The relation between the focal length of the lenses is as follows :— The focal
length of the field-glass is three times that of the eye-lens, and the distance
between their centres is half the sum of the focal length. It easily follows
from this that the image of the point d would, but for the interposition of
the field-lens, be formed at D, which is so situated that CD is three times
DO'; then the mean of the coloured images would be formed midway
between C and O'.

593. Field of view. — By the field of view of an optical instrument is
meant all those points which are visible through the eyepiece. The advan-
tage obtained by the use of an eyepiece in enlarging the field of view will be
readily understood by an inspection of the accompanying figure. As before
(fig. 553), O is the object-glass, C the field-lens, O' the eye-lens, and E the
eye placed on the axis of the instrument. Let a be a point of the object ; if
we suppose the field-lens removed, the pencil of rays from a would be

Fig. 553.

brought to a focus at A, and none of them would fall on the eye-lens O',
nor pass into the eye E. Consequently, a is beyond the field of view. But
when the field-glass C is interposed, the pencil of rays is brought to a focus
at A', and emerges from O' into the eye. Consequently, a is now within
the field of view. It is in this manner that the substitution of an eyepiece
for a single eye-lens enlarges the field of view.

594. IMCag-nifyingr power. Micrometer. — The magnifying power of any
optical instrument is the ratio of the magnitude of the image to the mag-
nitude of the object. The magnifying power in a
compound microscope is the product of the respec-
tive magnifying powers of the object-glass and of
the eyepiece ; that is, if the first of these magnifies
20 times, and the other 10, the total magnifying
power is 200. The magnifying power depends on
the greater or less convexity of the object-glass
and of the eyepiece, as well as on the distance be-
tween these two glasses, together with the distance
of the object from the object-glass. A magnifying
power of 1,500 and even upwards has been ob-
tained ; but the image then loses in sharpness
what it gains in extent. To obtain precise and
well-illuminated images, the magnifying power ought not to exceed 500 to
600 diameters, which gives a superficial enlargement 250,000 to 360,000 times
that of the object.

The magnifying power is determined experimentally by means of the
glass tnicroinctcr : this is a small glass plate, on which, by means of a
diamond, a scries of lines is drawn at a distance from each other of y^ or yi,,
of a millimetre. The mi( rometcr is placed in front of the object-glass, and

Fig- 554-

-595] Astronomical Telescope. 569

then, instead of viewing- directly the rays emerging from the eyepiece O,
they are received on a piece of glass A (fig. 554), inclined at an angle of 45°,
and the eye is placed above so as to see the image of the micrometer lines,
which is formed b)' reflection on a screen E, on which is a scale divided into
millimetres. By counting the number of divisions of this scale correspond-
ing to a certain number of lines of the image, the magnifying power may be
deduced. Thus, if the image occupies a space of 45 millimetres on the scale
and contains 1 5 lines of the micrometer, the distance between each of which
shall be assumed at jj^ millimetre, the absolute magnitude of the object will
be i"y millimetre ; and as the image occupies a space of 45 millimetres, the
magnification will be the quotient of 45 by y*,,";,, or 300. The eye in this
experiment ought to be at such a distance from the screen E that the screen
is distinctly visible : this distance varies with different observers, but is
usually 10 to 12 inches. The magnifying power of the microscope can also
be determined by means of the camera hccida ; it is increased at the expense
ot brightness, definition, and field. Hence it is usual to have several eye-
pieces with each microscope so as to obtain greater definition of higher
magnification.

Noberfs Hires are frequently used as test objects ; these are lines ruled
on glass in series ; in the first group the lines are at a distance of jgi-^^ of an
inch from the middle of one line to the middle of the next ; in the finest the
lines are at a distance of ^-^^^-^ of a line. Other test objects are the scales
of certain butterflies, and various kinds of diatoms.

When once the magnifying power is known, the absolute magnitude of
objects placed under the microscope is easily deduced. For, as the magni-
fying power is the cjuotient of the size of the image by the size of the object,
it follows that the size of the image divided by the magnifying power gives
the size of the object : in this manner the diameters of all microscopic objects
are determined.

TELESCOPES.

595. Astronomical telescope. — The astVo7iomical telescope is used for
obser\-ing the heavenly bodies ; like the microscope, it consists of a con-
densing eye-
piece and I
object-glass, j
The object-
glass, M (fig.
555), forms
between the
eyepiece, X,
and its prin-
cipal focus lig- 555-

an inverted image of the heavenly body ; and this eyepiece, which acts as
a magnifying glass, then gives a virtual and highly magnified image, a'b\ of
the image ab. The astronomical telescope appears, therefore, analogous to
the microscope : but the two instruments differ in this respect, that in the
microscope, the object being very near the object-glass, the image is formed
much beyond the principal focus, and is greatly magnified, so that both the

570

Oti Light.

[595-

object-glass and the eyepiece magnify ; while in the astronomical telescope,
the heavenly body being at a great distance, the incident rays are parallel,
and the image formed in the principal focus of the object-glass is much
smaller than the object. There is, therefore, no magnification except by the
eyepiece, and this ought, therefore, to be of very short focal length.

Fig. 556 shows an astronomical telescope mounted on its stand. Above
it there is a small telescope which is called the fi?idcr. Telescopes with a
large magnifying power are not convenient for finding a star, as they have
but a small field of view : the position of the star is, accordingly, first sought
by the finder, which has a much larger field of view — that is, takes in a far
greater extent of the heavens ; it is then viewed by means of the telescope.

that is, it equals

APR

The magnification (589) equals ^^v, (fig. 555)
a \J0

and therefore is approximately equal to

OF'

bOC

F being the focus of the object-
glass M, and
being supposed
very nearly

to
coincide with
the focus of the
eyepiece N ; it
may, therefore,
be concluded
that the magni-
fying power is
greater in pro-
portion as the
object-glass is
less convex, and
the eyepiece
more so.

When the
telescope is

used to make
an accurate ob-
servation of the
stars — for ex-
ample, the zenith distance, or their passage over the meridian — a cross wire
is added. This consists of two very fine metal wires or spider threads
stretched across a circular aperture in a small metal plate (fig. 557). The
wires ought to be placed in the position where the inverted image is pro-
duced by the object-glass, and the point where the wires cross ought to be
on the optical axis of the telescope, which thus becomes the litie of sight or
collimation.

596. Terrestrial telescope. — The terrestrial telescope differs from the
astronomical telescope in producing images in their right positions. This is
effected by means of two condensing glasses, P and Q (fig. 558), placed
between the object-glass M and the eyepiece R. The object being sup-
posed to be at Al$, at a greater distance than can he shown in the drawing,

Fig. 556.

596]

Terrestrial Telescope.

571

an inverted and much smaller image is formed at ba on the other side of
the object-glass. But the second lens, P, is at such a distance that its
principal focus coincides with the image ab ; from which it follows that the
luminous rays which pass through b, for example, after traversing the lens
P, take a direc-
tion parallel to
the secondar\
axis ^O (552).
Similarly, the
rays passing by
a take a direc- Fig. 558.

tion parallel to

the axis aO. After crossing in H, these various rays traverse a third lens Q,
whose principal focus coincides with the point H. The pencil B^H con-
verges towards b\ on a secondary axis O'b', parallel to its direction ; the
pencil AizH converging in the same manner at a', an erect image of the
object AB is produced at a'b'. This image is viewed, as in the astrono-
mical telescope, through a condensing eyepiece R, so placed that it acts as
a magnifying glass ; that is, its distance from the image a'b' is less than the
principal focal distance ; hence there is formed, at a"b", a virtual image of
a'b'^ erect and much magnified. The lenses P and Q, which only serve to
rectify the position of the image, are fixed in a brass tube, at a constant
distance, which is equal to the sum of their principal focal distances. The
object-glass M moves in a tube, and can be moved to or from the lens P,
so that the image ab is always formed in the focus of the lens, whatever be
the distance of the object. The distance of the lens R may also be varied
so that the image a"b" may be formed at the distance of distinct vision.

This instrument may also be used as an astronomical telescope by using
a different eyepiece : this must have a much greater magnifying power than
in the former case.

In the terrestrial telescope the magnifying power is the same as in the
astronomical telescope, provided always that the correcting glasses, P and
Q, have the same convexity.

In order to determine directly the magnifying power of a telescope when
this is not great, a divided scale at a distance, or the tiles of a house may
be viewed through the telescope with one eye and directly with the other.
This with a little practice is not difficult. It is thus ob-
served how many unmagnified divisions correspond to a
single magnified one. Thus, if two seen through the
telescope appear like seven, the magnifying power is 3^.
Reading ordinary printing from a distance is an excellent
means of testing and comparing telescopes.

The excellence of a telescope depends also on the
sharpness of the images. To test this, various circular
and angular figures are painted in black on a white '^' ^^'*

ground, as shown in fig. 559, in about ^^j the full size. When these are
looked at through the telescope at a distance of 80 or 100 paces, they should
appear sharply defined, perfectly black, without distortion, and without
coloured edges. The penetration or penet7atjt7g power of a telescope by

572 On Light. [596-

which stars are seen which are not visible to the naked eye depends mainly
on the aperture of the object-glass. Even with the strongest magnification
the fixed stars appear as luminous points without apparent diameter.

597. Galileo's telescope. — Galileo's telescope is the simplest of all tele-
scopes, for it only consists of two lenses ; namely, an object-glass, M, and a

diverging or double concave
eyepiece, R (fig. 560), and
it gives at once an erect
image. Opera-glasses are
constructed on this prin-
ciple.

Fig. 360 If the object be repre-

sented by the right line AB,
a real but inverted and smaller image would be formed at ba ; but in
traversing the eyepiece R, the rays emitted from the points A and B are
refracted and diverge from the secondary axis bO' and aO' which coire-
spond to the points b and a of the image. Hence, these rays produced
backward meet their axes in a' and b' ; the eye which receives them sees
accordingly an erect and magnified image in a'b\ which appears nearer
because it is seen under an angle, a'0'b\ greater than the angle, AOB,
under which the object is seen.

The magnifying power is equal to the ratio of the angle a'O'b' to the
angle AOB, and is usually from 2 to 4.

The distance of the eyepiece R from the image ab is pretty nearly equal
to the principal focal distance of this eyepiece ; it follows, therefore, that the
distance between the two lenses is the distance between their respective
focal distances ; hence Galileo's telescope is very short and portable. It
has the advantage of showing objects in their right position ; and, further,,
as it has only two lenses, it absorbs very little light : in consequence, how-
ever, of the divergence of the emergent rays, it has only a small field of view,
and in using it the eye must be placed very near the eyepiece. The eye-
piece can be moved to or from the object-glass, so that the image a'b' \s
always formed at the distance of distinct vision.

The opera-glass is usually double, so as to produce an image in each eye,
by which greater brightness is attained.

The time at which telescopes were invented is not known. Some attri-
bute their invention to Roger Bacon in the thirteenth century ; others to J. B.
Porta at the end of the sixteenth ; others, again, to a Dutchman, Jacques
Metius, who, in 1609, accidentally found that by combining two glasses, one
concave and the other convex, distant objects appeared nearer and much
larger. Galileo's was the first telescope directed towards the heavens. By
its means Galileo discovered the mountains of the moon, Jupiter's satellites,
and the s])ots on the sun.

598. Keflectlng- telescope*. — The telescopes previously described are
refractiftg or dioptric telescopes. It is, however, only in recent times that it
has been possible to construct achromatic lenses of large size ; before this a
concave metallic mirror was used instead of the object-glass. Telescopes
of this kind are called reflecting or catoptnc telescopes. The principal forms
are those devised by Gregory, Newton, Hcrschel, and Cassegrain.

-589] The Gregorian Telescope. 573

599. The Greg-orlan telescope. — Fig. 561 is a representation of Gre-
gory's telescope ; it is mounted on a stand, about which it is movable, and
can be inclined at any angle. This mode of mounting is optional ; it may
be equatorially mounted. Fig. 562 ^

gives a longitudinal section. It
consists of a long brass tube closed
at one end by a concave metallic
mirror, M, which is perforated in
the centre by a round aperture
through which rays reach the eye.
There is a second concave metal
mirror, N, near the end of the '
tube: it is somewhat larger than
the central aperture in the large
mirror, and its radius of curvature
is much smaller than that of the
large mirror. The axes of both
mirrors coincide with the axis of
the tube. As the centre of curva-
ture of the large mirror is at O,
and its focus at ab, rays such as SA
emitted from a heavenly body are
reflected from the mirror M, and
form at ab an inverted and very
small image of the heavenly body.

Fig. 56

The distance of the mirrors and their curvatures is so arranged that the
position of this image is between the centre, 0, and the focus _/j of the small
mirror ; hence the rays, after being reflected a second time from the mirror
N, form at a'b' a magnified and inverted image of ab, and therefore in the
true position of the heavenly body. This image is viewed through an eye-
piece, P, which may either be simple or compound, its object being to
magnify it again, so that it is seen at a"b".

Fig. 562.

As the objects viewed are not always at the same distance, ihe focus of
the large mirror, and therefore that of the small one, vary in position.

And as the distance of distinct vision is not the same with all eyes, the
image a"b'' ought to be formed at different distances. The required adjust-
ments may be obtained by bringing the small mirror nearer to or farther from
the larger one ; this is effected by means of a milled head, A (fig. 561),
which turns a rod, and this by a screw moves a piece to which the mirror is
fixed.

574

On Lio'ht.

[600-

600. The xrewtonian telescope. — This instrument does not differ much
from that of Gregory ; the large mirror is not perforated, and there is a
small plane mirror inclined at an angle of 45° towards an eyepiece placed
in the side of the telescope.

The difficulty of constructing metallic mirrors caused telescopes of
Gregorian and Newtonian construction to fall into disuse. Of late, how-
ever, the process of silvering glass mirrors has been carried to a high state
of perfection, and Foucault applied these mirrors to Newtonian telescopes
with great success. His first mirror was only four inches in diameter, but
he has successively constructed mirrors of 8, 12, and 13 inches, and at the
time of his death had completed one of 32 inches in diameter.

Fig. 564 represents a Newtonian telescope mounted on an equatorial
stand, and fig. 563 gives a horizontal section of it. This section shows how
the luminous rays reflected from the parabolic mirror M meet a small rect-
angular prism, w, which replaces the inclined plane mirror used in the old
form of Newtonian telescope. After undergoing a total reflection from ;«,
the rays form at a'b' a very small image of the heavenly body. This image
is viewed through an eyepiece with four lenses placed on the side of

the telescope, and magnifying from 50 to 800 times according to the size of
the silvered mirror.

In reflectors the mirror acts as object-glass, but there is, of course, no
chromatic aberration. The spherical aberration is corrected by the form
given to the reflector, which is paraboloid, but slightly modified by trial to
suit the eyepiece fitted to the telescope.

The mirror when once polished is immersed in a silvenng liquid, which
consists essentially of ammoniacal solution of nitrate of silver, to which some
reducing agent is added. When a polished glass surface is immersed in
this solution, silver is deposited on the surface in the form of a brilliant
metallic layer, which adheres so firmly that it can be polished with rouge in
the usual manner. These new telescopes with glass mirrors have the ad-
vantage over the old ones that they give purer images, they weigh less, and
are much shorter, their focal distance being only about six times the diameter
of the mirror.

These details known, the whole apparatus remains to be described. The
body of the telescope (fig. 564) consists of an octagonal wooden tube. The end
G is open ; the mirror is at the other end. At a certain distance from this
end two axles are fixed, which rest on bearings supported by two wooden
uprights, A and 15. These are themselves fi.xed to a table, PQ, which turns
on a fixed plate, R.S, placed e.xactly parallel to the equator. On the circum-
ference of the turning-table there is a brass circle divided into 360 degrees ;

-600]

TJic Neivtonian Telescope.

575

and beneath it, but also fixed to the turning-table, there is a circular toothed
wheel, in which an endless screw, V, works. By moving this in either
direction by means of the handle m, the table PQ, and with it the telescope,
can be turned. A vernier, x, fixed to the plate RS, gives fractions of a
degree. On the axis of the motion of the telescope there is a graduated
circle, O, which serves to measure the declination of the star — that is, its

Fig. 564.

angular distance from the equator ; while the degrees traced round the table
RS ser\^e to measure the right ascension— that is, the angle which the de-
clination circle of the star makes with the declination circle passing through
the first point of Aries.

In order to fix the telescope in declination, there is a brass plate, E, fixed
to the upright ; it is provided with a clamp, in which the limb O works, and

576

On Light.

[600-

which can be screwed tight by means of a screw with a milled head r. On
the side of the apparatus there is the eyepiece fl, which is mounted on a
shding copper plate, on which there is also the small prism w, represented
in section in fig. 562. To bring the image to the right place, this plate may
be moved by means of a rack and a milled head a. The handle n serves to
clamp or unclavip the screw V. The drawing was one taken from a tele-
scope the mirror of which is only 6i inches in diameter, and which gives a
magnifying power of 150 to 200.

6or. The Herschellan telescope. — Sir W. Herschel's telescope, which
until recently was the most celebrated instrument of modern times, was con-
structed on a method differing from those described. The mirror was so in-
clined that the image of the star was formed at ab on the side of the telescope
near the eyepiece 0 : hence it is termed the front-view telescope. As the
rays in this telescope only undergo a single reflection, the loss of light is less
than in either of the preceding cases, and the image is therefore brighter.
The magnifying power is the quotient of the principal focal distance of the
mirror by the focal distance of the eyepiece.

Herschel's great telescope was constructed in 1789; it was 40 feet in
length, the great mirror was 50 inches in diameter. The quantity of light

obtained by this instru-
ment was so great as
to enable its inventor to
use magnifying powers
far higher than anything
which had hitherto been
attempted.

Herschel's telescope
has been exceeded by
one constructed by the
late Earl of Rosse. This magnificent instrument has a focal distance of 53
feet, the diameter of the spec^um being six feet. It is at present used as
a Newtonian telescope, but it can also be arranged as a front-view tele-
scope.

INSTRUMENTS FOR FORMING l'ICTURi:S OF OBJECTS.

602. Camera obacura. — The camera obsciira (dark chamber) is, as its
name implies, a closed space impervious to light. The principle of this

apparatus is illus-
trated by fig. 566.
The rays proceed-
ing from an external
object AI), and en-
tering by the aper-
ture O, form on the
opi)osite side an
image of the ob-
ject ba in its natural
colours, but of reduced dimensions, and in an inverted position.

Porta, a Neapolitan physician, the inventor of this instrument, found that

Fig- 565.

604]

Camera Liicida.

577

the im.'i"c on a

by tixiny a double convex lens in the aperture, and receiving
white screen, it was much brighter and more definite.

603. Camera luclda. — The camera liicida is a small instrument depend-
ing on internal reflection, and serves for taking an outline of any object. It
was invented by Wollaston in 1804. It consists of a small four-sided glass
prism, of which fig. 567 gives a section perpendicular to the edges. A is a
right angle, and C an angle of 135° ; the other angles, 15 and D, are 67.}°.
The prism rests on a stand, on which it can be raised or lowered, and turned
more or less about an axis parallel to the prismatic edges. When the face
AB is turned towards the object, the rays from the object fall nearly per-
pendicular on this face, pass into the prism without any appreciable refrac-
tion, and are totally reflected from BC ; for as the line ab is perpendicular ta
BC, and «L to A15, the angle anV, will equal the angle B : that is, it will
contain 671°, and this being greater than the critical angle of glass (540),
the ray L« will undergo total reflection. The rays are again totally reflected
from (?, and emerge near the summit, D, in a direction almost perpendicular
to the face DA, so that the eye which receives the rays sees at L' an image
of the object L. If the outlines of the image are traced with a pencil, a
very correct design is obtained ; but unfortunately there is a great diffi-
culty in seeing both the image and the point of the pencil, for the rays
from the object give an image which is farther from the eye than the pencil.
This is corrected by placing between the eye and prism a lens, I, which
gives to the rays from the pencil and those from the object the same
divergence. In this case, however, it is necessary to place the eye very
near the edge of the prism, so that the aperture of the pupil is divided
into two parts, one of which sees the image and the other the pencil.

Amici's camera lucida, represented in fig. 567, is preferable to that of
Wollaston, inasmuch as it allows the eye to change its position to a con-
siderable extent without ceasing to sec the image and the pencil at the
same time. It con-
sists of a rectangular
glass prism ABC,
having one of its
perpendicular faces
turned towards the
object to be depicted,
while the other is at
right angles to an in-
clined plate of glass,
7nn. The rays LI,
proceeding from the ^'«- 5^^- tis- 568.

object, and entering the prism, are totally reflected from its base at D, and
emerge in the direction KH. They are then partially reflected from the
glass plate inn at H, and form a vertical image of the object L, which is seen
by the eye in the direction OL'. The eye at the same time sees through
the glass the point of the pencil applied to the paper, and thus the outline
of the picture may be traced with great exactness.

604. Maeric lantern. -This is an apparatus by which a magnified image
of small objects may be projected on a white screen in a dark room. A typical

P P

578

On Light.

[604-

form is the sciopiicon, fig. 569. The box C, the side of which is shown re-
moved, is constructed of sheet iron ; e is the flame of a lamp V, with two
long flat wicks, fed by petroleum from the reservoir B. The box is airtight,
and the chimney F producing a good draught, the air is compelled to pass
through the wicks, by which smoke and smell are avoided, and a flame of
high illuminating power is produced.

The ends of the box are closed by glass plates z and i^. G is a hinged
door, and on its inside is a concave mirror ; o and 0^ are two plano-convex
lenses ; p a spring clamp, in which is placed the transparent picture. The
sliding piece supports the lens tube, in which are two achromatic lenses
a and b, the fine adjustment of which is effected by the screw S.

The rays from the flame e, reinforced by the reflection from G, falling
upon the lenses 0, 0^, are made parallel, or, at all events, very slightly diver-
gent ; these lenses are accordingly called the co?ide?isitig lenses. Passing

_^_ through the object

^^^^^^ which is depicted on

' ,, ' ^ the slide placed in /,
they are concentrated
to an image which is
received on a screen.
The image is in-
verted, and hence, if
objects are to be seen
in their erect position,
they must be drawn
inverted. But ordi-
nary drawings are
easily adjusted by
fixing an equilateral
rectangular prism, P (fig. 570), in front of
the lens tube, so that the hypotenuse sur-
face is horizontal. The parallel rays
falling on the prism are inverted in con-
sequence of refraction at the sides and
total reflection from the hypotenuse sur-
face, so that an upright position is ob-
tained instead of a reverse one. The
dotted lines abcde and fg/iik gi\e the
path of two rays.

The apparatus can be used for projecting on a screen not only flat
images, but also simple physical experiments, such as the expansion of a
liquid in a thermometer, the divergence of the gold leaves of an electroscope,
and so forth.

Dissolving 7'ic7i>s are obtained by arranging two magic lanterns, which
are quite alike, with different pictures, in such a manner that both pictures
are produced on exactly the same part of a screen. The object-glasses of
both lanterns arc closccl by shades, which are so arranged that according as
one is raised the other is lowered, and 7'itc 7'crsit In this way one picture
is gradually seen to change into the other.

Fig. 570.

-605]

Solar Microscope.

579

The magnifying power of the magic lantern is obtained by dividing the
•distance of the lens from the image by its distance from the object. If the
image is loo or i,ooo times farther from the lens than the object, the image
will be loo or i,ooo times as large. Hence a lens with a very short focus
can produce a very large image, provided the screen is sufficiently large.

605. Solar microscope. — The solar microscope is in reality a magic
lantern illuminated by the sun's rays ; it serves to produce highly magnified
images of very small objects. It is worked in a dark room : fig. 571 repre-
sents it fitted in the shutter of a room, and fig. 572 gives the internal details.

The sun's rays fall on a plane mirror, M, placed outside the room, and
arc reflected towards a condensing lens, /, and thence to a second lens, o

Fig. 571.

(fig. 572), by which they are concentrated at its focus. The object to be
magnified is at this point ; it is placed between two glass plates, which, by
means of a spring, n, are kept in a firm position between two metal plates,
in. The object thus strongly illuminated is very near the focus of a system
of three condensing lenses, a-, which forms upon a screen at a suitable distance
an inverted and greatly magnified image, ab. The distance of the lenses o
and X from the object is regulated by means of screws, C and D.

As the direction of the sun's light is continually varying, the position of
the mirror outside the shutter must also be changed, so that the reflection is
always in the direction of the axis of the microscope. The most exact
apparatus for this purpose is the heliostat (534) ; but as this instrument is
very expensive, the object is usually attained by inclining the mirror to a
greater or less extent by means of an endless screw B, and at the same time
turning the mirror itself round the lens / by a knob A, which moves in a
fixed slide.

The solar microscope labours under the objection of concentrating great
heat on the object, which soon alters it. This is partially obviated by
interposing a layer of a saturated solution of alum, which, being'' a power-
fully athe'rmanous substance (434), cuts off a considerable portion of the
heat.

58o

Oyi Light,

[605-

The magnifying power of the solar microscope may be deduced experi-
mentally by substituting for the object a glass plate marked with lines at a
distance of }^ or ji^ of a millimetre. Knowing the distance of these lines on
the image, the magnifying power may be calculated. The same method is
used with the electric light. According to the magnifying power which it is
desired to obtain, the objective x is formed of one, two, or three lenses,
which are all achromatic.

The solar microscope furnishes the means of exhibiting'to a large audience

Fig. 572

many curious phenomena, such, for instance, as the circulation of blood in
the smaller animals, the crystallisation of salts, the occurrence of minute
organisms in water, vinegar, (S:c. &c.

606. Photo-electric microscope. — This is in effect a solar microscope
which is illuminated by the electric light instead of by the sun's rays. The
electric light, by its intensity, its steadiness, and the readiness with which
it can be produced at any time of the day, is far preferable to the solar light.
The microscope alone will be described here : the production of the electric
light will be considered under the head of Galvanism.

Fig. 573 represents the arrangement devised by Duboscq. A solar
microscope, ABD, identical with that already described, is fi.xed on the
outside of a brass box. In the interior are two charcoal points which do
not quite touch, the space between them being exactly on the axis of the
lenses. The electricity of one end of a powerful battery reaches the charcoal
a by means of a copper wire K ; while the electricity from the opposite end
of the battery reaches c by a second copper wire H.

During the passage of the electricity a luminous arc is formed between
the two ends of the carbons, which gives a most brilliant light, and power-
fully illuminates the microscope. This is effected by placing at D in the
inside of the tube a condensing lens, whose principal focus corresponds to
the space between the two charcoals. In this manner the luminous rays
which enter the tubes U and B are parallel to their axis, and the same
effects are produced as with the ordinary solar microscope ; a magnified
image of the object placed between two plates of glass is produced on the
screen.

In continuing the experiment the two carbons become consunTed, and to
an unequal extent, a more quickly than c. Hence, their distance increasing,

607J

IJcJithojisc Lenses.

581

the light becomes weaker, and is ultimately extinguished. In speaking
afterwards of the electric light, the working of the apparatus P, which keeps
these charcoals at a constant distance, and thus ensures a constant light,
will be explained.

The part of the apparatus MN may be considered as a .universal photo-
genic apparatus. The microscope can be replaced by the headpieces of the
phantasmagoria, the polyorama, the megascope, by polarising apparatus, &c.,
and in this manner is admirably adapted for exhibiting optical phenomena
to a large auditory Instead of the electric light, we may use with this
apparatus the oxyhydrogett or Driimmond's light, which is obtained by heat-

Fig. 573.
ing a cylinder of lime in the flame produced by the combustion of a mixture
of hydrogen or of coal gas with oxygen gas.

607. Iiighthouse lenses. — Lenses of large dimensions are very difficult
of construction ; they further produce a considerable spherical aberration,
and their thickness causes the loss of much light. In order to avoid these
inconveniences, echelo7i lenses have been constructed. They consist of a
plano-convex lens, C (figs. 574 and 575), surrounded by a series of annular
and concentric segments, A, B, each of which has a plane face on the same
side as the plane face of the central lens, while the faces on the other side
have such a curvature that the foci of the different segments coincide in the

582

On Light.

[607-

same point. These rings form, together with the central lens, a single lens,
a section of which is represented in fig. 575. The drawing was made from
a lens of about 2 feet in diameter, the segments of which are formed of a
single piece of glass ; but, with larger lenses, each segment is likewise formed
of several pieces.

Behind the lens there is a support fixed b)- three rods, on which a body
can be placed and submitted to the sun's rays. As the centre of the support

coincides with the
focus of the lens,
the substances
placed there are
melted and vola-
tilised by the high
temperature pro-
duced. Gold, pla-
tinum, and quartz
are melted. The
experiment proves
that heat is re-
fracted in the same
way as light ; for
the position of the
calorific focus is
identical with that
of the luminous
focus.

Formerly para-
bolic mirrors were
used in sending
the light of bea-
cons and light-
houses to great
distances, but they
have been sup-
planted by the use
of lenses of the
above construc-
tion. In most

cases oil is used in a lamp of peculiar construction, which gives as much
light as 20 moderators. The light is placed in the principal focus of the
lens, so that the emergent rays form a parallel beam (fig. 503), which loses
intensity only by absorption in the atmosphere, and can be seen at a dis-
tance of above 40 miles. In order that all points of the horizon may be
successively illuminated, the lens is continually moved round the lamp by
a clockwork motion, the rate of which varies with different lighthouses.
Hence, in different parts the light alternately appears and disappears after
equal intervals of time. These alternations serve to distinguish lighthouses
from an accidental fire or a star. By means, too, of the number of times the
light disappears in a given time, and by the colour of the light, sailors are

-608J PJiotography. 583

enabled to distinguish the lighthouses from one another, and hence to know
their position.

Of late years the use of the electric light has been substituted for that
of oil lamps. A description of the apparatus will be given in a subsequent
chapter.

PHOTOGRAPHY.

60S. Pbotograptay is the art of fixing the images of the camera obscura
on substances sensitive to light. The various photographic processes may
be classed under three heads : photography on metal, photography on
paper, and photography on glass.

Wedgwood was the first to suggest the use of chloride of silver in fixing
the image, and Davy, by means of the solar microscope, obtained images of
small objects on paper impregnated with chloride of silver ; but no method
was known of preserving the images thus obtained, by preventing the further
action of light. Niepce, in 18 14, obtained permanent images of the camera
by coating glass plates with a layer of a varnish composed of bitumen dis-
solved in oil of lavender. This process was tedious and inefficient, and it
was not until 1839 that the problem was solved. In that year Daguerre
described a method of fixing the images of the camera which, with the sub-
sequent improvements of Talbot and Archer, has rendered the art of photo-
graphy one of the most marvellous discoveries ever made, whether as to the
beauty and perfection of the results, or as to the celerity with which they are
produced.

In Daguerre's process, the Dagiierrotypc, the picture is produced on a
plate of copper coated with silver. This is first very carefully polished — an
operation on which much of the success of the subsequent processes depends.
It is then rendered sejisitive by exposing it to the action of iodine vapour,
which forms a thin layer of iodide of silver on the surface. The plate is now
fit to be exposed in the camera ; it is sensitive enough for views which re-
quire an exposure of ten minutes in the camera, but when greater rapidity is
required, as for portraits, &c., it is further exposed to the action of an accele-
rator^ such as bromine or hypobromite of calcium. All the operations must
be performed in a room lighted by a candle, or by the daylight admitted
through yellow glass, which cuts off all chemical rays. The plate is preserved
from the action of light by placing it in a small wooden case provided with
a slide on the sensitive side.

The third operation consists in exposing the sensitive plate to the action
of light, placing it in that position in the camera where the image is pro-
duced with greatest delicacy. For photographic purposes a camera obscura
of peculiar construction is used. The brass tube A (figs. 576 and 577) con-
tains an achromatic condensing lens, which can be moved by means of a rack-
work motion, to which is fitted a milled head D. At the opposite end of the
box is a ground-glass plate, E, which slides in a groove, B, in which the case
containing the plate also fits. The camera being placed in a proper position
before the object, the sliding part of the box is adjusted until the image is
produced on the glass with the utmost sharpness ; this is the case when the
glass slide is exactly in the focus. The final adjustment is made by means
of the milled head D.

584

On Light.

[608-

The glass slide is then replaced by the case containing the sensitive
plate ; the slide which protects it is raised, and the plate exposed for a time,

the duration of which varies
in dififerent cases, and can
only be hit exactly by great
practice. The plate is then
removed to a dark room.
No change is perceptible to
the eye, but those parts on
which the light has acted
have acquired the property
of condensing mercuiy ; the
plate is next placed in a box
and exposed to the action of
mercurial vapour at 60 or 70
degrees.

The mercury is deposited
on the parts affected, in the
form of globules imperceptible to the naked eye. The shadows, or those
parts on which the light has not acted, remain covered with the layer of
iodide of silver. This is removed by treatment with hyposulphite of sodium,
which dissolves iodide of silver without affecting the rest of the plate. The
plate is next immersed in a solution of chloride of gold in hyposulphite of
sodium, which dissolves the silver, while some gold combines with the

Fig. 576.

mercury and silver of the parts attacked, and greatly increases the intensity
of the lustre.

Hence the light parts of the image arc those on which the mcrcur>' has
been deposited, and the shaded those on which ihc metal has retained its
reflecting lustre.

Fig. 577 represents a section of the camera and the object-glass. At first
it consisted of a double convex lens, but now double achromatic lenses, LL',
are used as object-glasses. They act more quickly than objectives with a
.single lens, have a shorter focus, and can be more easily focusscd liy moving
the lens L' by means of the rack and pinion D.

609. PliotoffrapliH on paper. — In Daguerrc's process, which has just
liecn described, the images are jiroduced •directly on metal plates. With

-609] Photograplis on Paper. 585

paper and glass, photographs of two kinds may be obtained : those in which
an image is obtained with reversed tints, so that the hghtest parts have be-
come the darkest on paper, and vice versa ; and those in which the hghts
and shades are in their natural position. The former are called ticgative
and the \dX\.&x positive pictures.

A negative may be taken either on glass or on paper ; it serves to produce
a positive picture.

Negatives on glass. — A glass plate of the proper size is carefully cleaned
and coated with a uniformly thick layer of collodion impregnated with iodide
of potassium. The plate is then immersed for about a minute in a bath of
nitrate of silver containing 30 grains of the salt in an ounce of water. This
operation must be performed in a dark room. The plate is then removed,
allowed to drain, and, when somewhat dry, placed in a closed flame, and
afterwards exposed in the camera, for a shorter time than in the case of a
Daguerrotype. On removing the plate to a dark room no change is visible ;
but on pouring over it a solution called the developer., an image gradually
appears. The principal substances used for developing are protosulphate
of iron and pyrogallic acid. The action of light on iodide of silver appears
to produce some molecular change, or else some actual chemical decom-
position, in virtue of which the developers have the property of reducing
to the metallic state those parts of the iodide of silver which have been most
acted upon by the light. When the picture is sufficiently brought out, water
is poured over the plate, in order to prevent the further action of the
developer. The parts on which light has not acted are still covered with
iodide of silver, which would be aff'ected if the plate were now exposed to
the light. It is, accordingly, washed with solution of hyposulphite of sodium,
which dissolves the iodide of silver and leaves the image unaltered. The
picture is then coated with a thin layer of spirit varnish, to protect it from
mechanical injury.

When once the negative is obtained, it may be used for printing an in-
definite number of positive pictures. For this purpose paper is coated with
a layer of egg-albumen containing a certain proportion of chloride of
ammonium, and then left to dry. The paper is then made sensitive by float-
ing it on a bath containing 30 to 40 grains to the ounce of nitrate of silver.
Chloride of silver is formed by the double decomposition of the two salts,
and this again acting on the albumen forms an obscure compound containing
chloride and albuminate of silver. The negative is placed on a sheet of
this paper in a copying frame, and exposed to the action of light for a
certain time. The chloride of silver becomes acted upon— the light parts of
the negative being most affected, and the dark parts least so. A copy is
thus obtained, on which the lights of the negative are replaced by shades,
and inversely. The picture is then immersed in a bath of chloride of gold,
which gives it tone, and preserves it from fading. In order to fix the picture
it is now immersed in a solution of hyposulphite of sodium, which dissolves
the unaltered chloride of silver. The print must now be washed in a stream
of water for several hours in order to get rid of all traces of the hyposulphite,
^vhich if left in would ruin the picture.

Of late years permanent and very beautiful prints have been obtained
from negatives by making use of the chemical change produced by light on

586 On Light. [609-

a mixture of bichromate of potass and gelatine. On this reaction are based
the various carbon processes, and those for mechanical printing. Very
beautiful prints, with an effect resembling that of steel engravings, are pro-
duced by what is known as the. platinum process. This consists in exposing
paper charged with ferric oxalate to light and then developing the prmts thus
produced by platinum salt ; the ferric salt by exposure to light is reduced to
a ferrous oxalate, which in turn reduces the platinum salt to black metallic
platinum.

6 ID. iregatlves on g-elatine emulsions. Dry plates. — In 1 87 1 Dr.
Maddox demonstrated that the sensitiveness of the salts of silver is enor-
mously increased by employing gelatine instead of collodion as the basis ot
an emulsion, and also that such gelatine emulsions could be dried and kept
for an almost indefinite time without losing its value. Bennet showed in
1878 that the sensitiveness of such emulsions is still further increased by
heating the emulsion to 32° C. for several days.

Glass plates coated with gelatine emulsion containing bromide or other
haloid salts of silver are made commercially in vast quantities and sold under
the name of diy plates.

In 1 88 1 Dr. Eder showed that a bromiodide emulsion could be made
sensitive to a far greater range of the spectrum by adding a minute propor-
tion of eosin, or other aniline dye. These ortJiochromatic plates, as they are
called, are not merely sensitive to the ultra-violet rays, but are highly sensi-
tive to the D line of the spectrum, and thus yellow objects, instead of
appearing black, or dark-blue objects appearing white, as in photographic
prints from ordinary plates, appear in their true visible relation of brightness
to one another.

611. Positives on griass. — Very beautiful positives are obtained by pre-
paring the plates by the ' wet process ' (§ 609) ; the exposure in the camera,
however, is not nearly so long as for the negatives. The picture is then
developed by pouring over it a solution of protosulphate of iron, which
produces a negative image ; and by afterwards pouring a solution of cyanide
of potassium over the plate, this negative is rapidly converted into a
positive. It IS then washed and dried, and a coating of varnish poured
over the picture. Positives may also be obtained by placing a gelatine ' dry
plate ' in direct contact with a negative in a printing frame, and exposing it
to an artificial light for a few seconds ; the time of exposure depending upon
the density of the negative and the intensity of illumination. The exposed
plate is then developed in the ordinary way, except that the process must be
prolonged in order to get greater density than is rcciuired for ordinaiy print-
ing purposes.

-612]

Structure of the Human Eye.

587

CHAPTER VI.

THE EYE CONSIDERED AS AN OPTICAL INSTRUMENT.

612. Structure of tbe human eye. — The eye is placed in a bony cavity
called the orbit ; it is maintained in its position by the muscles which serve
to move it, by the optic nerve, the conjunctiva, and the eyelids.

Fig. 578 represents a transverse section of the eye from back to front.
The general shape is that of a sphere, or more strictly speaking it consists
of the segments of two spheres of unequal size, of which the anterior is much
the smaller and constitutes the cornea, while the posterior, forming the chief
envelope of the eyeball, receives
the name of the sclerotica. The
eye is composed of the following
parts : the cornea, the sclerotic,
the iris, the pupil, the aqueous
htwtour, the crystalline, the vi-
treous body, the hyaloid mem-
brane, the choroid, the reti?ta,
and the optic nerve.

Cornea. — The cornea, a, is a
transparent circular tunic form-
ing the anterior segment of the
eye. It is nothing more than
a continuation of the sclerotic
forwards, and is formed by the
fibres of the latter becoming
more systematically arranged and rendered quite transparent. Its front
surface is lined throughout by the conjttnctiva. This is a soft membrane
which not only covers the cornea but, passing in a loose fold to the circum-
ference of the orbit, is reflected over the under surface of the lids, thus com-
pletely closing-in the cavity of the eyeball, and yet being so loose that the
eye can roll freely in its socket. The two surfaces of the cornea are so
nearly parallel that optically they may be considered as a single surface.

Sclerotic. — This (fig. 578, /) is a strong tough tunic enveloping the whole
of the eye behind the cornea. At its back part it is reflected over the optic
nerve, forming a sheath for it as far as the apex of the orbit. The chief func-
tions of the sclerotic are to maintain the shape of the organ, and to protect
it from injur}' and pressure.

Iris. — The iris, d, is an annular, opaque diaphragm, placed between the
cornea and the crystalline lens. It constitutes the coloured part of the eye,
and is perforated by an aperture called the pupil, which in man is circular

588 On Light. [612-

In some animals, especially those belonging to the genus Fclis, it is narrow
and elongated in a vertical direction ; in the ruminants it is elongated in a
transverse direction. It contains a large number of muscular fibres, which
are disposed partly as a narrow ring close to the pupil, called the sphincter
zridis, and partly in the form of fibres radiating from the circumference to
the sphincter, called the dilator iridis. Thus, as the one or the other set
of fibres are stimulated, the pupil is able to contract or dilate. The diameter
of the pupil is constantly varying, the variation ranging from | to ^V of an
inch, but these limits may be -exceeded. In total darkness the pupil is en-
larged to its utmost limits, but it contracts instantly in a bright light. The
movements of the iris are involuntary.

It appears from this description that the iris is a screen with a variable
aperture, whose function is to regulate the quantity of light which penetrates
into the eye ; for the size of the pupil diminishes as the intensity of light
increases. The iris serves also to correct the spherical aberration, as it
prevents the marginal rays from passing through the edges of the crystalline
lens. It thus plays the same part with reference to the eye that a stop does
in optical instruments (558).

Aqueous huinoiir. — Between the posterior part of the cornea and the
front of the crystalline there is a transparent liquid called the aqueous
humour. The space, ^, occupied by this humour is called the anterior
in contradistinction to the posterior chamber., a space which the older ana-
tomists imagined to exist between the iris and the capsule of the lens. But
inasmuch as later observations have shown that the iris lies in contact with
the lens in its capsule throughout the greater part of its length this space
has no practical existence.

Crystalline lens. — This is a double convex transparent body placed im-
mediately behind the iris, which it supports, though not attached to it. The
lens is enclosed in a transparent membrane, called \is capsule. The structure
of the lens can be best seen by boiling it in water, which converts it into a
hard opaque mass. A succession of concentric lamini^, like the coats of an
onion, may be stripped off, leaving a hard central spherical nucleus of the
same material. These lamina: increase in density and refracting power from
the circumference to the centre. They consist entirely of long ribbon-shaped
fibres, which overlap one another concentrically, and are united together
by a kind of cement. Optically, the lens may be considered as a system
made up of a biconvex lens of high refracting power and short focal length.
Opticians have constructed achromatic lenses on the same Imes for photo-
graphic purposes by cementing two meniscus lenses to an intermediate flint
lens.

To the anterior surface of the capsule, near its margin, is fixed a firm
transparent membrane, and known as the suspensory ligament or zonule oj
Zinn, which is attached behind to the front of the hyaloid membrane, and
indirectly to the ciliary muscle. This ligament exerts attraction, all round,
on the front surface of the lens, and renders it loss convex than it would
otherwise be, and its relaxation plays an important ])art in the adaptation of
the eye for sight at different distances.

Vitreous body. Hyaloid membrane. — The vitreous body, or vitreous
humour, is a transparent gelatinous mass resembling the white of an ^g^^

-612] Structure of the Human Eye. 5 89

which occupies all the part of the ball of the eye, h, behind the lens. The
vitreous humour is surrounded by the hyaloid membrane^ /, which lines the
posterior face of the crystalline capsule, and also the inner face of another
membrane called the retina.

Retina. Optic 7ten'e. — The retina, w, is the name given to a layer of
specially modified cells which receives the impression of light. It is really
nothing more than the terminal fibres of the optic nerve, altered in such a
way as to be sensitive to the waves of light. Each optic nerve which
conveys to the mind the impression produced by light arises from three
centres in the brain, and the fibres, after being collected into a thick cord,
pass forward along the base of the brain. Here each cord after forming a
junction with its fellow of the opposite side again separates, and, passing
through a hole at the back of each socket, reaches and enters the eyeball, in-
side which it expands into a cup-shaped network of nerves called the retitta.
The nerve fibres themselves are not sensitive to light, but are only stimu-
lated by it indirectly through the intervention of certain specially adapted cells.
The fibres of the optic nerve, when they spread out to form the inner layer of
the retina, after running a shorter or longer distance turn abruptly outward,
and each fibre becomes connected with a larger ganglion cell, which again is
connected by other processes with smaller cells ; and each group of these
finally ends in either a peculiarly shaped cylinder called a rod, or a thicker
flask-shaped structure called a cone. All are ranged perpendicular to the
surface of the retina, closely packed together, so as to form a regular mosaic
layer when viewed from the outside. In the retina is a remarkable spot
which is situated in the axis of vision a little to the outside of the place
where the optic nerve enters the eyeball. From its colour it is called the
macula littea or yellow spot. The retina is here somewhat thick, but in the
middle of the yellow spot is found a depression, the fovea centralis, where
the retina is reduced to those elements alone which are absolutely necessary
for exact vision. Thxs fovea, or pit of the retina, is of great importance for
vision, since it is the spot where the most exact discrimination of distance
is made. Only those parts of the retinal image which fall on the yellow
spot are sharp, all the rest are more inaccurate the nearer they fall to the
limits of the retina. The field of view of the eye is like a drawing, the
centre of which is done with great accuracy and delicacy while the sur-
rounding part is only roughly sketched. Where the optic nerve enters there
are no rods or cones ; this part of the retina, therefore, is insensitive to
light, and is called the pimctuni ccccuni or bli7id spot. When examined in
the living subject by means of the ophthalmoscope it appears as a slightly
oval pinkish disc crossed by numerous blood-vessels.

The only property of the retina and optic nerve is that of receiving and
transmitting to the brain the impression of objects. These organs have
been cut and pricked without causing any pain to the animals submitted to
these experiments ; but there is reason to believe that irritation of the optic
nerve causes the sensation of a flash of light.

Choroid. — The choroid, k, is a membrane between the retina and the
sclerotic. It is highly vascular, and supplies the nourishment necessary for
the chemical and physiological processes concerned in vision. On its inner
surface, and in close contact with the ends of the rods and cones, is a layer

590 On Light. [612-

of densely black pigment cells, which secrete a peculiar yellowish purple
pigment called the visual purple^ and which is rapidly bleached by light. It
is evidently connected with the act of vision, but its precise use is uncertain.

The choroid forms a series of convoluted folds in front, called ciliary
'Processes, which penetrate between the iris and the lens capsule, forming
round the latter a disc resembling a radiated flower. The ciliary pro-
cesses secrete the colourless fluid necessary for the nourishment of the
transparent parts of the eye, which, being transparent for visual purposes,
cannot be nourished by means of blood-vessels.

613. Refractive indices of the transparent media of the eye. — The
refractive indices from air into the transparent parts of the eye were deter-
mined by Brewster, and have since been carefully examined by Von Helm-
holtz. Their results are contained in the following table, compared with
water as a standard : —

Brewster

Helmholtz

1-3358 .

• 1-3358

1-3366 .

• 1-33(^5

1-3394 •

■ 1-3365

• 1-3365

1-3767 .

• 1-3930

1-3990 .

• 1-4541

1-3839 .

• I -4371

Water

Aqueous humour ....
Vitreous humour ....
Cornea

External coating of the lens

Centre of the lens ....

Mean refraction of the lens

From this it will be noticed that the refractive index of all the media ex-
cepting the lens is the same.

614. Curvatures and dimensions of various parts of the human

eye.— According to the latest tables of Von Helmholtz (1888), these are :—

Radius of curvature of the cornea 7-83

„ „ anterior surface of the crj'^stalline . . 10-00

„ „ posterior surface „ „ . . . 6-oo

Distance from apex of the cornea to the anterior surface of the lens . 3-60

„ „ „ posterior „ „ . 7-20

Thickness of the crystalline lens 3-60

615. Path of rays In the eye. — From what has been said as to the
structure of the eye, it may be compared to a camera obscura (602), of which
the i)upil is the aperture, the crystalline is the condensing lens, and the

Fifi. 579-

retina is the screen on which the image is formed. Hence, the eftect is the
same as when the image of an object placed in front of a double convex lens
is formed at its conjugate focus. Let AB (fig. 579) be an object placed
before the eye, and let us consider the rays emitted from any point of the

-617 j Optic Axis, Optic Angle, Visual Angle. 591

object A. Of all these rays, those which are directed towards the pupil are
the only ones which penetrate the eye, and are operative in producing vision.
These rays, on passing into the aqueous humour, experience a first refraction
which brings them near the secondary axis ha drawn through the optic
centre of the crystalline ; they then traverse the crj'stalline, which again
refracts them like a double convex lens, and, having experienced a final
refraction by the vitreous humour, they meet in a point <z, and form the
image of the point A. The rays issuing from the point B form in like manner
an image of it at the point ^, so that a very small, real, and inverted image is
formed exactly on the retina, provided the eye is in its normal condition.

616. Inversion of images. — In order to show that the images formed
on the retina arc really inverted, the eye of an albino or any animal with
pink eyes may be taken ; this has the advantage that, as the choroid is
destitute of pigment, light can traverse it without loss. This is then deprived
at its posterior part of the cellular tissue surrounding it, and fixed in a hole
in the shutter of a dark room ; by means of a lens it may be seen that the
inverted images of external objects are depicted on the retina.

The inversion of images in the eye has greatly occupied both physicists
and physiologists, and many theories have been proposed to explain how it
is that we do not see inverted images of objects. The chief difficulty seems
to have arisen from the conception of the mind or brain as something
behind the eye, looking into it, and seeing the image upon the retina ;
whereas really this image simply causes a stimulation of the optic nerve,
which produces some molecular change in some part of the brain ; and it is
only of this change, and not of the image as such, that we have any conscious-
ness. The mind has thus no direct cognisance of the image upon the retina,
nor of the relative positions of its parts, and, sight being supplemented by
touch in innumerable cases, it learns from the first to associate the sensations
brought about by the stimulation of the retina (although due to an inverted
image) with the correct position of the object as taught by touch.

617. Optic axis, optic angle, visual angle. — 'Y\v& principal optic axis
of an eye is the axis of its figure ; that is to say, the straight line in reference
to which it is symmetrical. In a well-shaped eye it is the straight line passing

Fig. 580.

through the centre of the pupil and of the crystalline. The lines A«, ^b,
(fig. 581) are secondary axes. The eye sees objects most distinctly in the
direction of the principal optic axis.

The optic angle is the angle BAC (fig. 5S0), formed between the principal
optic axes of the two eyes when they are directed towards the same point.
This angle is smaller in proportion as the objects are more distant.

592 On Light. [617-

The visual angle is the angle AOB (fig. 581), under which an object is seen ;
that is to say, the angle formed by the secondary axes drawn from the optic
centre of the crystalline to the opposite extremities of the object. P^or the
same distance, this angle increases with the magnitude of the object, and for
the same object it decreases as the distance increases, as is the case when
the object passes from AB to A'B'. It follows, therefore, that objects appear

Fig. 53

smaller in proportion as they are more distant ; for as the secondaiy axes,
AO, BO, cross in the centre of the crystalline, the size of the image projected
on the retina depends on the size of the visual angle AOB.

618. Estimation of the distance and size of objects. — The estimation
of distance and of size depends on numerous circumstances ; these are — the
visual angle, the optic angle, the comparison with objects whose size is
familiar to us ; to these must be added the effect of what is called aerial
perspective ; that is, a more or less vaporous medium which enshrouds the
distant objects, and thereby diminishes not only the sharpness of the out-
lines, but also softens the contrast between light and shade, which close at
hand are marked.

When the size of an object is known, as the figure of a man, the height
of a tree or of a house, the distance is estimated by the magnitude of the
visual angle under which it is seen. If its size is unknown, it is judged
relatively to that of objects which surround it.

A colonnade, an avenue of trees, the gas-lights on the side of a road,
appear to diminish in size in proportion as their distance increases, because
the visual angle decreases ; but the habit of seeing the columns, trees, &c.,
in their proper height, leads our judgment to rectify the impression produced
by vision. Similarly, although distant mountains are seen under a veiy
small angle, and occupy but a small space in the field of view, our familiarity
with the effects of aerial perspective enables us to form a correct idea of
their real magnitude.

The optic angle is also an essential element in appreciating distance.
Since this angle increases or diminishes according as objects approach or
recede, we move our eyes so as to make their optic axes converge towards
the object which we are looking at, and thus obtain an idea of its distance.
Nevertheless, it is only by long custom that we can establish a relation
between our distance from the objects, and the corresponding motion of the
eyes. It is a curious fact that persons born blind, and whose sight has been
restored by the operation for cataract, imagine at first that all objects are at
the same distance.

Vertical distances are estimated too low compared with horizontal ones ;
on high mountains and over large surfaces of water, distances are estimated
too low owing to the want of intervening objects. Practice and experience
have great infiuence on our correct estimation of magnitude and distance.

-618a] Scheifiers Experiment. 593

As \vc ascend mountains much less frequently than \vc walk on the level, we
err more easily in estimating a height than in judging a horizontal distance.
A room filled with furniture appears larger than an empty room of the same

We cannot recognise the true form of an object if, with moderate illu-
mination, the visual angle is less than half a minute. A white square, a
metre in the side, appears at a distance of about 5 miles under this angle as
a bright spot which can scarcely be distinguished from a circle of the same
size.

A very bright object, however, such as an incandescent platinum wire,
is seen in a dark ground under an angle of 2 seconds. So too a small dark
object is seen against a bright ground ; thus a hair held against the sky can
be seen at a distance of i or 2 metres.

b\Za. Sclieiner's experiment. — If we look at a small object placed
either within or beyond the point on which the eye is focussed, through a
number of minute openings in a diaphragm, arranged so close together that
they fall within the circumference of the pupil, the object appears multiple,
each object furnishing a separate retinal image. This forms what is known
as Scheincr's expcjivient. This may be made as follows : By means of a
sewing needle, two small holes are pricked in a piece of cardboard, not more
than Y^,.; of an inch apart, i.e. less than the diameter of the pupil. The card
is held before one eye with the holes horizontally in front of the pupil, and
with the other hand a needle is held at ordinary reading distance in the line
of vision. If the eye be fixed on the needle itself, it appears single and
clearly defined ; as soon, however, as we look at a more distant object, the
needle appears double, and at the same time blurred. If we block out the
right-hand hole, the left-hand image disappears, and vice versa.

If we now fix the eye on an object nearer than the needle, the latter
again appears double and blurred, and blocking either hole causes the image
on the same side to vanish. The explanation of these phenomena may be
simplified by the following diagram.

Fig. 382.

Let AB (fig. 582) be the two holes in the card CC, O a luminous point in
the needle, OA, OB the pencils of rays passing through the apertures in the
card. Let H, E, M represent the position of a hypermetropic, normal, and
myopic eye respecti\-ely. When the normal eye E is accommodated for O
the rays OA, OB meet at the point E, and the needle appears sharply

594 Oti Light. [618a-

defined and single. If the eye is fixed on a point beyond, or, what amounts
to the same thing, if the eye be hypermetropic, the retina may be considered
to he no longer at E, but in front at H, and the rays 0\p not only do not
meet in a focus at p, but do not meet the rays OV>p' ; hence the luminous
spot O will be seen at two points, and the points themselves being out of
focus will appear blurred. Moreover, the rays passing through the right-
hand hole A will cut the retina at p, and will appear to the mind on the
reverse side, i.e. on the left ; therefore blocking the right-hand hole A
causes a disappearance of the left-hand image, and vice versa.

For similar reasons, if the eye be accommodated for a point nearer the
eye than O, or, what amounts to the same thing, if the eye be myopic, the
retina may be considered to lie behind E at M, and the image will again be
seen doubled and blurred ; only in this case blocking out the right-hand
hole A will cause the right-hand image to disappear. Stampfer constructed
an optometer based on this principle. He employed a tube containing two
diaphragms, one furnished with two slits i'"™ apart, the other with a single
slit covered with ground glass. The diaphragm is moved to or from the
eye until the slit is seen single. This distance from the eye is the measure
of distinct vision.

619. Distance of distinct vision. — The dista?tce oj distinct vision., as
already stated (587), is the distance at which objects must be placed so as to
be seen with the greatest distinctness. It varies in different individuals, and
in the same individual it is often different in the two eyes. For small objects,
such as print, it is from 10 to 12 inches in normal cases.

Persons who see objects distinctly only at a very short distance away are
called myopic^ or short-sighted, and those who require a convex glass to see
objects distinctly at a long distance are hypermetropic, or long-sighted (629).

Sharpftess of sight may be compared by reference to that of a normal eye
taken as a unit. Such a standard eye, according to Snellen, recognises
quadrangular letters when they are seen under an angle of 6' ; if, for instance,
such letters are lo""" high at a distance of 6 metres. The sharpness
of vision of one who recognises these letters at a distance of 6 metres is

then -.
6

620. Accommodation. — By this term is meant the changes which occur
in the eye to fit it for seeing distinctly objects at different distances from it.

If the eye be supposed fixed and its parts immovable, it is evident that
there could only be one surface whose image would fall exactly upon the
retina ; the distance of this surface from the eye being dependent on the
refractive indices of the media and the curvatures of the refractive surfaces
of the eye. The image of any point nearer the eye than this distinctly seen
surface would fall behind the retina ; the image of any more distant point
would be formed in front of it ; in each case the section of a luminous cone
would be perceived instead of the image of the point, and the latter would
appear diffused and indistinct.

Experience, however, shows us that a normal eye can see distinct images
of objects at very different distances. We can, for example, see a distant
tree through a window, and also a scratch on the pane, though not both dis-
tinctly at the same moment ; for when the eye is arranged to see one clearly,

-621] Binocular Vision. 595

the image of the other does not fall accurately upon the retina. An eye
completely at rest seems adapted for seeing distant objects ; the sense of
effort is greater in a normal eye when a near object is looked at, after a
distant one, than in the reverse case ; and in paralysis of the nerves govern-
ing the accommodating apparatus, the eye is persistently adapted for distant
sight. There must, therefore, be some mechanism in the eye by which it
can be voluntarily altered, so that the more divergent rays proceeding from
near objects shall come to a focus upon the retina. There are several con-
ceivable methods by which this might be effected ; it is actually brought
about by a drawing forwards of the crystalline lens and a greater convexity of
its front surface.

This is shown by the foUowmg experiment : — If a candle be placed on
one side of the eye of a person looking at a distant object, and his eye be
observed from the other side, three distinct images of the flame will be
seen ; the first, virtual and erect, is reflected from the anterior surface of
the cornea ; the next, erect and less bright, is reflected from . the anterior
surface of the lens ; the third, inverted and brilliant, is formed on the
posterior surface of the lens. If now the person look at a near object, no
change is observed in the first and third images, but the second image
becomes smaller and approaches the first ; which shows that the anterior
surface of the crystalline lens becomes more convex and approaches the
cornea. In place of the candle. Von Helmholtz throws light through two holes
in the screen upon the eye, and observes the distance on the eye between
the two shining points, instead of the size of the flame of the candle.

This change in the lens is effected chiefly by means of a circular muscle
(ciliary muscle), the contraction of which relaxes the suspensory ligament,
and so allows the front surface of the lens to assume more or less of that
greater convexity which it would normally exhibit were it not for the drag
exercised upon it by the ligament. Certain other less important changes
occur, tending to make the lens more convex and to push it forwards, which
cannot, however, be explained without entering into minute anatomical
details. When the eye is accommodated for near vision, the pupil contracts
and so partially remedies the greater spherical aberration.

The r(^;z^i?(?/(^£r^tf'w;;z£'^<:?/'/<?«, called by Bonders , is measured by first

of all determining the greatest distance, R, at which a person can read with-
out spectacles, and then the smallest, P, at which he can so read ; then

I _ I _ I
A~P R'

621. Binocular vision. — A single eye sees most distinctly any point
situated on its optical axis, and less distinctly other points also, towards
which it is not directly looking, but which are still within its circle of vision.

It is able to judge of the directio7t of any such point, but unable by itself
to estimate its distance. Of the distance of an object it may, indeed, learn
to judge by such criteria as loss of colour, indistinctness of outline, decrease
in magnitude, &c. ; but if the object is near, the single eye is not infallible,
even with these aids.

When the two eyes are directed upon a single point, we then gain the

'.' <.) 2

596

On Light.

[621-

•

power of judging of its distance as compared with that of any other point,
and this we seem to gain by the sense of greater or less effort required in
causing the optical axes to converge upon the one point or upon the other.
Now a solid object may be regarded as composed of points which are at
different distances from the eye. Hence, in looking at such an object, the
axes of the two eyes are rapidly and insensibly varying their angle of con-
vergence, and we as rapidly are gaining experience of the difference in
distance of the various points of which the object is composed, or, in other
words, an asurance of its solidity. Such kind of assurance is necessarily
unattainable in monocular vision.

622. The principle of tbe stereoscope. — Let any solid object, such as
a small box, be supposed to be held at some short distance in front of the

two eyes. On what-
ever point of it they
are fixed, they will
see that point the
most distinctly, and
other points more or
less clearly. But it
is evident that, as the
two eyes see from
different points of
/ '• view, there will be

^'"- 5-3- formed in the right

eye a picture of the object different from that formed in the left ; and it is by
the apparent union of these two dissimilar pictures that we see the object
in relief. If, therefore, we delineate the object, first as seen by the right
eye, and then as seen by the left, and afterwards present these dissimilar
pictures again to the eyes, taking care to present to each eye that picture
which was drawn from its point of view, there would seem to be no reason
why we should not see a representation of the object, as we saw the object
itself, in relief. Experiment confirms the supposi-
tion. If the object held before the eyes were a
truncated pyramid, r and /, fig. 583, would repre-
sent its principal lines, as seen by the right and left
eyes respectively. If a card is held between the
figures, and they are steadily looked at, r by the
right eye, and / simultaneously by the left, for a
few seconds, there will be seen a single picture
having the unmistakable appearance of relief. Even
without a card interposed, the eye, by a little prac-
tice, may soon be taught so to combine the two as
to form this solid picture. Three pictures will in
that case be seen, the central one being solid, and
the two outside ones plane. Kig. 584 will explain
this. Let r and / be any two corresponding points,
say the points markctl by a large dot in the figures
drawn above ; R ami L the positions of the right and left eyes ; then the
right eye sees the point r in the direction R^, and the left eye the point / in

-624]

TJie Refractmg Stereoscope

597

the direction Lf, and accordingly each by itself judging only by the direc-
tion, they together see these two points as one, and imagine it to be situated
at o. But the right eye, though looking in the direction Rr, also receives
an image of / on another part of the retina, and the left eye in the same way
an image of r, and thus three images arc seen. A card, however, placed
in the position marked by the dotted line will, of course, cut off the two side
pictures. To assist the eye in combining such pairs of dissimilar pictures,
both mirrors and lenses have been made use of, and the instruments in
which either of these are adapted to this end are called stereoscopes.

623. The reflecting- stereoscope. — In the reflecting stereoscope plane
mirrors are used to change the apparent position of the pictures, so that they
are both seen in the same direction, and their combination by the eye is
thus rendered easy and almost inevitable. If ab., ab (fig. 585) are two plane
mirrors inclined to one another at an angle of 90°, the two arrows, x, j', would
both be seen by the eyes situated at R and L in the position marked by the
dotted arrow. If, instead of the arrows, we now substitute such a pair of
dissimilar pictures as we have spoken of above, of the same solid object, it
is evident that, if the margins of the pictures coincide, other corresponding

<:-

■4 ^T-

points of the pictures will not. The eyes, however, almost without effort,
soon bring such points into coincidence, and in so doing make them appear
to recede or advance, as they are farther apart or nearer together than any
two corresponding points (the right-hand corner, for instance) of the margins
when the pictures are placed side by side, as in the diagram, fig. 585. It will
be plain, also, on considering the position for the arrows in fig. 585, that to
adapt such figures as those in fig. 584 for use in a reflecting stereoscope one
of them must be reversed, or drawn as it would be seen through the paper
if held up to the light.

624. The refracting- stereoscope. — Since the rays passing through a
convex lens are bent always towards the thicker part of the lens, any seg-
ment of such a lens may be readily adapted to change the apparent position
of any object seen through it. Thus, if (fig. 586) two segments be cut from
a double convex lens, and placed with their edges together, the arrows, :r,^,
would both be seen in the position of the dotted arrow by the eyes at R
and L.

If we substitute for the arrows two dissimilar pictures of the same solid

598 On Light. [624-

object, or the same landscape, we shall then, if a diaphragm, ab., be placed
between the lenses to prevent the pictures being seen crosswise by the eyes,
see but one picture, and that apparently in the centre, and magnified. As
before, if the margins are brought by the power of the lenses to coincide,
other corresponding points will not be coincident until combined by an
almost insensible effort of the eyes. Any pair of corresponding points which
are farther apart than any other pair will then be seen farther back in the
picture, just as any point in the background of a landscape would be found
(if we came to compare two pictures of the landscape, one drawn by the
right eye, and the other by the left) to be represented by two points farther
apart from one another than two others which repre-
£ r sented a point in the foreground.

I\ /I It will be instructive to notice that there is also a

\ / I second point on tJiis side of the paper, at which, if a

\ / 1 person look steadily, the diagrams in fig. 587 will
\o/ I combine, and form quite a different stereoscopic pic-

"7^' Y"" ture. Instead of a solid pyramid, a hollow pyramidal

/ \ 1 box will then be seen. The point may easily be found

/ \ 1 ^y experiment. Here again two external images will

/ \ 1 also be seen. If we wish to shut these out, and see

\ I only their central stereoscopic combination, we must
\| use a diaphragm of paper held parallel to the plane of
Ji ,. B the picture with a square hole in it. This paper screen

'^' ^"'^' must be so adjusted that it may conceal the right-hand

figure from the left eye, and the left-hand figure from the right eye, while
the central stereoscopic picture may be seen through the hole. It will be
plain from the diagram that o is the point to which the eyes must be
directed, and at which they will imagine the point to be situated, which
is formed by the combination of the two points r and /. The dotted line
shows the position of the screen. A stereoscope with or without lenses
may easily be constructed, which will thus give us, with the ordinary stereo-
scopic slides, a reversed picture ; for instance, if the subject be a landscape,
the foreground will retire and the background come forward.

\Mien the two retinas view simultaneously two different colours, the im-
pression produced is that of a single mixed tint. The power, however, of
combining the two tints into a single one varies in different individuals,
and in some is extremely weak. If two white discs at the base of the stereo-
scope be illuminated by two pencils of complementary colours, and if each
coloured disc be looked at with one eye, a single white one is seen, showing
that the sensation of white light may arise from two complementary and
simultaneous chromatic impressions on each of the two retinas.

Dove found that if a piece of printing and a copy are viewed in the stereo-
scope, a difference in the distance of the words, which is not apparent to the
naked eye, causes them to stand out from the plane of the paper.

625. Persistence of impressions on the retina. — When an ignited
l)iccc of charcoal is rapidly rolatcil, wc cannot distinguish it; the appearance
of a circle of fire is ])roduccd ; similarly, rain, in falling drops, appears m
the air like a scries of liquid threads. In a rapidly rotating toothed wheel
the individual teeth cannot be seen. But if, during darkness, the wheel be

-626] Accidental IiiKigcs. 599

suddenly illuminated, as by the electric spark, the individual parts may be
clearly made out. The following experiment is a further illustration of this
property : — A series of equal sectors are traced on a disc of glass, and they
are alternately blackened ; in the centre there is a pivot, on which a second
disc is fixed of the same dimensions as the first, but completely blackened
with the exception of a single sector ; then placing the apparatus between a
window and the eye, the second disc is made to rotate. If the movement
is slow, all the transparent sectors are seen, but only one at a time ; by a
more rapid rotation we see simultaneously two, three, or a greater number.
These various appearances are due to the fact that the impression of these
images on the retina remains for some time after the object which has pro-
duced them has disappeared or become displaced. The duration of the per-
sistence varies with the sensitiveness of the retina and the intensity of light.

Plateau investigated the duration of the impression by numerous similar
methods, and has found that it is, on the average, half a second. Among
many curious instances of these phenomena, the following is one of the most
remarkable. If, after having looked at a brightly illuminated window, the
eyes are suddenly closed, the image remains for a few instants — that is, a
sashwork is seen consisting of luminous panes surrounded by dark frames ;
after a few seconds the colours become interchanged, the same framework
is now seen, but the frames are now bright, and the glasses are perfectly
black ; this new appearance may again revert to its original appearance.

The impression of colours remains as well as that of the form of objects ;
for if circles divided into sectors are painted in different colours, they become
confounded, and give the sensation of the colour which would result from
their mixture. Yellow and red give orange ; blue and red violet ; the seven
colours of the spectrum give white, as shown in Newton's disc (fig. 524).
This is a convenient method of studying the tints produced by mi.xed
colouis.

A great number of pieces of apparatus are founded on the persistence
of sensation on the retina ; such are the thauiiiatrope, the phettakistoscopc,
Faraday's wheel, the kaleidophone, and the zoetrope.

The zoetrope 1 or luheel of life, is very convenient for representing a number
of optical, acoustical, and other vibratory motions. It consists of an open
cylinder which can be rotated about its vertical axis. At the top are a
number of vertical slips. If now the various positions of a vibrating pendu-
lum, for instance, are drawn on a narrow strip of paper, the length of which
is equal to the circumference, and this is placed inside the cylinder, when
the wheel is rapidly rotated, on looking through the slits the pendulum
seems as if it were steadily vibrating.

626. Accidental Imagres. — When a coloured object placed upon a black
ground is steadily looked at for some time, the eye is soon tired, and the
intensity of the colour is enfeebled ; if now the eyes are directed towards a
white sheet, or to the ceiling, an image will be seen of the same shape as
the object, but of the complementary colour (570) ; that is, such a one as
united to that of the object would form white. For a green object the image
will be red ; if the object is yellow, the image will be violet.

Accidental colours are of longer duration in proportion as the object has
been more brilliantly illuminated, and has been longer looked at. When a

6oo On Light. [626-

lighted candle has been looked at for some time, and the eyes are turned
towards a dark part of the room, the appearance of the flame remains, but it
gradually changes colour ; it is first yellow, then it passes through orange
to red, from red through violet to greenish blue, which is gradually feebler
until it disappears. If the eye which has been looking at the light be turned
towards a white wall, the colours follow almost the opposite direction : there
is first a dark picture on a white ground, which gi-adually changes into blue,
is then successively green and yellow, and ultimately cannot be distinguished
from a white ground.

The reason of this phenomenon is, doubtless, to be sought in the fact
that the subsecjuent action of light on the retina is not of equal duration for
all colours, and that the decrease in the intensity of the subsequent action
docs not follow the same law for all colours. According to Kiilp, the dura-
tions of the after-image with moderate illumination are for white, yellow,
red, and blue, o-i, 0-09, o-o8, and o-o66 of a second respectively.

627. Irradiation. — This is a phenomenon in virtue of which white objects,
or those of a very bright colour, when seen on a dark ground, appear larger
than they really are. Thus a white square upon a black ground seems
larger than an exactly equal black square upon a white ground (fig. 588).
Irradiation arises from the fact that the impression produced on the retina
extends beyond the outline of the image. It bears the same relation to the
space occupied by the image, that the duration of the impression does to the
time during which the image is seen.

The effect of irradiation is very perceptible in the apparent magnitude of

stars, which may thus appear much larger than they really are ; also in the

appearance of the moon when two or three days old, the

H^mgM| brightly illuminated crescent seeming to extend beyond

^^^^^^1 the darker portion of the disc, and hold it in its grasp.

■ |HH ■ Plateau found that irradiation difters ^•ery much in

n ^H| I different people, and even in the same person it differs

I I on different days. He also found that irradiation in-

nH^^HBp creases with the lustre of the object, and the length of

^^^^^B time during which it is viewed. It manifests itself at

■ H all distances ; diverging lenses increase and condensing

Hhh^I lenses diminish it.

_^^^^_J Accidental haloes are the colours which, instead of

Fig. 5S8. succeeding the impression of an object like accidental

colours, appear round the object itself when it is looked

at fixedly. The impression of the halo is the opposite to that of the object :

if the object is bright the halo is dark, and 7-ice versa. These appearances

are best produced in the following manner :— A white surface, such as a

sheet of paper, is illuminated by coloured light, and a narrow opaque body

held so as to cut off some of the coloured rays. In this manner a narrow

shadow is obtained which is illuminated by the surrounding white daylight,

and appears complementary to the coloured ground. If red glass is used,

the shadow appears green, and blue when a yellow glass is used.

The contrast of colours is a reciprocal action exerted between two adja-
cent colours, and in virtue of which to each one is added the complementary
colour of the other. Chevrcul found that when red and yellow colours are

-628] Tlie Eye is not Achromatic. 60 1

adjacent, red acquires a violet and yellow an orange tint. If the experiment
is made with red and blue, the former acquires a yellow, and the latter a
green tint ; with yellow and blue, yellow passes to orange, and blue towards
indigo ; if a narrow strip of grey paper be laid on a sheet of light green
paper, it appears reddish, if laid on blue paper it seems yellow, and so on
for a vast number of combinations ; in all cases the colour is complementary
to the colour of the base. The importance of this phenomenon in its appli-
cation to the manufacture of coloured cloths, carpets, curtains, &c., may be
readily conceived.

The contrast may be conveniently ex-
amined by means of the apparatus shown
in fig. 589 in about ^ scale. It consists
of a thin vertical board, AB, painted
white, and the base, DC, painted black,
on which are painted circles about % of
an inch in diameter, black and white
respectively. A sheet of coloured glass
is inclined at an angle of 45° ; if now the
eye be so held that the image of the
white circle on DC reflected from the Fig. 5S9.

under surface of the glass plate is looked

at in front of the circle on AB, the image appears of a colour complementary
to that of the glass. Thus with a green plate a red spot is seen on a green
ground.

62S. The eye Is not achromatic- — It had long been supposed that the
human eye was perfectly achromatic ; but this is clearly impossible, as all
the refractions are made the same way, viz. towards the axis ; moreover, the
experiments of Wollaston, of Young, of Fraunhofer, and of Miiller have
shown that it was not true in any absolute sense.

Fraunhofer showed that in a telescope with two lenses, a very fine wire
placed inside the instrument in the focus of the object-glass is seen distinctly
through the eyepiece, when the telescope is illuminated with red light ; but
it is invisible by violet light even when the eyepiece is in the same position.
In order to see the wire again, the distance of the lenses must be diminished
to a far greater extent than would correspond to the degree of refrangibility
of violet light in glass. In this case, therefore, the effect must be due to a
chromatic aberration in the eye.

^^liiller, on looking at a white disc on a dark ground, found that the image
is sharp when the eye is accommodated to the distance of the disc — that is,
when the image forms on the retina ; but he found that, if the image is
formed in front of or behind the retina, the disc appears surrounded by a
very narrow blue edge. If a finger be held up in front of one eye (the other
being closed) in such a manner as to allow the light to enter only one half
of the pupil, and, of course, obliquely, and the eye be then directed to any
well-defined line of light, such as a slit in the shutter of a darkened room,
or a strip of white paper on a black ground, this line of light will appear as a
complete spectrum.

Miiller concluded from these experiments that the eye is sensibly achro-
matic as long as the image is received at the focal distance, or when it is

6o2 On Light. [628-

accommodated to the distance of the object. The cause of this apparent
achromatism cannot be exactly stated. It has generally been attributed to
the tenuity of the luminous beams which pass through the pupillary' aperture,
and that these unequally refrangible rays, meeting the surfaces of the media
of the eye almost at the normal incidence, are ver}' little refracted, from
which it follows that the chromatic aberration is imperceptible (584).

Spherical aberration, as we have already seen, is corrected by the iris
(612). The iris is, in point of fact, a diaphragm, which stops the marginal
rays and only allows those to pass which are near the axis.

629. Short siiTht and long sig:bt. IVXyopia and Iiypermetropia.
Astigmatism. Presbyopia. — The most usual affections of the eye are
myopia, Jiyper})ictropia, pfcsbyopia, and astigmatism. Myopia, or short sight,
is the inability to see objects clearly defined beyond a variable but always
limited distance. The usual cause of myopia is an abnormal increase in
length of the eyeball along the axis of vision, so that the retina lies behind
the focus of the dioptric systems of the eye for parallel rays, thereby render-
ing objects on the retina indistinct. It may be remedied by means of
diverging concave glasses, which, in making the rays deviate from their
common axis, throw the focus farther back, and cause the image to be
formed on the retina.

The habitual contemplation of small objects, sedentary occupations, a
stooping position while studying, in fact anything which tends to congest
the eyes, and cause an unequal strain on the muscles of convergence, may
produce short sight. It is common in the case of young people, and, when
once acquired, tends to become hereditary ; hence the percentage of myopes
is continually on the increase.

Hypermetropia, or long sight, is the contrary of short sight. The eye is
abnormally short along the axis of vision, so that the retina lies in front of
the dioptric system of the eye for parallel rays, thereby rendering objects on
the retina indistinct unless the rays be rendered more convergent by exerting
the muscles of accommodation. Hence the ciliary' muscle can never be
relaxed without the image becoming blurred, even when looking at distant
objects. When regarding near objects, however, the accommodator has to
be brought into play, not from a position of rest, but from the state of con-
traction of the ciliary muscle, which was necessary- to see distant objects
clearly. Hence, owing to this increased strain of accommodation, the eye
becomes easily fatigued when regarding near objects, which thus become
blurred. Hypermetropia is corrected by means of converging (convex) lenses*
These glasses converge the rays before their entrance into the eye, and,
therefore, if the converging power is properly chosen, the image will be
formed exactly on the retina.

Presbyopia. — As we grow older the range of accommodation, in other
words, the power of focussing near objects, decreases. Now there comes a
time with everyone who is not myopic when an object cannot be distmctly
seen nearer than eight inches (the distance arbitrarily chosen by Bonders)-
This occurs in a normal or emmetropic eye at 40 years of age. Hence
presbyopia, as it is called, may be defined as the contraction of the visual
range due to physiological weakening of the accommodating mechanism. It
IS clear, according to the standard of Donders, that it can never occur in very

-630] Eye-glasses. Spectacles. 603

short-sighted persons, as their near point is always much less than 8 inches
to begin with, whereas in hypermetropes, on the other hand, it may become
evident at a much earlier age. Presbyopia is corrected by suitable convex
glasses, which, by converging the rays, bring the point of near vision to eight
inches.

Astigmatism. — We have hitherto considered the dioptric surfaces as
portions of true spheres. Should, however, one of the surfaces have a curve
of shorter radius in one of its meridians, all the rays from a luminous point
cannot be focussed on the same plane, but will possess two linear foci, one
anterior corresponding to the curvature of shorter radius, and the other
behind corresponding to the curve of greater radius. This defect is called
astigtnatism ; it is usually most marked in the cornea, and sometimes causes
serious impairment of vision. It may be corrected by applying a lens ground
on a cylindrical surface in which one of the axes only is a plane ; a curve of
such a radius being chosen as will enable the two linear foci to unite on the
same plane.

630. Eye-glasses. Spectacles. — The glasses commonly used by short-
or long-sighted persons are known under the general name of eye-glasses or
spectacles. Generally speaking, numbers are engraved on the trial glasses
which express their focal length in inches or diopters. This latter term is
applied to the standard focal length of all spectacle glasses adopted by the
Ophthalmological Congress at Heidelberg, and now the only standard
officially recognised thx'oughout Europe and America. This standard is the
refractive power of a lens having a focal length of a metre (39"37 inches),
and is represented by the letter D. Here the refractive power is the inverse

of the focal distance, i.e. D = — and F = ^. Hence to find the number of
F D

diopters which represent the focal length m inches, we must divide 39"37 by
that focal distance, and, conversely, to find the number of inches correspond-
ing to a given number of diopters, we have only to divide 39-37 by this
latter.

The spectacles must be so chosen that they are close to the eye, and
that they make the distance of most distinct vision 10 or 12 inches.

The number which a short- or long-sighted person ought to use may be
calculated, knowing the distance of most distinct vision. The formula

/^i4 w

ser\-es for long-sighted persons, where /"being the ' number ' of the spectacles
which ought to be taken — that is, the number expressing the focal length
—p is the distance of distinct vision in ordinary cases (about 12 inches), and
d the distance of distinct vision for the person affected by long sight.

The above formula is obtained from the equation = - by substi-

p p' f
tuting d for p'. In this case the formula (6) of article 5 59 is used, and not
formula (5), because the image seen by spectacles being on the same side
of the object in reference to the lens, the sign^' ought to be the opposite
of that of p, as in the case of virtual images from the paragraph already
cited.

604 On Light. [630-

For short-sighted persons, / is calculated by the formula - - , = -
(559), which refers to concave lenses, and which, replacing/' by d, gives

f'f', ■ ■ ■ ■ ■ <=>

To calculate, for instance, the number of a glass which a person ought
to use in whom the distance of distinct vision is 36, knowing that the dis-
tance of ordinary distinct vision is 12 inches ; making/ = 12 and ^^'=36 in

the above formula (i), we get /=^>^7^ = 18.

631. Diplopia. — Diplopia is an affection of the eye which causes objects
to be seen double ; that is, that two images a:re seen instead of one. Usually
the two images are almost entirely superposed, and one of them is much
more distinct than the other. Diplopia is usually due to a want of power in
one or more of the ocular muscles, but it may be due to the prismatic action
of badly centred spectacles. It may also affect a single eye. The latter
case is, doubtless, due to some defect of conformation in the crystalline iris
or other parts of the eye which produces a bifurcation of the luminous ray,
and thus two images are formed on the retina instead of one.

632. Achromatopsy. — Achfoinatopsy., or colour blijtdncss, is a curious
affection which renders us incapable of distinguishing colours, or at any
rate certain colours. Persons affected in this manner can distinguish the
outlines of bodies without difficulty, and they can also discriminate between
light and shade, but they are unable to distinguish all the different colours.

The commonest case is that of red-blindness ; Dalton had it in a pre-
eminent degree, and from the fact that he very carefully described it, the
disease has been sometimes called Daltonism. To a person so affected red
appears like black, and the brighter shades bluish-green ; bluish-green
and pink seem the same, or at all events only different in shade. Yellow
appears like green, but he distinguishes between them, for the yellow
appears brighter.

He who is blind for green, sees that colour as black, and its lighter
shades red. He only sees red and blue with their intermediate stages ;
yellow appears bright red ; white and pink are alike, the spectrum is only
red and blue ; in the green there is a grey band. Violet blindness is \'ery
infrequent and not well known ; it can be artificially produced by taking
santonine. Colour disease is often congenital. It is far more frequent
with males than with females.

Owing to the difference in really healthy individuals as regards their
perception of different shades of colour, the only certain means of discerning
any particular tint is to define its position by means of the nearest Fraun-
hofcr's line (574). Owing to the danger which may arise from the observa-
tion of coloured signals on railways and the like, numerous methods have
l:)een proposed for the qualitative and quantitative observation of the colour
sense.

The best test for ordinary use is to give the patient a standard skein of
wool of a particular tint, green, rose, or red, and to require him to match it,
with others which appear to him of the same tint, among a large bundle of

-633]

Oph thalviascopc

605

skeins of many colours. In order to detect simulation the experiment should
be repeated within a few weeks.

633. Ophthalmoscope. — This instrument, as its name indicates, is de-
signed for the examination of the eye, and was invented in 185 1 by Professor
Helmholtz. It consists :— r. Of a concave spherical reflector of glass or
metal, M (figs. 590, 591), in the middle of which is a small hole about a
sixth of an inch in diameter. The focal length of the reflector is from 8 to
10 inches. 2. Of a converging lens, 0, which is held in front of the eye of
the patient.

To make use of the ophthalmoscope, the patient is placed in a room, and

Fig. 596.

a lamp put beside him, E. The screen serves to shade the light from his
head, and keep it in darkness. The observer, A, holding in one hand the
reflector, employs it to concentrate the light of the lamp near the eye, B,
of the patient, and with his other hand holds the achromatic lens, <?, in front
of the eye. By this arrangement the back of the eye is lighted up, and its
structure can be clearly discerned.

Fig. 591 shows how the image of the back of the eye is produced, which
the observer. A, sees on looking through the hole in the reflector. Let nh

Fig. 591-

be the part of the retina on which the light is concentrated, pencils of rays
proceeding from ab would form an inverted and aerial image of ah at ab'.
These pencils, however, on leaving the eye, pass through the Jens ^, and
thus the image a"b" is in fact formed, inverted, but distinct, and in a position
fit for vision.

Modern ophthalmoscopes are now usually provided with either one or

6o6 On Light. [633-

more discs of metal carrying a complete series of convex and concave lenses,
or with a similar series of lenses forming a chain of discs fitted in the handle
and body of the instrument. These lenses are so arranged that the observer
by rotating a small wheel can bring a lens of any focal length he pleases
behind the aperture of the mirror. This mirror is usually of a much shorter
focal length than in the instrument previously described, and is tilted at an
angle so that its plane is not parallel to the lenses behind the mirrors. By
this means, the ophthalmoscope can be held almost touching the patient's
eye, while the light can still be reflected into the patient's eye from the
mirror. In this form of ophthalmoscope the lens o is dispensed with, and by
placing behind the mirrors the lens which corrects the sum (or difference)
of the refractive errors of the patient's and the observer's eye, the observer's
eye is rendered emmetropic for the pencils of light which reach it. In this case
the rays of light from the lamp are reflected from the mirrors directly on the
back of the patient's eye, and proceeding from ab., are converted by the lens
placed behind the mirrors in such a manner that they form a distinct image
on the retina of the observer's eye. In the latter case the image is erect and
enlarged about fourteen times, while in the former indirect method the image
is inverted and enlarged only about four or five times. By a simple contrivance
in the form of a swivel carrying the two kinds of mirrors, either can be at
once rotated in front of the aperture, and thus the same instrument can be
employed for both methods of examination. The direct method just
described affords a ready means of estimating the refraction of the patient's
eye, or, in other words, of ascertaining at once the focal length of the lens
necessary to enable the patient to see distant objects. To find this, all that
is necessary is that the observer should previously ascertain the exact
number of diopters necessary to correct his eye for distant vision, and to
accustom himself to relax his accommodation to the full when using the
instrument. On the patient's part this relaxation occurs insensibly. The
eye of both persons being adjusted for distant objects, the observer now
looks through the aperture of the mirror, holding the instrument as close to
the patient's eye as possible. Should both eyes be emmetropic (normal),
the rays of light which are practically parallel would be focussed on the
retinae of both the eyes, and no correcting lens would be needed. Should
the observer's eye be at fault, the lens which wull correct it for parallel rays
will enable him to see the details of the patient's retina. Should both eyes
want correcting, then the number of diopters which are found necessary to
add to or subtract from the number which correct the observer's eye will
indicate the error in the patient's eye. By thus correcting for the vessels in
the retina which run in every direction, both the ;ixis and the amount of
astigmatism present may be readily ascertained.

-635j Phosphorescence. 607

CHAPTER VII.

SOURCES OF LIGHT. PHOSPHORESCENCE.

634. Various sources of llgrht. — The various sources of light are the
sun, the stars, heat, chemical combination, phosphorescence, electricity, and
meteoric phenomena. The last two sources will be treated under the articles
Electricity and Meteorology.

The origin of the light emitted by the sun and by the stars is unknown ; the
sun is the chief source ; its temperature is estimated at hundreds of thousands
of degrees. The ignited envelope by which the sun is surrounded is gaseous,
because the light of the sun, like that emitted from all gaseous bodies, gives
no trace of polarisation in the polarising telescope, chap. viii.

Terrestrial bodies become sources of heat when they are raised to a
sufficiently high temperature ; according to Draper all bodies begin to glow
with a red heat at 525° ; the light is brighter as the temperature is higher,
and at 1,170° it is a white heat.

The luminous effects witnessed in many chemical combinations are due
to the high temperatures produced. Ordinar)' luminous flames are nothing
more than gases containing solids heated to incandescence.

635. Pbosphorescence. — Certain bodies have the property of becoming
luminous in the dark without any considerable rise of temperature. This
phenomenon, which is well seen in phosphorus, is for this reason known as
phosphorescence. Here it is undoubtedly due to a slow oxidation, for it
ceases in spaces where no oxygen is present. Phosphorus is also exhibited
under certain conditions by decaying animal and vegetable matter. This is
also due to slow oxidation.

Phosphorescence is observed in living animals, of which the best known
case is that of the glowworm ; here it is very intense, and the brightness
seems to depend on the will. Its light consists of a continuous spectrum
from C to near b., and is particularly rich in blue and green rays. In tropical
climates the sea is often covered with a bright phosphorescent light due to
myriads of small luminous infusoria {iioctiliica milians).

Phosphorescence by rise of temperature. This is best seen in certain
species of diamonds, and particularly in chlorophafte, a variety of fluorspar,
which, when heated to 300° or 400°, suddenly becomes luminous, emitting a
greenish-blue light which lasts for several days.

Hagenbach examined the spectrum of phosphorescent fluorspar, and
found that it consisted of only nine bands : four blue, two green, two yellow,
and one orange. As the relative intensities of these bands are continually
changing, it is easy to understand the difl'ercnt colours presented by diftercnt
specimens of this mineral.

6o8 On Light. [635-

Phosphoresccnce by ineclianical effects^ such as friction, percussion, cleavage,
&c. ; for example, when two crystals of quartz are rubbed against each other
in darkness, when a lump of sugar is broken, or when a plate of mica is
cleft. To this category belong also the disengagement of light when
arsenious acid crystallises.

Phosphorescence by electricity, like that which results from the friction of
mercury against the glass in a barometric tube.

636. Phosphorescence by insolation. — A large number of substances,
after having been exposed to the direct action of sunlight, or even of the
diffused light of the atmosphere, emit in darkness a phosphorescence the
colour and intensity of which depend on the nature and physical condition
of these substances.

This was first observed in 1604 in Bolognese phosphorus (sulphide of
barium), but it also exists in a great number of substances. The sulphides
of calcium and strontium are those which present it in the highest degree.
They must be prepared in the dry way and at high temperatures. \\'hen
well prepared, after being exposed to the light, they are luminous for several
hours in darkness. But as this phosphorescence takes place in a vacuum as
well as in a gaseous medium, it cannot be attributed to a chemical action, but
rather to a temporary modification which the body undergoes from the action
of light. A phosphorescent sulphide of calcium is prepared for industrial
purposes, and is known as Balmain's luminous paint.

After the substances above named, the best phosphorescents are the
following, in the order in which they are placed : a large number of diamonds
(especially yellow ones), and most specimens of fluorspar ; then arragonite,
calcareous concretions, chalk, apatite, heavy spar, dried nitrate of calcium,
and dried chloride of calcium, cyanide of calcium, a large number of stron-
tium or barium compounds, magnesium and its carbonate, &c. Besides
these a large number of organic substances also become phosphorescent by
insolation ; for instance, dry paper, silk, cane-sugar, milk-sugar, amber, the
teeth, &c.

The different spectral rays are not ecjually well fitted to render substances
phosphorescent. The maximum effect takes place in the violet rays, or
even a little beyond ; while the light emitted by phosphorescent bodies
generally corresponds to rays of a smaller refrangibility, that is, of greater
wave-length, than those of the light received by them and giving rise to the
action.

The tint which phosphorescent bodies assume is very variable, and even
in the same body it changes with the manner in which it is prepared. In
strontium compounds green and blue tints predominate; and orange, yellow,
and green tints in the sulphides of barium.

The duration of phosphorescence varies also in different bodies. In the
sulphides of calcium and strontium, phosphorescence lasts as long as thirty
hours ; with other substances it does not exceed a few seconds, or even a
fraction of a second.

The colour emitted by an artificial phosphorescent alters with the tem-
perature during insolation. Thus with sulphide of strontium the light is dark
violet at -20° C, Ijright blue at +40°, bluish-green at 70°, greenish-j^ellow
at 100°, and reddish-yellow of feeble luminosity at .200° C.

-636]

Pliosplioroscopc.

Gog

When a phosphorescent body has been heated the Hght emitted is
brighter, but the greater the emission of Hght the shorter is the duration of
the phosphorescence. Heat, therefore, produces a more rapid irradiation
of the hght.

PhospJioroscope. In experimenting with bodies whose phosphorescence
lasts a few minutes or even a few seconds, it is simply necessary to expose
them to solar or diffused light for a short time, and then place them in dark-
ness : their luminosity is very apparent, especially if care has been taken to

close the eyes previously for a few moments. But in the case of bodies whose
phosphorescence lasts only a very short time, this method is inadequate.
Becquerel invented an ingenious apparatus, the phosphoroscope, by which
bodies can be viewed immediately after being exposed to light : the interval
which separates the insolation and observation can be made as small as
possible, and measured with great precision.

This apparatus consists of a closed cylindrical box, AB (fig. 592), of
blackened metal ; on the ends are two apertures opposite each other which
have the form of a circular sector. One only of these, (?, is seen in the

R R

6io On Light. [636-

figure. The box is fixed, but it is traversed in the centre by a movable axis,
to which are fixed two circular screens, MM and PP, of blackened metal
(fig. 593). Each of these screens is perforated by four apertures of the
same shape as those in the box ; but while the latter correspond to each
other, the apertures of the screens alternate, so that the open parts of the
one correspond to the closed parts of the other. The two screens, as
already mentioned, are placed in the box, and fixed to the axis, which by
means of a train of wheels, worked by a handle, can be made to turn with
any velocity.

In order to investigate the phosphorescence of any body by means of
this instrument, the body is placed on a stirrup interposed between the two
rotating screens. The light cannot pass at the same time through the
opposite apertures of the sides A and B, because one of the closed parts of
the screen MM, or of the screen PP, is always between them. So that when
a body, a, is illuminated by light from the other side of the apparatus, it
could not be seen by an observer looking at the aperture, o^ for then it would
be masked by the screen PP. Accordingly, when an observer saw the body
(?, it would not be illuminated, as the light would be intercepted by the closed
parts of a screen MM. The body a would alternately appear and disappear;
it would disappear during the time of its being illuminated, and appear when
it was no longer so. The time which elapses between the appearance and
disappearance depends on the velocity of rotation of the screens. Suppose,
for instance, that they made 150 turns in a second ; as one revolution of the
screens is effected in -^ of a second, there would be four appearances and
four disappearances during that time. Hence the length of time elapsing
between the time of illumination and of observation would be i of j',„ of a
second or o-ooo8 of a second.

Observations with the phosphoroscope are made in a dark chamber, the
observer being on that side on which is the wheelwork. A ray of solar or
electric light is allowed to fall upon the substance <?, and, the screens being
made to rotate more or less rapidly, the body a appears luminous by trans-
parence in a continuous manner, when the interval between insolation and
observation is less than the duration of the phosphorescence of the body.
By experiments of this kind, Becquerel has found that substances which
usually are not phosphorescent become so in the phosphoroscope ; such, for
instance, is Iceland spar. Uranium compounds present the most brilliant
appearance in this apparatus ; they emit a very bright luminosity when the
observer can see them 0-03 or 0-04 of a second after insolation. But a large
number of bodies produce no effect in the phosphoroscope ; for instance,
(juartz, sulphur, phosphorus, metals, and licjuids.

-637J 6ii

CHAPTER VIII.

DOUBLE REFRACTION. INTERFERENCE. POLARISATION.

637. Tbe undulatory tbeory of lig:ht. — It has been already stated (499)
that the phenomenon of Hght is ascribed to undulations propagated through
an exceedingly rare medium called the luminiferous ether, which is supposed
to per\-ade all space, and to exist between the molecules of the ordinary
forms of matter. In short, it is held that light is due to the undulations of
the ether, just as sound is due to undulations propagated through the air.
In the latter case the undulations cause the drum of the ear to vibrate and
produce the sensation of sound. In the former case, the undulations cause
points of the retina to vibrate and produce the sensation of light. The two
cases differ in this, that in the case of sound there is independent evidence
of the existence and vibration of the medium (air) which propagates the
undulation ; whereas in the case of light the existence of the medium and
its vibrations is assumed, because that supposition connects and explains in
the most complete manner a long series of very various phenomena. There
is, however, no independent evidence of the existence of the luminiferous
ether.

The analogy between the phenomena of sound and light is very close ;
thus, the intensity of a sound is greater as the amplitude of the vibration of
each particle of the air is greater, and the intensity of light is greater as the
amplitude of the vibration of each particle of the ether is greater. Again, a
sound is more acute as the length of each undulation producing the sound is
less, or, what comes to the same thing, according as the number of vibrations
per second is greater. In like manner, the colour of light is different ac-
cording to the length of the undulation producing the light : a red light is
due to a comparatively long undulation, and corresponds to a deep sound,
while a violet light is due to a short undulation, and corresponds to an acute
sound.

Although the length of the undulation cannot be observed directly, yet
it can be inferred from certain phenomena with great exactness. The
following table gives the lengths, in inches and millimetres, of the undulations
corresponding to the light at the principal dark lines of the spectrum : —

Length of Length of

Undul.-ition Undulation-

Dark line in inches in millimetres

B . 0-0000271 00006874

C 00000258 0-0006562

D, 0-0000232 0-0005897

E 0-0000207 0-0005271

F 0000019 1 0-0004S62

G . . . . . . . 0-0000169 0-0004311

H, . . . . . . . 0-0000159 0-0003969

6i2 On Light. [637-

It will be remarked that the limits are very narrow within which the
lengths of the undulations of the ether must be comprised, if they are to
be capable of producing the sensation of light. In this respect light is in
marked contrast to sound. For the limits are very wide within which the
lenLjths of the undulations of the air may be comprised when they produce
the sensation of sound (244).

The undulatory theory readily explains the colours of different bodies.
According to that theory, certain bodies have the property of exciting undula-
tions of different lengths, and thus producing light of given colours. White
light or daylight results from the coexistence of undulations of all possible
lengths.

The colour of a body is due to the power it has of extinguishing certain
vibrations, and of reflecting others ; and the body appears of the colour pro-
duced by the coexistence of the reflected vibrations. A body appears white
when it reflects all different vibrations in the proportion in which they are
present in the spectrum ; it appears black when it reflects light in such
small quantities as not to affect the eye. A red body is one which has the
property of reflecting in predominant strength those vibrations which pro-
duce the sensation of red. This is seen in the fact that, when a piece of red
paper is held against the daylight, and the reflected light is caught on a
white wall, this also appears red. A piece of red paper in the red part of
the spectrum appears of a brighter red, and a piece of blue paper held in
the blue part appears a brighter blue ; while a red paper placed in the
violet or lolue part appears almost black. In the last case the red paper
can only reflect red rays, while it extinguishes the blue rays, and as the blue
of the spectrum is almost free from red, so little is reflected that the paper
appears black.

The undulatory theory likewise explains the colours of transparent bodies.
Thus, a vibrating motion on reaching a body sets it in vibration. So also the
vibrations of the luminiferous ether are communicated to the ether in a body,
and, setting it in motion, produce light of different colours. When this motion
is transmitted through any body, it is said to be transparent or translucent,
according to the different degrees of strength with which this transmission is
effected. In the opposite case it is said to be opaque.

When light falls upon a transparent body, the body appears colourless if
all the vibrations are transmitted in the proportion in which they exist in the
spectrum. Hut if some of the vibrations are checked or extinguished, the
emergent light will be of the colour produced by the coexistence of the un-
checked vibrations. Thus, when a piece of blue glass is held before the eye,
the vibrations producing red and yellow are extinguished, and the colour is
due to. the emergent vibrations which produce blue light.

The undulatory theory also accounts for the reflection and refraction of
light, as well as oilier phenomena which arc yet to be described. The ex-
planation of the refraction of light is of so much importance that we shall
devote to it the following article.

638. Physical explanation of single relVactlon. — The cxjilanation of
this phenomenon by means of the undulatory theory of light presupposes
that of the mode of propagation of a plane wave. Now, if a disturbance
originated at any /fvV// of the ether, it would be propagated as a spherical

-639]

Double Refraction.

613

wave in all directions round that point with a uniform velocity. If, instead
of a single point, we consider the front of a plane wave, it is evident that
disturbances originate simultaneously at all points of the front, and that
spherical waves proceed from each point with the same uniform velocity.
Consequently, all these spheres will at any subsequent instant be touched by
a plane parallel to the original plane. The disturbances propagated from
the points in the first position of the wave will mutually destroy each other,
except in the tangent plane ; consequently the wave advances as a plane
wave, its successive positions being the successive positions of the tangent
plane. If the wave moves in any medium with a velocity ?/, it will describe
a space vt in a time /, in a direction at right angles to the wave-front.

In any given moment let tun (fig. 594) be the position of the wave-front of
a ray of light, which, moving through any medium, meets the plane surface
AB of any denser refract-

ing medium. In the same
moment in which the
wa\e-front reaches «, in
becomes the centre of a
spherical wave system
which moves in the second
medium ; and, as the elas-
ticity of the second me-
dium is different from
that of the first, the velo-
city of propagation of the
wave in the two media will be dififerent.
71 to K, the corresponding wave startin

Fig- 594-

While the plane wave moves from
from 1)1 reaches the surface of a
sphere the radius of which is less than «K, if the second medium is denser
than the first. The incident wave in like manner reaches in' and ;/ simul-
taneously, and while n' moves to K, m' moves to o', the surface of a sphere
the radius of which, m'o\ is to mo as «'K is to «K. All the elementary
waves proceeding from points intermediate to n and K which arise from
the same incident wave, touch one and the same plane Y.0'0, and the
refracted ray proceeds in the new medium perpendicular to this tangent
plane.

Now ;;K and nio are proportional to the velocities of light in the two
media respectively : let ;«K be taken as unit of length, then
7zK = sin «;//K and mo = sin niKo.

Now fn?iK is the angle of incidence of the ray, and mKo is the angle of
refraction, and nK and mo are proportional to the velocities of light in the
two media respectively ; hence we see that these velocities are to each
other in the same ratio as the sines of the angles of incidence and refraction ;
a conclusion which agrees with the results of direct observation (506), and
forms a beautiful confirmation of the truth of the undulatory theory.

DOUBLE REFRACTION.

6j9. Double refraction. — It has been already stated (536) that a large
number of crystals possess the property of double refraction, in virtue of

6i4 On Light.

which a single incident ray in passing through any one of them is divided
into two, or undergoes bifurcation^ whence it follows that, when an object
is seen through one of these crystals, it appears double. The fact of the
existence of double refraction in Iceland spar was first stated by Bartholin
in 1669, but the law of double refraction was first enunciated exactly by
Huyghens, in his treatise on light, written in 1678 and published in 1690.

Crystals which possess this peculiarity are said to be double-refracting.
It is found to a greater or less extent in all crystals which do not belong to
the cubical system. Bodies which crystallise in this system, and those
which, like glass, are destitute of crystallisation, have no double refraction.
The property can, however, be imparted to them when they are unequally
compressed, or when they are cooled quickly after having been heated, in
which state glass is said to be ujumnea/ed. Of all substances, that which
possesses it most remarkably is Iceland spar or crystallised carbonate of
calcium. In many substances, the power of double refraction can hardly
be proved to exist directly by the bifurcation of an incident ray ; but its
existence is shown indirectly by their being able to depolarise light (665).

Fresnel explained double refraction by assuming that the ether in double-
refracting bodies is not equally elastic in all directions ; from which it
follows that the vibrations, in certain directions at right angles to each
other, are transmitted with unequal velocities ; these directions being depen-
dent on the constitution of the crystal. This hypothesis is confirmed by
the property which glass acquires of becoming double-refracting by being
unannealed and by pressure.

640. Vniaxial crystals. — In all double-refracting crystals there is one
direction, and in some a second direction, possessing^ the following property : —
When a point is looked at through the crystal in this particular direction, it
does not appear double. The lines fixing these directions are called optic
axes ; and sometimes, though not very properly, axes of double refraction.
A crystal is called u?iiaxial when it has otie optic axis ; that is to say, when
there is one direction within the crystal along
which a ray of light can proceed without
bifurcation. When a crystal has two such
axes, it is called a biaxial crystal.

The uniaxial crystals most frequently
used in optical instruments are Iceland spar,
cjuartz, and tourmaline. Iceland spar crystal-
lises in rhombohedra, whose faces form with
each other angles of 105° 5' or 74° 55'. It
has eiglit solid angles (see fig. 595). Of these, two, situated at the extremi-
ties of one of the diagonals, are severally contained by three obtuse angles.
A line drawn within one of these two angles in such a manner as to be
equally inclined to the three edges containing the angle is called the axis of
the crystal. If all the edges of the crystal were equal, the axis of the crystal
would coincide with the diagonal, ab.

Brewster showed that in all uniaxial crystals the optic axis coincides with
the axis of crystallisation.

The principal plane with reference to a point of any face of a crystal,
whether natural or artificial, is a plane drawn througli that point at right

-642] Laws of Double Refraction in a Uniaxial Crystal. 615

angles to the face and parallel to the optic axis. If in fig. 595 we suppose
the edges of the rhombohedron to be equal, the diagonal plane abed contains
the optic axis {ab), and is at right angles to the faces aedf ^\\A chbg; conse-
quently it is parallel to the principal plane at any point of either of those
two faces. For this reason abed is often called the principal plane with
I'espect to those faces.

641. Ordinary and extraordinary ray. — Of the two rays into which
an incident ray is divided on entering a uniaxial crystal one is called the
ordinary and the other the extraordinary ray. The ordinal y ray follows
the laws of single refraction ; that is, with respect to that ray the sine of the
angle of incidence bears a constant ratio to the sine of the angle of refraction,
and the plane of incidence coincides with the plane of refraction. Except
in particular positions, the extraordinary ray follows neither of these laws.
The images corresponding to the ordinary and extraordinary rays are called
the ordinary and extraordinary images respectively.

If a transparent specimen of Iceland spar be placed over a dot of ink,
on a sheet of white paper, two images will be seen. One of them, the
ordinary image, will seem slightly nearer to the eye than the other, the extra-
ordinary image. Suppose the spectator to view the dot in a direction at
right angles to the paper, then, if the crystal, with the face still on the paper,
be turned round, the ordinary image will continue fixed, and the extraordinary
image will describe a circle round it, the line joining them being always in
the direction of the shorter diagonal of the face of the crystal, supposing its
edges to be of equal length. In this case it is found that the angle between
the ordinary and extraordinary ray is 6° 12'.

642. The laMTS of double refraction in a uniaxial crystal. — These
phenomena are found to obey the following laws : —

i. Whatever be the plane of incidence, the ordinary ray always obeys
the two general laws of single refraction (537). The refractive index for the
ordinary ray is called the ordinary refractive index.

ii. In every section perpendicular to the optic axis the extraordinary ray .
also follows the laws of single refraction. Consequently, in this plane, the
extraordinary ray has a constant refractive index, which is called the ordinary
refractive index.

iii. In every principal section the e.xtraordinary ray follows the second
law only of single refraction ; that is, the planes of incidence and refraction
coincide, but the ratio of the sines of the angles of incidence and refraction
is not constant.

iv. The velocities of light along the rays are unequal. It can be shown
that the difference between the squares of the reciprocals of the velocities
along the ordinary and extraordinary rays is proportional to the square of the
sine of the angle between the latter ray and the axis of the crystal.

There is an important difference between the velocity of the ray and the
velocity of the corresponding plane wave. If the velocities of the plane
waves corresponding to the ordinary and extraordinary rays are considered,
the difference between the squares of these velocities is proportional to the
square of the sine of the angle between the axis of the crystal, and the normal
to that plane wave which corresponds to the extraordinary ray. The normal
and the ray do not generally coincide.

6i6 On Light. [642-

Huyghens gave a very simple geometrical construction, by means of
which the directions of the refracted rays can be determined when the direc-
tions of the incident ray and of the axis are known relatively to the face of
the crystal. This construction was not generally accepted by physicists
until Wollaston, and subsequently Malus, showed its truth by numerous exact
measurements.

643. Positive and neg'ative uniaxial crystal. — The term extraordinary
refractive index has been defined in the last article. Yox the same crystal
its magnitude always differs from that of the ot'dinary refractive index ; for
example, in Iceland spar the ordinary refractive index is 1-654, while the
extraordinary refractive index is r483. In this case the ordinary' index
exceeds the extraordinary index. When this is the case the crystal is said to
be negative. On the other hand, when the e.xtraordinary index exceeds the
ordinary index, the crystal is said to be positive. The following list gives the
names of some of the principal uniaxial crystals : —

Negative Uniaxial Crystals.
Iceland spar Ruby Pyromorphite

Tourmaline Emerald Ferrocyanide of potassium

Sapphire Apatite Nitrate of sodium

Positive Uniaxial Crystals.
Zircon Apophyllite Titanite

Quartz Ice Boracite

644. Double refVactlon In biaxial crystals. — A large number of crystals,
including all those belonging to the tri/netric, the monoclinic, and the triclinic
systems, possess two optic axes ; in other words, in each of these crystals
there are two directions along which a ray of light passes without bifurcation.
A line bisecting the acute angle between the optic axes is called the medial
line ; one that bisects the obtuse angle is called the supplementary line.
It has been found that the medial and supplementary lines and a third line
at right angles to both are closely related to the fundamental form of the
crystal to which the optic axes belong. The acute angle between the optic
axes is different in different crystals. The following table gives the magnitude
of this angle in the case of certain crystals : —

Xitre .

. 5° 20'

Mica .

• 45°

.Strontianite

. 6 56

.Sugar .

• 50

•A.rragonite .

. 18 iS

Selenite

. 60

Anhydrite .

. 28 7

Epidote

• «4

Heavy spar

■ 7>1 42

Sul])hate

of iron .

. 90

When a ray of light enters a biaxial crystal, and passes in any direction
not coinciding with an optic axis, it bifurcates ; in this case, however,
neither ray conforms to the laws of single refraction, but both are extra-
ordinary rays. To this general statement the following exception must be
made : — In a section of a crystal at right angles to the medial line one ray
follows the laws of ordinary refraction, and in a section at right angles to
the supplementary line the other ray follows the laws of ordinary refraction.

-645]

Intcrfcroicc of Light.

617

INTERFERKNCK AMI DIFKRACTIOX.

645. Interference of ligrbt. — The name ////tvymv/t^^ is given to the re-
ciprocal action which two rays of light exert upon each other when they are
emitted from two neighbouring sources, and meet each other under a very
small angle. This action may be observed by means of the following ex-
periment : — In the shutter of a dark room two very small apertures of the
same diameter are made close to each other. The apertures are closed
by pieces of coloured glass— red, for example — by which two pencils of
homogeneous light are mtroduced. These two pencils form two divergent
luminous cones, which meet at a certain distance ; they are received on a
white screen a little beyond the place at which they meet, and in the segment
common to the two discs which form upon this screen some very well-defined
alternations of red and black bands are seen. If one of the two apertures
be closed, the fringes disappear, and are replaced by an almost uniform red
tint. From the fact that the dark fringes disappear when one of the beams
is intercepted, it is concluded that they arise from the interference of the two
pencils which cross obliquely.

This experiment was first made by Cirimaldi, but was modified by
Young. Grimaldi had drawn from it the conclusion that light added to light

Fig. 596.

produced darkness. The full importance of this principle remained for
a long time unrecognised, until these inquiries were resumed by Young
and Fresnel, of whom the latter, by a modification of Grimaldi's experi-
ment, rendered it an experitneniuvi crucis of the truth of the undulator\-
hypothesis.

In Grimaldi's experiment diffraction (646) takes place, for the luminous
rays pass by the edge of the aperture. In the following experiment, which
is due to Fresnel, the two pencils interfere without the possibility of diffrac-
tion.

Two plane mirrors, AB and BC (fig. 596), of metal, are arranged close to
each other, so as to form a very obtuse angle, ABC, which must be very little

6i8 On Light. [645-

less than i8o°. A pencil of monochromatic light — red, for instance — which
passes into the dark chamber, is brought to a focus, F, by means of a lens,
L. On diverging from F the rays fall partly on AB, and partly on BC. If
BA is produced to P and FPFj is drawn at right angles to AP, and if PFj is
made equal to PF, then the rays which fall on AB will, after reflection, pro-
ceed as if they diverged from Fj. If a similar construction is made for the
rays falling on BC, they will proceed after reflection as if they diverged from
F... A little consideration will show that Fj and Fo are very near each other.
Suppose the reflected rays to fall on a screen SSj placed nearly at right
angles to their directions. Every point of the screen which receives light
from both pencils is illuminated by both rays, viz., one from F,, the other

from F„ : thus the
jjoint H is illuminated
iDy two rays, as also
are K and I. Now
the combined action
of these two pencils is
to form a series of
parallel bands alter-
nately light and dark
on the screen at right
angles to the plane of
the paper (fig. 597).
They are distributed

Fig 597.

symmetrically in reference to one of them cc, which is more brilliant than
the others, and which is called the central fringe. This is the fundamental
phenomenon of interference ; and that it results from \\\^ joint action of the
two pencils is plain, for if the light which falls upon either of the mirrors is
cut off, the dark bands altogether disappear.

The experiment may also be made by means of Ohm's prism, which is a
prism in which the refracting angle is very nearly 180°.

This remarkable experiment is explained in the most satisfactoiy manner
by the undulatory theory of light. The explanation exactly resembles that
already given of the formation of nodes and loops by the combined action of
two aerial waves (262) ; the only difference being that in that case the vibrat-
ing particles were supposed to be particles of air, whereas, in the present
case, the vibrating particles are supposed to be those of the luminiferous
ether. Consider any point K on the screen, and first let us suppose the dis-
tance of K from F, and F.^ to be equal. Then the undulations which reach
K will always be in the same phase, and the particle of ether at K will vibrate
as if the light came from one source : the amplitude of the vibration, how-
ever, will be increased in exactly the same manner as happens at a loop or
ventral point ; c()nset|uently, at K the intensity of the light will be increased.
And the same will Ije true for all parts on the screen, such that the difference
between their distances from the two images equals the length of one, two
three, &c., undulations. If, on the other hand, the distances of K from F,
and v., differ by tlie length of half an undulation, then the two waves would
reach K in exactly opposite phases. Consequently, whatever velocity would
be communicated at any instant to a particle of ether by tlic one findulation,

-646]

Diffraction and Fringes.

619

an exactly equal and opposite velocity would be communicated by the other
undulation, and the particle would he pcnna/ioi/ly at rest, or there would be
darkness at that point ; this result being produced in a manner precisely re-
sembling the formation of a ?iodal point already explained. The same will
be true for all positions of K, such that the difference between its distances
from Fj and F,_, is equal to three halves, or five halves, or seven halves, &:c.,
of an undulation. Accordingly, there will be on the screen a succession of
alternations of light and dark points, or rather lines— for what is true of points
in the plane of the paper (fig. 597) will be equally true of other points on the
screen, which is supposed to be at right angles to the plane of the paper.
Between the light and dark lines the intensity of the hght will vary, increas-
ing gradually from darkness to its greatest intensity, and then decreasing
to the second dark line, and so on.

If instead of red light any other coloured light were used — for example,
violet light— an exactly similar phenomenon would be produced, but the dis-
tance from one dark line to another would be different. If white light were
used, each separate colour tends to produce a different set of dark lines.
Now these sets being superimposed on each other, and not coinciding, the
dark lines due to one colour are illuminated by other colours, and instead of
dark lines a succession of coloured bands is produced. The number ot
coloured bands produced by white light is much smaller than the number of
dark lines produced by a homogeneous light ; since at a small distance from
the middle band the various colours are completely blended, and a uniform
white light produced.

646. Diffraction and frlngres. — Diffraction is a modification which light
undergoes when it passes the edge of a body, or when it traverses a small
aperture — a modification in virtue of which the luminous rays appear to
become bent, and to penetrate into the shadow.

This phenomenon may be observed in the following manner : — A beam of
sunlight is allowed to pass through a very small aperture in the shutter of

Fig. 59S.

a dark room, where it is received on a condensing lens, L (fig. 59S), with a
short focal length. A red glass is placed in the aperture so as to allow only
red light to pass. An opaque screen, e, with a sharp edge a — a razor, for
instance — is placed behind the lens beyond its focus, and intercepts one por-
tion of the luminous cone, while the other is projected on the screen b, of
which B represents a front view. The following phenomena are now seen : —
Within the geometrical shadow, the limit of which is represented by the line
ab, a faint light is seen, which gradually fades in proportion as it is farther
from the limits of the shadow. In this part of the screen — which, being above
the line ab, might be expected to be uniformly illuminated— a series of
alternate dark and light bands or fringes is seen parallel to the line of shadow,
which gradually become more indistinct and ultimately disappear. The limits

620 On Light. [646-

between the light and dark fringes are not quite sharp lines : there are parts
of maximum and minimum intensity which gradually fade off into each other.
All the colours of the spectrum give rise to the same phenomenon, but
the fringes are broader in proportion as the light is less refrangible. Thus
with red light they are broader than with green, and with green than with
violet. Hence, with white light, which is composed of different colours, the
dark spaces of one tint overlap the light spaces of another, and thus a series
of prismatic colours will be produced.

If, instead of placing the edge of an opaque body between the light and
the screen, a very narrow body be interposed, such as a hair or a fine metallic
wire, the phenomena will be different. Outside the space corresponding to
the geometrical shadow, there is a series of fringes, as in the former case.
Hut within the shadow also there is a series of alternate light and dark bands.
They are called interior fringes, and are much narrower and more numerous
than the external fringes.

When a small opaque circular disc is interposed, white light being used,
its shadow on the screen shows in the middle a bright spot surrounded by a
series of coloured concentric rings ; the bright spot is of various colours
according to the relative positions of the disc and screen. The haloes some-
times seen round the sun and moon belong to this class of phenomena. They
are due, as Fraunhofer showed, to the diffraction of light by small globules
of fogr in the atmosphere. Fraunhofer even gave a method of estimating
the mean diameter of these globules from the dimensions of the haloes.

647. Gratlng^s. — Phenomena of diffraction of another class are produced
by allowing the pencil of light from the luminous point to traverse an aper-
ture in the form of a narrow slit in an opaque screen. The diffracted light

may be received on a sheet

TirWninnriiBM ofwhite paper, but the images

are much better seen through
a small telescope placed be-
hind the aperture. If the
aperture is very small, the
telescope may be dispensed
with, and the figure may be
viewed by placing the aper-
ture before the eye. If now
be allowed to fall through such

iistance(572)-
rcd light is seen, and right and left of it a
y diminishing in brightness and separated by

monociiromatic light — red, for
a narrow slit, a bright band (
series of similar bands gradiui
dark bands.

The brcatltii of these bands tliffcrs wilii liu- nature of the light, being
narrower and nearer together in violet than in green, and these again nar-
rower and nearer than in red, as shown in fig. 599. If ordinary white light
i)e used, then the i olours are not exactly superposed, but a series of equi-
distant spectra is fonned on each side of tiie bri-hl line, with their violet
side turned inwards.

In order to explain this, let us refer to li;^. 600, which represents the
formation of the first daik band. When light is incident on the slit, AB, the
particles of ether there, which we will rejjresent Ijy the dotted lines, will be

-647]

Gnitiiios.

621

set in vil)iation, and each point w ill become the centre of a new series of
oscillations. Consider now the undulations which constitute a ray proceed-
ing at riijht angles to the plane of the slit : all such undulations will form a
band of light on the screen MN. Those which are not parallel but proceed
at equal inclinations, and meet at the point r, will be in the same phase and
will reinforce each other, and the line of maximum brightness will be at r.
Consider, however, a pencil of rays which proceeds from the slit in an
oblique direction and which meets the screen, or the retina, in the point s,
and let us suppose that the difference between the lengths of the paths of
the undulations proceeding from the edges b and a — that is, bs and as — is
equal to the length of an undulation. Make sc = sb and join be; then ac is
the length of the undulation.

Let us suppose that the whole set of undulations which proceeds from
the slit ab is divided at d into two equal groups of undulations. Then a
little consideration will show that at any part of the path there will be a dif-
ference of phase of half an undulation l^etween the ray from the margin a,
and that from the centre d ; and to each
of the undulations constituting the group
on the left there will be a corresponding one
among the groups on the right, which just
differs from it by half an undulation ; the
general effect will be that the group on
the left will be half an undulation behind
the group on the right, and both arriving
at the screen in opposite phases neutralise
each other and produce darkness.

When the difference between the paths
of the marginal undulations is equal to
half a wave-length, a partial destruction
of light takes place ; the luminous inten-
sity corresponding to this obliquity is a
little less than half that of the undiffracted
light. If the marginal distance is one
and a half undulations, we can, as before,
conceive the whole pencil divided into

three parts, of w-hich two will neutralise each other, and the third only will
be effective. There will be a luminous band, but one of less intensity. In
like manner where the marginal undulations differ by two whole wave-
lengths, they will again extinguish each other, and a dark band will be the
result. Thus there will be formed a series of alternate dark and bright
bands of rapidly diminishing intensity. In general, when the difference of
path of the rays proceeding from the margin of the slit amounts to n wave-
lengths, 71 being any whole number, we have a dark band, and when it
amounts io fi + ^ wave-lengths, a bright band.

The phenomena of diffraction produced when other than straight lines are
used are often of great beauty. They have been more particularly examined
by Schwerdt, and the whole of the phenomena are in exact accordance with
the undulatory theory, though the explanation is in many cases somewhat
intricate. The theory renders it possible to predict the appearance which

Fis. 600.

622 On Light. [647-

any particular aperture will produce, just as astronomy enables us to foretell
the motions of the heavenly bodies. Some of the simpler fonns — such as
straight lines, triangles, squares — may be cut out of tinfoil pasted on glass,
and apertures of any form may be produced with great accuracy by taking
on glass a collodion photograph of a sheet of paper on which the required
shapes are drawn in black.

Looking through any of these apertures at a luminous point, we see it sur-
rounded with coloured spectra of very various forms, and of great beauty.
The beautiful colours seen on looking through a bird's feather at a distant
source of light, and the colours of striated surfaces, such as mother-of-pearl,
are due to a similar cause. A beautiful phenomenon of the same kind is the
aureole observed on looking at a candle flame through lycopodium powder
strewn on glass. Two crossed gratings give a splendid picture, in which a
bright point is surrounded in all directions by spectra.

648. Diffraction spectra. — The most important of these figures are the
gratifigs proper., which may be produced by arranging a series of fine wires
parallel to each other, or by careful ruling on a piece of smoked glass, or by
photographic reduction. Nobert has made such gratings by ruling lines on
glass with a diamond, in which there are no less than 12,000 lines in an inch
in breadth. Dr. Stone has constructed such gratings for reflection, by ruling
lines on plates of nickel ; this metal has the advantage of hardness, non-
liability to tarnish, and great reflecting power.

If a grating be used instead of a single slit, as above described, the
phenomena are in general the same, though of greater brilliancy. With
homogeneous light and such a grating, there is seen, on each side of the
central bright line, a series of sharply defined narrow bands and lines of
light, gradually increasing in breadth and diminishing in intensity as their
distance from the central line increases. If white light be used the white
band is seen in the centre, and on each side of it a sharply defined isolated
spectrum with the violet edges inwards. Next to this, and separated by a
dark interval, is on each side a somewhat broader but similar spectrum,
and then follow others which become fainter and broader and overlap each
other. The brightness and sharpness of these spectra depend on the close-
ness of the lines, and on the opacity of the intemiediate space. In those
which are ruled by diamond on glass, the parts scratched represent the
opaque parts.

For objective representation the image of a slit in a dark shutter, through
which the sunlight enters, is focussed by means of a convex lens on a screen
at a distance, and then a grating is placed in the path of the rays.

The spectra produced by means of a grating are known as interference or
diffraction spectra. Very accurate gratings can now be easily and cheaply
prepared by means of photography, and their use for scientific purposes is
extending.

There are many points of difference between these spectra and those
produced by the prism, and for scientific work the former are preferable.

A diffraction spectrum is the purer the greater the number of lines in the
grating, provided they are equidistant. Tiie spectra arc, however, not more
than ,'„ as bright as prismatic spectra ; and, to olnain tlic maximum bright-

-649]

Determination of Wave-length.

623

ness, the opaque intervals should be as opaque and the transparent ones as
transparent as possible.

On the other hand, in diffraction spectra, the colours are uniformly dis-
tributed in their true order and extent according to the difference in their
wave-lengths, and according therefore to a property which is inherent in the
light itself ; while in prismatic spectra the red rays are concentrated, and
the violet ones dispersed. In diffraction spectra the centre is the brightest
part.

Fig. 601 represents a grating spectrum, together with an equally long
spectrum produced by a flint-glass prism ; the upper being that produced by
the grating. It will be seen that D in the one spectrum is in almost exactly
the same position as F in the other.

Diffraction spectra have, moreover, the advantage of giving a far larger
number of dark lines, and of giving them in their exact relative positions.
Thus, in a particular region in which Angstrom had mapped 118 lines,

Fig. 601.

Draper, by means of a diffraction spectrum, was able to photograph at least
293. Diffraction spectra also extend farther in the direction of the ultra-
violet, and give more dark lines in that region.

The most perfect gratings have quite recently been constructed by
Professor Rowland, of Baltimore, by means of a machine specially planned
and constructed for the purpose, and the chief feature in which is a practi-
cally perfect screw. Using this machine, he has been able to rule gratings
with as many as 43,000 lines to the inch, nor does this represent the limit of
the power of the machine. Gratings with 14,000 or 28,000 lines give, however,
the best definition. Another great improvement is to rule the gratings on
spherical instead of on flat surfaces ; in this way the spectrum can be formed
without a telescope, which is a matter of great importance, as telescopes
interfere with a great many experiments. The spectroscope is thus reduced
to its simplest form, so that an instrument of very high power may be con-
structed at a small cost.

By means of his gratings Professor Rowland has been able to resolve
lines in the spectrum which had never hitherto been separated.

It has been proposed to use the fine quartz threads prepared by Mr.
Boys (89) for making gratings.

649. Betermination of wave-lengrth. — The relative positions of these
bright and dark lines furnish a means of calculating the wave-length or

624 On U^ht. [649-

len"-th of undulation of any particular colour. We must first of all know the
distance rs of the first dark band from the bright one. The bands are not
uniform in brightness or darkness, but there is in each case a position of
maximum intensity, and it is from these that the distances are measured.
If the bands are viewed through a telescope, the angle is observed through
which the axis must be turned from the position in which the cross wire
coincides with the centre of the bright band to that in which it coincides
with the centre of the dark band. From this angle, which can be very ac-
curately measured, the distance is easily calculated. When the diffraction
bands are received on a screen, the distance may be directly measured, and
most accurately by taknig half the distance between the centres of the first
pair of dark bands.

We have thus the similar triangles abc, and rds, in which ac :bc = rs : rd
(fig. 600). Now be may be taken equal to ab^ the width of the slit, which can
be measured directly with great accuracy by means of a micrometric screw
(II), and rd is the distance of the screen. Hence

rs X ab
"'^--Vd-

Now rtf, the difference between as and sc^ is equal to the length of an undu-
lation of this particular colour. In one experiment with red light the width
of the slit ab was 0-015 in., the distance rs 0-15 in., and the distance of the

screenosin., which gave at- = —^''°°' ^ = 0-000024 in. as the wave-length

93
of red light. Using blue light the distance of r.y was found to be o-i, which
gives o-ooooi6.

Knowing the length of the undulations, we can easily calculate their

number in a second, «, from the formula 71 = -^(232), where v is the velocity

of light. Taking this at 186,000 miles, we get for the red corresponding to
the dark line B 434,420,000,000,000 as the number of oscillations in a second,
and for the H in the violet 758,840,000,000,000 undulations.

If, instead of a single slit, gratings be used, we have the possibility of
more accurate results, for the contrast is greater, and thus the distance is
more easily determined. The width of the slit is easily calculated by count-
ing the number of lines in a given s|)ace.

650. Colours of tliln plates. Newrton's ring's. — All transparent bodies,
solids, liquids, or gases, when in sufficiently fine laminit, appear coloured
with very bright tints, especially by reflection. Crystals which cleave easily,
and can be obtained m very thin plates, such as mica and selenite, show this
l)henomenon, which is also well seen in soap-bubbles and in the layers of air
in cracks in glass and in crystals. Steel becoming covered with a thin layer
of oxide exhibits the colour of thin plates, which change during heating as
the oxide changes its thickness. A drop of oil spread rapidly over a large-
sheet of water exhibits all the colours of the spectrum in a constant order.
A soap-bubble appears white at first, but, in proportion as it is blown out,
brilliant iridescent colours appear, especially at the top, where it is thinnest.
These colours arc arranged in horizontal zones around the summit, which

-651] Explanation of Neivton's Rings. 625

appears black when there is not thickness enough to reflect Hght, and the
bubble then suddenly bursts.

Newton, who first studied the phenomena of the coloured rings in soap-
bubbles, wishing to investigate the relation between the thickness of the
thin plate, the colour of
the rings, and their extent,
produced them by means
of a layer of air interposed
between two glasses, one
plane and the other con-

J . , , Fig. 602.

vex, and with a very long

focus (fig. 602). The two surfaces being cleaned and exposed to ordinary
light in front of a window, so as to reflect light, there is seen at the point of
contact a black spot surrounded by six or seven coloured rings, the tints of
which become gradually less strong. If the glasses are viewed by transmitted
light, the centre of the rings is white, and each of the colours is exactly com-
plementary of that of the rings by reflection. The lens and the glass plate
are usually arranged in a brass mount which by means of three screws allows
the pressure to be regulated.

With homogeneous light, red for example, the rings are successively
black and red ; the diameters of corresponding rings are less as the colour
is more refrangible, but with white light the rings are of the different colours
of the spectrum, which arises from the fact that, as the rings of the different
simple colours have different diameters, they are not exactly superposed, but
are more or less separated.

It is usual to speak of the successive rings as the first, second, third, &c.
By XhG. first ring is understood that of least diameter. Knowing the radius
of any particular ring, p, and the radius of curvature, R, of the lens, the thick-
ness, d^ of the corresponding layer of air is given approximately by the
formula

Newton found that the thicknesses corresponding to the successive dark

rings are proportional to the numbers o, 2, 4, 6 , while for the

(^;7]§/// rings the thicknesses were proportional to I, 3, 5 He found

that for the first bright ring the thickness was fyg^ojo ,, vc „

of an inch, when the light used was the brightest part \\

of the spectmm ; that is, the part on the confines of \\

the orange and yellow rays. U ,/

If the focal length of the lens is from three to four ^ -'' —

yards, the rings can be seen with the naked eye ; but 1
if the length is less, the rings must be viewed with a ts —
lens.

651. Explanation ot N'ewton's rings. — Newton's
rings, and all phenomena of thin plates, are simple ^•' y
cases of interference. ^'S- 603.

In fig. 603, let MNOP represent a thin plate of a transparent body, on
which a pencil of parallel rays of homogeneous light, ab, impinges ; this

626 On Light. [651-

will be partially reflected in the direction be, and partially refracted towards
d. But the refracted ray will undergo a second reflection at the surface, OP ;
the reflected ray will emerge at c in the same direction as the pencil of light
reflected at the first surface ; and consequently the two pencils be and ef
will destroy or augment each other's effect according as they are in the
same or different phases. We shall thus have an effect produced similar to
that of fringes (646).

POLARISATION OF LIGHT.

652. Polarisation by double refraction. — It has been already seen that
when a ray of light passes through a crystal of Iceland spar (641), it becomes
divided into two rays of equal intensity ; viz. the ordinary ray, and the ex-
traordinary ray. These rays are found to possess other peculiarities, which
are expressed by saying they are polarised; namely, the ordinary ray in a
principal plane, and the extraordinary ray in a plane at right angles to a
principal plane. The phenomena which are thus designated may be de-
scribed as follows : — Suppose a ray of light which has undergone ordinary
refraction in a crystal of Iceland spar, to be allowed to pass through a second
crystal, it will generally be divided into two rays ; namely, one ordinary, and
the other extraordinary, but of imeqiial intensities. If the second crystal
be turned round until the two principal planes coincide — that is, until the
crystals are in similar or in opposite positions— then the extraordinaiy ray
disappears, and the ordinary ray is at its greatest intensity ; if the second
crystal is turned farther round, the extraordinary ray reappears, and increases
in intensity as the angle increases, while the ordinary ray diminishes in in-
tensity until the principal planes are at right angles to each other, when the
extraorchnary ray is at its greatest intensity and the ordinary ray vanishes.
These are the phenomena produced when the ray which experienced ordi-
nary refraction in the first crystal passes through the second. If the ray
which has experienced extraordinary refraction in the first crystal is allowed
to pass through the second crystal, the phenomena are similar to those above
described ; but when the principal planes coincide, an extraordinary ray alone
emerges from the second crystal, and when the planes are at right angles, an
ordinary ray alone emerges.

These phenomena may also be thus described: — Let O and E denote
the ordinary and extraordinary rays produced by the first crj'stal. When
O enters the second crystal, it generally gives rise to two rays, an ordinary
(0(?), and an extraordinary {Oe), of unecjual intensities. When E enters the
second crystal, it likewise gives rise to two rays, viz. an ordinary (Ef) and
an extraordinary (E^), of unecjual intensities, the intensities varying with
the angle between the principal planes of the crystals. When the principal
planes coincide, only two rays, viz. Oo and Er, emerge from the second
crystal, and when the planes are at right angles, only two rays, viz. Oe and
E<9, enicrge from the second crystal. Since O gives rise to an ordinary ray
when the jjrincijjal planes are parallel, and E gives rise to an ordinary ray
when they are at right angles, it is manifest that O is related to the principal
plane in the same manner that E is related to a plane at right angles to a
|)rincipal plane.

-654] Angle of Polafisation. 627

This phenomenon, which is produced by all double-refracting^ crystals,
was tlrst observed by Huyghens in Iceland spar, and in consequence of a
suggestion of Newton's was afterwards called
polarisation. It remained, however, an isolated
fact until the discovery of polarisation by re-
flection recalled the attention of physicists to
the subject. The latter discovery was made by
Mai us in 1808.

653. Polarisation by reflection. — When
a ray of light, ab (fig. 604), falls on a polarised
unsilvered glass surface, ^/«, inclined to it at
an angle of 35° 25', it is reflected, and the
reflected ray is polarised in the plane of re-
flection. If it were transmitted through a
crystal of Iceland spar, it would pass through
without bifurcation, and undergo an ordinary jt
refraction ; when the principal plane coincides
with the plane of reflection, it would also be
transmitted without bifurcation, but undergo
extraordinary refraction, when the principal plane is at right angles to the
plane of reflection ; in other positions of the crystal it would give rise to an
ordinary and an extraordinary ray of different intensities, according to the
angle between the plane of reflection and the principal plane of the crystal.
The peculiar property which the light has acquired by reflection at the sur-
face fghi can also be exhibited as follows : — Let the polarised ray be be
received at r, on a second surface of unsilvered glass, at the same angle, viz.
35° 25'. If the surfaces are parallel, the ray is reflected; but if the second
plate is caused to turn round cb, the intensity of the reflected ray continually
diminishes, and when the glass surfaces are at right angles to each other, no
light is reflected. By continuing to turn the upper mirror the intensity of
the reflected ray gradually increases, and attains a maximum value when the
surfaces are again parallel.

The above statement will serve to describe the phenomenon of polarisa-
tion by reflection so far as the principles are concerned ; the apparatus best
adapted for exhibiting the phenomenon will be described farther on.

654. Angrle of polarisation. — T\\& polarising afigle of a substance is the
angle which the incident ray must make with the perpendicular to a plane
polished surface of that substance in order that the polarisation be complete.
For glass this angle is 54° 35', and if in the preceding e.xperiment the lower
mirror were inclined at any other angle than this, the light would not be
completely polarised in any position ; this would be shown by its being
partially reflected from the upper surface in all positions. Such light is
said to he. partially polarised. The polarising angle for water is 52° 45' ;
for quartz, 57° 32' ; for diamond, 68° ; and it is 56° 30' for obsidian, a kind
of volcanic glass which is often used in these experiments.

Light which is reflected from the surface of water, from a slate roof, from
a polished table, or from oil paintings, is all more or less polarised. The
ordinary light of the atmosphere is frequently polarised, especially in the
earlier and later periods of the day, when the solar rays fall obliquely on

628 On Light. [654-

the atmosphere. Almost all reflecting surfaces may be used as polarising
mirrors. Metallic surfaces form, however, an important exception.

Brewster discovered the following remarkably simple law in reference to
the polarising angle : —

The polanstfig- angle of a substance is that angle of ificidence for which
the reflected polarised ray is at right angles to the refracted ray.

Thus, in fig. 605, if si is the incident, ir
the refracted, and if the reflected ray, the
polarisation is most complete when // is at
right angles to ir.

The plane of polarisation is the plane of
reflection in which the light becomes polar-
ised ; it coincides with the plane of inci-
dence, and therefore contains the polarising
angle.

A simple geometrical consideration will
show that the above law may be thus ex-
'^" ^"^" pressed : — The tangent of the angle of polari-

sation of a substance is equal to its refractive index. As the refractive index
differs with the different colours, it follows that the angle of polarisation can-
not be the same for all colours. This explains why a ray of white light is
never completely polarised.

655. Polarisation by singrle refraction. — When an unpolarised lu-
minous ray falls upon a glass plate placed at the polarising angle, one part
is reflected ; the other part becomes refracted in passing through the glass,
and the transmitted light is now found to be partially polarised. If the light
which has passed through one plate, and whose polarisation is very feeble,
be transmitted through a second plate parallel to the first, the effects become
more marked, and by ten or tweh'e plates are tolerably complete. A bundle
of such plates, for which the best material is the glass used for covering
microscopic objects, fitted in a tube at the polarising angle, is frequently
used for examining or producing polarised light.

If a ray of light fall at any angle on a transparent medium, the same
holds good with a slight modification. In fact, part of the light is reflected
and part refracted, and both are found to be partially polarised, equal quan-
tities in each beifig polarised, and their planes of polarisation being at right
angles to each other. It is, of course, to be understood that the polarised
portion of the reflected light is polarised in the plane of reflection, which is
likewise the plane of refraction.

656. Polarising' Instruments. — Every instrument for investigating the
properties of polarised light consists essentially of two parts — one for polaris-
ing the light, the other for ascertaining or exhibiting the fact of light having
undergone polarisation. The former part is called the polariser, the latter
the analyser. Thus in art. 652 the crystal producing the first refraction is
the polariser, that producing the second refraction is the analyser. In art.
653 the mirror at which the first reflection takes place is the polariser, that
at which the second reflection takes place is the analyser. Some of the
most convenient means of producing polarised light will now be described,
and it will be remarked that any instrument that can be used as a polariser

657]

Norrcmberg's Apparatus.

629

can also be used as an analyser. The experimenter has therefore consider-
able liberty of selection.

657. STorrembergr's apparatus. — The most simple but complete instru-
ment for polarising light is that invented by Norremberg. It may be used
for repeating most of the experiments on polarised light.

It consists of two brass rods, b and d (fig. 606), which support an unsil-
vered mirror, //, of ordinary glass, movable about a horizontal axis. A small
graduated circle indicates the angle of inclination of the mirror. Between
the feet of the two columns there is a silvered glass,/, which is fixed and
horizontal. At the upper end of the columns is a graduated plate, z, in
which a circular disc, o, rotates. This disc, in which there is a square
aperture, supports a mirror of black glass, w, which is inclined to the vertical
at the polarising angle. An annular disc, k, can be fixed at different heights
on the columns by means of a screw. A second ring, a^ may be moved
around the axis. It supports a black screen, in the centre of which there is
a circular aperture.

When the mirror n makes with the vertical an angle of 35° 25', which is
the complement of the polarising angle for glass, the rays of light, S«,
which meet the mirror at this
angle, become polarised, and
are reflected in the direction np
towards the mirror /, which
sends them in the direction pnr.
After having passed through
the glass, 71^ the polarised ray
falls upon the blackened glass
m under an angle of 35° 25',
because the mirror makes ex-
actly the same angle with the
vertical. But if the disc, c, to
which the mirror, m, is fixed,
be turned horizontally, the in-
tensity of the light reflected
from the upper mirror gradually
diminishes, and totally disap-
pears when it has been moved
through 90°. The position is
that represented in the diagram :
the plane of incidence on the
upper mirror is then perpendi-
cular to the plane of incidence,
S;?_/>, on the mirror 71. When the
upper mirror is again turned, the
intensity of the light increases
until it has passed through 180°,
when it again reaches a maxi-
mum. The mirrors w and 71
are then parallel. The same phenomena are repeated as the mirror 171 con-
tinues to be turned in the same direction, until it again comes into its original

630 On Light. [667-

position ; the intensity of the reflected Hght being greatest when the mirrors
are parallel, and being reduced to zero when they are at right angles. If the
mirror m is at a greater or less angle than 35° 25', a certain quantity of
light is reflected in all positions of the plane of incidence.

658. Tourmaline. — The primary form of this crystal is a regular hex-
agonal prism. Tourmaline, as already stated, is a negative uniaxial crystal,
and its optic axis coincides with the axis of the prism. For optical purposes
a plate is cut from it parallel to the axis. When a ray of light passes
through such a plate, an ordinary ray and an extraordinary ray are produced
polarised in planes at right angles to each other ; viz. the former in a plane
at right angles to the plate parallel to the axis, and the latter in a plane at
right angles to the axis. The crystal possesses, however, the remarkable
property of rapidly absorbing the ordinary ray ; consequently, when a plate
of a certain thickness is used, the extraordinary ray alone emerges — in
other words, a beam of common light emerges from the plate of tourmaline
polarised in a plane at right angles to the axis of the crystal. If the light
thus transmitted be viewed through another similar plate held in a parallel
position, little change will be observed, excepting that the intensity of the
transmitted light will be about equal to that which passes through a plate of
double the thickness ; but if the second tourmaline be slowly turned, the
light will become feebler, and will ultimately disappear when the axes of the
two plates are at right angles.

The objections to the use of the tourmaline are that it is not very trans-
parent, and that plates of considerable thickness must be used if the polarisa-
tion is to be complete. Yox unless the ordinary ray is completely absorbed
the emergent light will be only partially polarised.

Herapath discovered that sulphate of iodoquinine has the property of
polarising light in a remarkable degree. Unfortunately, it is a very fragile
salt, and difficult to obtain m large crystals.

659. Bouble-refractingr prism of Iceland spar.— When a ray of light
passes through an ordinary rhombohedron of Iceland spar, the ordinary and
extraordinary rays emerge parallel to the original ray, consequently the
separation of the rays is proportional to the thickness of the prism. But if
the crystal is cut so that its faces are inclined to each other, the deviations
of the ordinary and extraordinary rays will be different, they will not emerge
parallel, and their separation will be greater as their distance from the

prism increases. The light, however, becomes decomposed in
passing through the prism, and the rays will be coloured. It
is tliercforc necessary to acliroiiiatisc (584) the prism, which is
done by combining it with a prism of glass with its refracting
angle turned in the contrary direction (fig. 608). In order
to obtain the greatest amount of divergence, the refracting
edges of the prism should be cut parallel to the optic axis,
Fig. 608. 'ind this is always done.

Let us suppose that a ray of polarised light passes along
the axis of the cylinder (fig. 608), and let us suppose that the cylinder is
caused to turn slowly about its axis ; then the resulting phenomena are
exactly like those already described (643). Generally there will be an ordi-
nary and extraordinary ray produced, whose relative intensities will vary as

-661] riiysical Theory of Polarised Light. 631

the tube is turned. But in two opposite positions the ordinaiy ray alone
will emerge, and in two others at right angles to the former the extraordinary
ray will alone emerge. When the ordinaiy ray alone emerges, the principal
plane of the ciystal— that is, a plane at right angles to its face, and parallel
to its refracting edge — coincides with the original plane of polarisation of the
ray. Consequently, by means of the prism, it can be ascertained both that
the ray is polarised, and likewise the plane in which it is polarised.

66a sricol's prism. — The Nicol's prism is one of the most valuable
means of polarising light, for it is perfectly colourless, it polarises light com-
pletely, and it transmits only one beam of polarised light, the other being
entirely suppressed.

It is constructed from a rhombohedron of Iceland spar, about an inch
in height and \ of an inch in breadth. This is bisected in the plane which
passes through the obtuse angles as shown in fig. 611 ; that is, along the
plane acbd (fig. 597). The two halves are then again joined in the same
order by means of Canada balsam.

The principle of the Nicol's prism is this :— The refractive index of
Canada balsam, 1-549, is less than the ordinary index of Iceland spar 1-654,

Fig. 609. Fig. 610.

but greater than its extraordinarj' index 1-483. Hence when a luminous ray
SC (fig. 610) enters the prism, the ordinary ray is totally reflected on the sur-
face, ab., and takes the direction! C^O, by which it is refracted out of the
cr)'Stal, while the extraordinary ray, C^, emerges alone. Since the Nicol's
prism allows only the extraordinary ray to pass, it may be used, like a tour-
maline, as an analyser or as a polariser.

Foucault replaced the layer of Canada balsam by one of air, the two
prisms being kept together by the mounting. The advantage of this is that
the section ab (fig. 610) need not be so acute, so that the prism becomes
shorter, and therefore cheaper.

Nicol's prism is the most important feature of most polarising apparatus.
It is better than the polarising mirror on account of its more complete polar-
isation, and has the advantage over tourmaline of giving a colourless field
of view.

661. Pbysical theory of polarised llgrbt. — The explanation of the dark
bands produced by the interference of light is stated in art. 650 to resemble
exactly that of the formation of nodes and loops given in art. 276.

It might hence be supposed that the vibrations producing light are quite
similar to those producing sound. But this is by no means the case. In
fact, no assumption is made in art. 652 as to the direction in which the
vibrating particles move, and accordingly the explanation is equally true
whether the particles vibrate in the direction AB, BA, or at right angles
to AB. As a matter of fact, the former is the case with the vibrations pro-

632 071 Light. ' [661-

ducing sound, the latter with the vibrations producing hyht. In other words,
the vibrations producing sound take place in the direction of propagation, the
vibrations producing light are transvcfsal to the direction of propagation.

This assumption as to the direction of the vibration of the particles of
ether producing light is rendered necessary, and is justified, by the pheno-
mena of polarisation.

When a ray of light is polarised, all the particles of ether in that ray
vibrate in straight lines parallel to a certain direction in the front of the
wave corresponding to the ray.

When a ray of light enters a double-refracting medium, such as Iceland
spar, it becomes divided into two, as we have already seen. Now it can be
shown to be in strict accordance with mechanical principles that, if a medium
possesses unequal elasticity in different directions, a plane wave produced
by transversal vibrations entering that medium will give rise to two plane
waves moving with different velocities within the medium, and the vibrations
of the particles in front of these waves will be in directions parallel respec-
tively to two lines at right angles to each other. If, as is assumed in the
undulatory theory of light, the ether exists in a double-refracting ciystal in
such a state of unequal elasticity, then the two plane waves will be formed
as above described, and these, having different velocities, will give rise to
two rays of unequal refrangibility (638). This is the physical account
of the phenomenon of double refraction. It will be remarked that the
\ibrations corresponding to the two rays are transversal, rectilinear, and
in directions perpendicular to each other in the rays respectively. Accord-
ingly the same theory accounts for the fact that the t\\o rays are both
polarised, and in planes at right angles to each other.

It is a point still unsettled whether, when a ray of light is polarised with
respect to a given plane, the vibrations take place in directions within or
perpendicular to that plane. Fresnel was of the latter opinion. It is, how-
ever, convenient in some cases to regard the plane of polarisation as that
plane in which the vibrations take place.

COLOURS PRODUCED BY THE INTERFERENCE OF POLARISED LIGHT,

662. I.aws of the interference of polarised rays. — After the discovery
of polarisation, Fresnel and Arago tried whether polarised rays presented
the same phenomena of inteifcrencc as ordinary rays. They were thus led
to the discovery of the following laws in reference to the interference of
polarised light, and, at the same time, of the brilliant phenomena of colora-
tion, which will be presently described :—

I. When two rays polarised in the same plane interfere with each other,
they produce, by their interference, fringes of the very same kind as if they
were common light.

II. When two rays of light are polarised at right angles to each other,
tliey produce no coloured fringes in the same cirrumstances in which
two rays of common light would produce them. When the rays arc po-
larised in planes inclined to each other at any other angles, they produce
fringes of intermediate brightness : and if the angle is made to change, the

-664] Ejfcct produced ivlicn Plate of Crystal is very Thin. 633

fringes gradually decrease in brightness from 0° to 90°, and arc totally
obliterated at the latter angle.

III. Two rays originally polarised in planes at light angles to each other
may be subsequently brought into the same plane of polarisation without
acquiring the power of forming fringes by their interference.

I\'. Two rays polarised at right angles to each other, and afterwards
brought into the same plane of polarisation, produce fringes by their inter-
ference like rays of common light, provided they originated in a pencil the
whole of which was originally polarised in any one plane.

\. In the phenomena of interference produced by rays that ha\e suffered
double refraction, a difference of half an undulation must be allowed, as one
of the pencils is retarded by that tjuantity, from some unknown cause.

663. Effect produced by causing: a pencil of polarised rays to tra-
verse a double-refVactlng- crystal.- -The following important experiment
may be made most conveniently by Norremberg's apparatus (fig. 606). At
^((ig. 607) there is a Nicol's prism. A plate of a double-refracting crystal
cut parallel to its axis is placed on the disc at e. In the first place, however,
suppose the plate of the crystal to be removed. Then, since the Nicol's
prism allows only the extraordinary ray to pass when it is turned so that its
principal plane coincides with the plane of reflection, no light will be trans-
mitted (660). Place the plate of doubly refracting crystal, which is supposed
to be of moderate thickness, in the path of the reflected ray at c. Light is
now transmitted through the Nicol's prism. On turning the plate, the
intensity of the transmitted light varies ; it reaches its maximum when the
principal plane of the plate is inclined at an angle of 45° to the plane of
reflection, and disappears when these planes either coincide with or are at
right angles to each other. The light in this case is white. The interposed
plate may be called the depolarising plate. The same or equivalent phe-
nomena are produced when any other analyser is used. Thus, assume the
double-refracting prism to be used and suppose the depolarising plate to be
removed. Then, generally, two rays are transmitted ; but if the principal
plane of the analyser is turned in the plane of primitive polarisation, the
ordinary ray only is transmitted, and then, when turned through 90°, the
extraordinary ray only is transmitted. Let the analyser be turned into
the former position, then, when the depolarising plate is interposed, both
ordinary and extraordinary rays are seen, and when the depolarising plate
is slowly turned round, the ordinary and extraordinary rays are seen to vary
in intensity, the latter vanishing when the principal plane of the polarising
plate either coincides with, or is at right angles to, the plane of primitive
polarisation.

664. Effect produced when the plate of crystal Is very thin.— In
order to exhibit this, take a thin film of sclcnitc or mica between the twen-
tieth and sixtieth of an inch thick, and interpose it as in the last article. If
the thickness of the film is uniform, the light now transmitted through the
analyser will be no longer white, but of a uniform tint ; the colour of the
tint being different for different thicknesses— for instance, red, or green, or
blue, or yellow, according to the thickness ; the intensity of the colour de-
pending on the inclination of the principal plane of the film to the plane of
reflection, being greatest when the angle of inclination is 45°. Let us now

634 On Light. [664-

suppose the crystalline film to be fixed in that position in which the light is
brightest, and suppose its colour to be red. Let the analyser (the Nicol's
prism) be turned round, the colour will grow fainter, and when it has been
turned through 45°, the colour disappears, and no light is transmitted ; on
turning it further, the complementary colour, ^r^^;/, makes its appearance,
and increases in intensity until the analyser has been turned through 90° ;
after which the intensity diminishes until an angle of 135° is attained, when
the light again vanishes, and, on increasing the angle, it changes again into
red. Whatever be the colour proper to the plate, the same series of pheno-
mena will be observed, the colour passing into its complementarj' when the
analyser is turned. That the colours are really complementary is proved
by using a double-refracting prism as analyser. In this case two rays are
transmitted, each of which goes through the same changes of colour and in-
tensity as the single ray described above ; but whatever be the colour and
intensity of the one ray in a given position, the other ray will have the same
when the analyser has been turned through an angle of 90°. Consequently,
these two rays give simultaneously the appearances which are successively
presented in the above case by the same ray at an interval of 90°. If now
the two rays are allowed to overlap, they produce white light ; thereby
proving their colours to be complementary.

Instead of using plates of different thicknesses to produce different tints,
the same plate may be employed inclined at different angles to the polarised
ray. This causes the ray to traverse the film obliquely, and, in fact, amounts
to an alteration in its thickness.

With the same substance, but with plates of increasing thickness, the
tints follow the laws of the colours of Newton's rings (660). The thickness
of the depolarising plate must, however, be different from that of the layer
of air in the case of Newton's rings to produce corresponding colours. Thus
corresponding colours are produced by a plate of mica and a layer of air
when the thickness of the former is about 400 times that of the latter. In
the case of selenite the thickness is about 230 times, and in the case of Ice-
land spar about 13 times, that of the corresponding layer of air.

665. Theory of the phenomena of depolarisatlon. — The phenomena
described in the last articles admit of complete e.xplanation by the undulatory
theory, but not without the aid of abstruse mathematical calculations. What
follows will show the nature of the explanation. Let us suppose, for con-
venience, that in the case of a polarised ray the particles of ether vibrate
in the plane of polarisation (661), and that the analyser is a double refract-
ing prism, with its principal plane in the plane of primitive polarisation ;
then the vibrations, being wholly in that plane, have no resolved part
in a plane at right angles to it, and, consequently, no e.xtraordinary ray passes
through the analyser ; in other words, only an ordinary ray passes. Now
take the depolarising plane cut parallel to the axis, and let it be interposed
in such a manner that its principal plane makes any angle {6) with the plane
of primitive polarisation. The effect of this will be to cause the vibrations
of the primitive ray to be resolved in the principal plane and at right angles
to the principal plane, thereby giving rise to an ordinary ray (O) and an ex-
traordinary ray (E), which, however, do not become separated on account of
the thinness of the depolarising plate. They will not form a single plane

666] Coloured Rings produced by Polarised Light. 635

polarised ray on leaving the plate, since they are unequally retarded in pass-
ing- through it, and consequently leave it in different phases. Since neither
of the planes of polarisation of O and E coincides with the principal plane
of the analyser, the vibrations composing them will again be resolved — viz.
O gives rise to Oo and O^, and E gives rise to E^ and E^. But the vibra-
tions composing Oo and E<7, being in the same phase, give rise to a single
ordinary ray, I^, and in like manner Oe and E^ give rise to a single extra-
ordinary ray, \e. Thus the interposition of the depolarising plate restores
the extraordinary ray.

Suppose the angle i^ to be either 0° or 90°. In either case the vibrations
are transmitted through the depolarising plate without resolution, conse-
quently they remain wholly in the plane of primitive polarisation, and on
entering the analyser cannot give rise to an extraordinary ray.

If the Nicol's prism is used as an analyser, the ordinary ray is suppressed
by mechanical means. Consequently only \e will pass through the prism,
and that for all values of 6 except 0° and 90°.

A little consideration will show that the joint intensities of all the rays
existing at any stage of the above transformations must continue constant,
but that the intensities of the individual rays will depend on the magnitude
of ^; and when this circumstance is examined in detail, it explains the fact
that \e increases in intensity as 6 increases from 0° to 45°, and then decreases
in intensity as 6 increases from 45° to 90°.

In regard to the colour of the rays, it is to be observed that the formulae
for the intensities of \o and \e contain a term depending on the length of the
wave and the thickness of the plate. Consequently, when white light is used
the relative intensities of its component colours are changed, and therefore
\o and \e will each have a prevailing tint, which will be different for different
thicknesses of the plate. The tints will, however, be complementary, since
the joint intensities of \o and \e being the same as that of the original ray,
they will, when superimposed, restore all the components of that ray in their
original intensities, and therefore produce white light.

666. Coloured rings produced by polarised ligrht in traversing-
double refracting: films. — In the experiments with Norremberg's apparatus
Avhich have just been described (663), a pencil of parallel rays traverses the
film of crystal perpendicularly to its faces, and as all parts of the film act in
the same manner, there is everywhere the same tmt. But when the incident

rays traverse the plate under different obliquities, which comes to the same
thing as if they traversed plates differing in thickness, coloured rings are
formed similar to Newton's rings.

The best method of observing these new phenomena is by means of the
tourmaline pi7icette (fig. 611). This is a small instrument consisting of two
tourmalines, cut parallel to the axis, each of them being fitted in a copper

636 On Light. [666-

disc. These two discs, \vhich are perforated in the centre, and blackened,
are mounted in two rings of silvered copper, which is coiled, as shown in
the figure, so as to form a spring, and press together the tourmalines. The
tourmalines turn with the disc, and may be so arranged that their axes are
either perpendicular or parallel.

The crystal to be experimented upon, being fixed in the centre of a cork
disc, is placed between the two tourmalines, and the pincette is held before
the eye so as to view diffused light. The tourmaline farthest from the eye
acts as polariser and the other as analyser. If the crystal thus viewed is
uniaxial, and cut perpendicularly to the axis, and a homogeneous light —
red for instance — is looked at, a series of alternately dark and red rings
is seen. With another simple colour similar rings are obtained, but their
diameter decreases with the refrangibility of the colour. On the other
hand, the diametei^s of the rings diminish when the thickness of the plates
increases, and beyond a certain thickness no more rings are produced.
If, instead of illuminating the rings by homogeneous light, white light be
used, then since the rings of the different colours produced have not the
same diameter, they are partially superposed, and produce very brilliant
variegated colours.

The position of the crystal has no influence on the rings, but this is not
the case with the relative position of the two tourmalines. For instance,
in experimenting on Iceland spar cut perpendicular to the axis, and from i
to 20 millimetres in thickness, when the axes of the tourmalines are perpen-
dicular, a beautiful series of rings is seen, brilliantly coloured, and traversed
by a black cross, as shown in fig. i, Plate II. If the axes of the tourmalines
are parallel, the rings have tints complementary to those they had at first,
and there is a white cross (fig. 2, Plate II.) instead of a black one.

In order to understand the formation of these rings when polarised light
traverses double-refracting films, it must first be premised that these films
are traversed by a converging conical pencil, whose summit is the eye of the
observer. Hence it follows that the virtual thickness of the film which the
rays traverse increases with their divergence ; but for rays of the same
obliquity this thickness is the same ; hence there result different degrees of
retardation of the ordinary with respect to the extraordinary ray at different
points of the plate, and consequently different colours are produced at
different distances from the axis, but the same colours will be produced at
the same distance from the axis, and consequently the colours are arranged
in circles round the axis. The arms of the black cross are parallel to the
optic axis of each of the tourmalines, and are due to an absorption of the
polarised light in these directions. When the tourmalines are parallel the
vibrations are transmitted, and hence' the white cross.

Analogous effects are produced with all uniaxial crystals ; for instance,
tourmaline, emerald, sapjjhire, beryl, mica, jiyromorphite, and ferrocyanide
of potassium.

667. Hln^s In biaxial crystals. — ^In biaxial crystals, coloured rings are
also produced, liut their form is more complicated. The coloured bands,
instead of being circular and concentric, have the form of curves, with two
centres, the centre of each system corresponding to an axis of the crystal.
Figs. 4, 5, and 6, Plate II., represent the curves seen wIkmi a plate of either

f*^**i

'^^

M&N.Ka^^rt litn

-668] Colours produced by Compressed or Unanneakd Glass. 637

cerussite, topaz, or nitre, cut perpendicularly to the axis, is placed between
the two tourmalines, the plane containing the axis of the crystal being in the
plane of primitive polarisation. When the axes of the two tourmalines are
at right angles to each other, fig. 4, Plate II., is obtained. On turning the
crj'stal without altering the tourmalines, fig. 5, Plate II., is seen, which
changes into fig. 6, Plate II., when the crystal has been turned through 45°.
If the axes of the tourmalines are parallel, the same coloured curves are
obtained, but the colours are complementary, and the black cross changes
into white. The angle of the optic axis in the case of nitre is only 5° 20',
and hence the whole system can be seen at once. But when the angle exceeds
20° to 25°, the two systems of curves cannot be simultaneously seen. There
is then only one dark bar instead of the cross, and the bands are not oval,
but circular. Fig. 3, Plate II., represents the phenomenon as seen with
arragonite.

Sir John Herschel, who carefully measured the rings produced by biaxial
cr^'stals, referred them to the kind of curve known in geometry as the lem-
niscate, in strict accordance with the principles of the undulatory theory of
light.

The observation of the system of rings which plates of cr>'stals give in
polarised light presents a means of distinguishing between optical uniaxial
and optical biaxial crystals, even in cases in which no conclusion can be
drawn as to the system in which a mineral crystallises from mere morpho-
logical reasons. In this way the optical investigation becomes a valuable
aid in mineralogy ; as, for example, in the case of mica, of which there are
two mineralogical species, the uniaxial and the biaxial.

All the phenomenon which have been described are only obtained by
means of polarised light. Hence, a double refracting film, with either a
Nicol's prism or a tourmaline as analyser, may be used to distinguish between
polarised and unpolarised light ; that is as a polariscope.

668. Colours produced by compressed or by unannealed grlass. —
Ordinary glass is not endowed with the power of double refraction. It
acquires this property, however, if by any cause its elasticity becomes
more modified in one direction than in another. In order to effect this,
it may be strongly compressed in a given direction, or it may be curved,
or tempered ; that is to say, cooled after having been heated. If the
glass is then traversed by a beam of polarised light, effects of colour are
obtained which are entirely analogous to those described in the case of
doubly refracting crystals. They are, however, susceptible of far greater
variety, according as the plates of glass have a circular, square, rectangular,
or triangular shape, and according to the degree of tension of their particles.

When the polariser is a mirror of black glass, on which the light of the
sky is incident, and the analyser is a Nicol's prism, through which the
glass plates traversed by polarised light are viewed, figs. 612, 613, 615
represent the appearances presented successively, when a square plate
of compressed glass is turned in its own plane; figs. 614 and 617 re-
present the appearances produced by a circular plate under the same
circumstances ; and fig. 617 that produced when one rectangular plate is
supei-posed on another. This figure also varies when the system of plates
is turned.

638

07t Lio-ht.

[668-

In consequence of being rapidly cooled, glass often acquires a strained
condition. Hence, when the masses of glass, more especially the larger ones,
from which lenses are made, are examined by polarised light, the existence of

Fig. 612.

Fig. 615.

Fig. 616.

Fig. 617.

Strains may be revealed which would render it useless to go to the trouble
and expense of working such masses, as they would probably break in the
operation.

KLLIl'TICAL, CIRCULAR, AND ROTATORY POLARISATION.

669. Definition of elliptical and circular polarisation.— In the cases
hitherto considered, the particles of ether composing a polarised ray vibrate
in parallel straight lines ; to distinguish this case from those we are now to
consider, such light is frequently called plane polatised light. It sometimes
happens that the particles of ether describe ellipses about their positions of
rest, the planes of the ellipses being perpendicular to the direction of the
ray. If the axes of these ellipses are equal and parallel, the ray is said to be
elliptically polarised. In this case the particles which, when at rest, occu-
pied a straight line, are, when in motion, arranged in a helix round the hne
of their original position as an axis, the helix exchanging from instant to
instant. If the axes of the ellipses are equal, they become circles, and the
light is said to be circularly polarised. If the minor axes become zero, the
ellipses coincide with their major axes, and the light becomes plane polarised.
Consequently, /Ajz/r ]K)lariscd light and circularly polarised light are parti-
cular cases of ellii)ti(:ally polarised light.

670. Theory of the origin of elliptical and circular polarisation. —
Let us in the first place consider a simple pendulum (55) vibrating in any
plane, the arc of vibration being small. Suppose that, when in its lowest
position, it received a blow in a direction at right angles to the direction ol
its motion, such as would make it vibrate in an arc at right angles to its

-671] FresneVs R/iowb. 639

arc of primitive vibration, it follows from the law of the composition of
velocities (52) that the joint effect will be to make it vibrate in an arc inclined
at a certain angle to the arc of primitive vibration, the magnitude of the
angle depending on the magnitude of the blow. If the blow communicated
a velocity equal to that with which the body is already moving, the angle
would be 45°. Next suppose the blow to communicate an equal velocity,
but to be struck when the body .is at its highest point, this will cause the
particle to describe a circle, and to move as a conical pendulum. If the
blow is struck under any other circumstances, the particle will describe an
ellipse. Now as the two blows would produce separately two simple vibra-
tions in directions at right angles to each other, we may state the result
arrived at as follows : — If two rectilinear vibrations are superinduced on
the same particle in directions at right angles to each other, then : i. If
they are in the same or opposite phases, they make the point describe a
rectilinear vibration in a direction inclined at a certain angle to either of
the original vibrations. 2. But if their phases differ by 90° or a quarter
of a vibration, the particle will describe a circle, provided the vibrations
are equal. 3. Under other circumstances the particle will describe an
ellipse.

To apply this to the case of polarised light. Suppose two rays of light
polarised in perpendicular planes to coincide, each would separately cause
the same particles to vibrate in perpendicular directions. Consequently —
r. If the vibrations are in the same or opposite phases, the light resulting- from
the two rays is plane polarised. 2. If the rays are of equal intensity, and
their phases differ by 90°, the resulting light is circularly polarised. 3. Under
other circumstances the light is elliptically polarised.

As an example, if reference is made to arts. 665 and 666, it will be seen
that the rays denoted by O and E are superimposed in the manner above
described. Consequently, the light which leaves the depolarising plate is
elliptically polarised. If, however, the principal plane of the depolarising
plate is turned so as to make an angle of 45° with the plane of primitive
polarisation, O and E have equal intensities ; and if, further, the plate is
made of a certain thickness, so that the phases of O and E may differ by
90°, or by a quarter of a vibration, the light which emerges from the plate is
circularly polarised. This method may be employed to produce circularly
polarised light.

Circular or elliptical polarisation may be either right-handed or left-
handed^ or what is sometimes called dextrogyrate and hevogyrate. If the ob-
server looks along the ray in the direction of propagation, from polariser
to analyser, then, if the particles move in the same direction as the hands
of a watch with its face to the observer, the polarisation is right-handed.

671. Fresnel's rhomb. — This is a means of obtaining circularly polarised
light. We have just seen (670) that, to obtain a ray of circularly polarised
light, it is sufficient to decompose a ray of plane polarised light in such
a manner as to produce two rays of light of equal intensity polarised
in planes at right angles to each other, and differing in their paths by a
quarter of an undulation. Fresnel effected this by means of a rhomb which
has received his name. It is made of glass ; its acute angle is 54', and its
obtuse 126°. If a ray (a, fig. 618) of pLiin polarised light falls perpendicu-

640 0)1 Light. [671-

larly on the face of AB, it will undergo two total internal reflections at an angle
of about 54°, one at E, and the other at F, and will emerge perpendicularly.
If the plane ABCD be inclined at an angle of
45° to the plane of polarisation, the polarised ray
will be divided into two coincident rays, with their
planes of polarisation at right angles to each other,
and it appears that one of them loses exactly a
quarter of an undulation, so that on emerging from
the rhomb the ray is circularly polarised. If the ray
emerging as above from Fresnel's rhomb is ex-
amined, it will be found to differ from plane polarised
light in this, that, when it passes through a double
refracting prism, the ordinary and extraordinary
*"! rays are of ec^ual intensity in all positions of the

p. g^g prism. Moreover, it differs from ordinary light in

this, that, if it pass through a second rhomb placed
parallel to the first, a second quarter of an undulation will be lost, so that
the parts of the original plane polarised ray will differ by half an undulation,
and the emergent ray will be plane polarised ; moreover the plane of polar-
isation will be inclined at an angle of 45° to ABCD, but on the other side
from the plane of primitive polarisation.

672. Elliptical polarisation. — In addition to the method already men-
tioned (671), elliptically polarised light is generally obtained whenever plane
polarised light sufTers reflection. Polarised light reflected from metals
becomes elliptically polarised, the degree of ellipticity depending on the direc-
tion of the incident ray, and of its plane of polarisation, as well as on the nature
of the reflecting substance. When reflected from silver, the polarisation is
almost circular, and from galena almost plane. If elliptically polarised light be
analysed by the Nicol's prism, it never vanishes, though at alternate positions
it becomes fainter ; it is thus distinguished from plane and from circular
polarised light. If analysed by Iceland spar, neither image disappears, but
they undergo changes in intensity.

Light can also be polarised elliptically in P'resnel's rhomb. If the angle
between the planes of primitive polarisation and of incidence be any other
than 45°, the emergent ray is elliptically polarised.

673. Rotatory polarisation. — Rock crystal or quartz possesses a re-
markable property which was long regarded as peculiar to itself among all
crystals, though it has been since found to be shared by tartaric acid and its
salts, together with some other crystallised bodies. This property is called
rotatory polarisation, and may be described as follows : Let a ray of
homogeneous light be polarised, and let the analyser, say a Nicol's prism, be
turned till the light does not pass through it. Take a thin section of a quartz
crystal cut at right angles to its axis, and place it between the polariser and
the analyser with its plane at right angles to the rays. The light will now
pass through the analyser. The phenomenon is not the same as that pre-
viously described (663), for, if the rock crystal is turned round its axis, no
effect is produced, and if the analyser is turned, the ray is found to ht plane
polarised in a plane inclined at a certain angle to the plane of primitive
polarisation. If the light is red, and the plate i millimetre thick, this angle

-675J Coloration produced by Rotary Polarisation. 641

is about 17°. In some specimens of quartz the plane of polarisation is
turned to the right hand, in others to the left hand. Specimens of the
former kind are said to be right-handed, those of the latter kind left-handed
(670). This difference corresponds to a difference in crystallographic struc-
ture. The property possessed by rock crystal of turning the plane of polari-
sation through a certain angle was thoroughly investigated by Biot, who,
amongst other results, arrived at this : — For a given colour, the angle,
through which the plane of polarisation is turned, is proportional to the
thickness of the quartz.

674. Pbysical explanation of rotary polarisation. — The explanation
of the phenomenon described in the last article is as follows : When a ray
of polarised light passes along the axis of the quartz crystal, it is divided into
two rays of circularly polarised light of equal intensity, which pass through
the crystal with different velocities. In one the circular polarisation is right-
handed, in the other left-handed (670). The existence of these rays was
proved by Fresnel, who succeeded in separating them. On emerging from
the crystal, they are compounded into a plane polarised ray ; but, since they
move with unequal velocities within the crystal, they emerge in different
phases, and consequently the plane of polarisation will not coincide with the
plane of primitive polarisation. This can be readily shown by reasoning
similar to that employed in art. 670. The same reasoning will also show
that the plane of polarisation will be turned to the right or left, according
as the right-handed or left-handed ray moves with the greater velocity.
Moreover, the amount of the rotation will depend on the amount of the
retardation of the ray whose velocity is least ; that is to say, it will depend
on the thickness of the plate of quartz. In this manner the phenomena of
rotary polarisation can be completely accounted for.

675. Coloration produced by rotary polarisation. — The rotation is
different with different colours ; its magnitude depends on the refrangibility,
and is greatest with the most refrangible rays. In the case of red light a
plate I millimetre in thickness will rotate the plane 17°, while a plate of the
same thickness will rotate it 44° m the case of violet light. Hence with
white light there will, in each position of the analysing NicoFs prism, be a
greater or less quantity of each colour transmitted. In the case of a right-
handed crystal, when the Nicol's prism is turned to the right, the colours
will successively appear from the less refrangible to the more so — that is,
in the order of the spectrum, from red to violet ; with

a left-handed crystal in the reverse order. Obviously ^l|B^ .^-ifim^
in turning the Nicol's prism to the left, the reverse of m^BB
these results will take place. ^E^^&

When a quartz plate cut perpendicularly to the ^HS|F''fe;*isA<^
axis, and traversed by a ray of polarised light, is
looked at through a doubly refracting prism, two '^' "^'

brilliantly coloured images are seen, of which the tints are complementaiy :
for their images are partially superposed, and in this position there is
white light (fig. 619). When the prism is turned from left to right, the two
images change colour and assume successively all the colours of the
spectrum.

This will be understood from what has been said about the different

642 On Light. [675-

rotation for dififeient colours. Quartz rotates the plane of polarisation for
red 17° for each millimetre, and for violet 44° ; hence from the great difference
of these two angles, when the polarised light which has traversed the quartz
plate emerges, the various simple colours which it contains are polarised
in different planes. Consequently, when the rays thus transmitted by the
quartz pass through a double-refracting prism, they are each decomposed
into two others polarised at right angles to each other : the various simple
colours are not divided in the same proportion between the ordinary and
extraordinary rays furnished by the prism ; the two images are, therefore,
coloured ; but, since those which are wanting in one occur in the other, the
colours of the images are perfectly complementary.

These phenomena of coloration may be well seen by means of Norrem-
berg's apparatus (fig. 606). A quartz plate, J', cut at right angles to the axis
and fixed in a cork disc, is placed on a screen e ; the mirror « being then
so inclined that a ray of polarised light passes through the c[uartz, the latter
is viewed through a double-refracting prism, g ; when this tube is turned, the
complementary images furnished by the passage of polarised light through
the quartz are seen.

676. Rotary power of liquids. —Biot found that a great number of
liquids and solutions possess the property of rotary polarisation. He
further observed that the deviation of the plane of polarisation can reveal
differences in the composition of bodies where none is exhibited by chemical
analysis. For instance, the two sugars obtained by the action of dilute acids
on cane-sugar deflect the plane of polarisation, the one to the right and the
other to the left, although the chemical composition of the two sugars is the
same.

The rotary power of licjuids is far less than that of quartz. In con-
centrated syrup of cane-sugar, which possesses the rotary power in the
highest degree, the power is 5^5 that of quartz, so that it is necessary to
operate upon columns of liquids of considerable length— 8 inches, for
example.

Fig. 620 represents an apparatus devised by Biot for measuring the
rotary power of liquids. On a metal groove,^, fixed to a support, r, is a
brass tube,^, 20 centimetres long, in which is contained the liquid experimented
upon. This tube, which is tinned inside, is closed at each end by glass
plates fastened by screw collars. At ni is a mirror of black glass, inclined
at the polarising angle to the axis of the tubes bd and (X, so that the ray re-
flected by the mirror m, in the direction bda, is polarised. In the centre of
the graduated circle //, inside the tube a, and at right angles to the axis bda.,
is a double-refracting achromatic prism, which can be turned about the axis
of the apparatus by means of a button n. The latter is fixed to a limb c, on
which is a vernier, to indicate the number of degrees turned through. Lasth',
from the position of the mirror w, the plane of polarisation, Sod^ of the le-
llccted ray is vertical, and the zero of the graduation of the circle // is on
this plane.

Before i)lacing the tube d in the groove g, the extraordinary image fur-
nished by the double-refracting prism disappears whenever the limb c corre-
sponds to the zero of the graduation, because then the double-refracting prism
is so turned that its principal section coincides with the plane of polarisation

-677] Rotary poiver of Liquids. 643

(661). This is the case also when the tube d is full of water or any other
inactive Hquid, hke alcohol, ether, &c., which shows that the plane of polari-
sation has not been turned. But if the tube be filled with a solution of cane-
sugar or any other active liquid, the extraordinary image reappears, and to
extinguish it, the limb must be turned to a certain extent either to the right
or to the left of zero, according as the liquid is right-handed or left-handed,
showing that the polarising plane has been turned by the same angle. With
solution of cane-sugar the rotation takes place to the right ; and if with the
same solution tubes of different lengths are taken, the rotation is found to
increase proportionally to the length, in conformity with art. 673 ; further,

Fig. 620.

with the same tube, but with solutions of various strengths, the rotation
increases with the quantity of sugar dissolved, so that the quantitative
analysis of a solution may be made by means of its angle of deviation.

In this experiment homogeneous light must be used ; for, as the various
tints of the spectra have different rotary powers, white light is decomposed
in traversing an active liquid, and the extraordinary image does not disappear
completely in any position of the double-refracting prism — it simply changes
the tint. The transition tint (677) may, however, be observed. To avoid
this inconvenience, a piece of red glass is placed in the tube between the eye
and the double-refracting prism, which only allows red light to pass. The
extraordinary image disappears in that case, whenever the principal section
of the prism coincides with the plane of polarisation of the red ray.

677. Soleil's Saccbarlmeter. — Soleil constructed an apparatus, based
upon the rotary power of liquids, for analysing- saccharine substances,
to which the name saccJuiri meter is applied. Fig. 621 represents the sac-

T T 2

644

On Li<rht.

[677-

charimeter fixed horizontally on its foot, and fig. 622 gives a longitudinal
section.

The principle of this instrument is not that of observing the amplitude
of the rotation of the plane of polarisation, as in Biot"s apparatus, but that
of compensation ; that is to say, a second active substance is used acting in the
opposite direction to that analysed, and whose thickness can be altered until
the contrary actions of the two substances completely neutralise each other.

Fig. 621

Instead of measuring the deviation of the plane of polarisation, the thick-
ness is measured which the plate of quartz must have in order to obtain
perfect compensation.

The apparatus consists of three parts— a tube containing the lit|uid to be
analysed, a polariser, and an analyser.

The tube m, containing the licjuid, is made of copper, tinned on the
inside, and closed at both ends by two glass plates. It rests on a support,
/', terminated at both ends by tubes, r and a, in which are the cr>'stals used
as analysers and polarisers, and which are represented in section (fig. 622).

In front of the aperture S (fig. 622) is placed an ordinary lamp.
The light emitted by this lamp in the direction of the axis first meets a
double-refracting prism r, which serves as polariser (659). The ordinary
image alone meets the eye, the extraordinary image being projected out of
the field of vision in consec[uence of the amplitude of the angle which the
ordinary makes with the extraordinary ray. The double refracting prism is
in such a position that the plane of polarisation is vertical, and passes through
the axis of the apparatus.

Emerging from the double-refracting prism, the polarised ray meets a
plate of quartz with double rotation ; that is, this plate rotates the plane

-677]

Sfl/cil ' J Saccharimetcr.

645

both to the right and to the left. This is effected by constructing the plate
of two quartz plates of opposite rotation placed one on the other, as shown
in fig. 623, so that the line of separation is vertical and in the same plane as
the axis of the apparatus. These plates, cut perpendicularly to the axis,
have a thickness of 3-65 millimetres, corresponding to a rotation of 90°, and
gi\e a rose-violet tint, called the ///// of passage, or transitiojt tint. As the
quartz, whether right-handed or left-handed, turns always to the same extent
for the same thickness, it follows that the two quartz plates a and b turn
the plane of polarisation equally, one to the right and the other to the left.
Hence, looked at through a double-refracting prism, they present e.xactly the
same tint.

Having traversed the quartz, q, the polarised ray passes into the liquid
in the tube ;//, and then meets a single plate of quartz, /, of any thickness,
the use of which will be seen presently. The compensator, ;/, which destroys
the rotation of the column of liquid, w, consists of two quartz plates, with the
same rotation either to the right or the left, but opposite to that of the plate
/. These two quartz plates, a section of which is represented in fig. 623, are

Fig. 622.

m%L

wir

Fig. 623.

Fig. 624.

Fig. 625.

obtained by cutting obliquely a quartz plate with parallel sides, so as to form
two prisms of the same angle, N, N', which is called a biqiiartz ; super-
posing, then, these two prisms, as shown in the figure, a single plate is
obtained with parallel faces, which can be varied at will. This is effected
by fixing each prism to a slide, so as to move it in either direction without
disturbing the parallelism. This motion is effected by means of a double
rackwork and pinion motion turned by a milled head, b (figs. 621, 622).

When these plates move in the direction indicated by the arrows (fig. 623),
it is clear that the sum of their thicknesses increases, and that it diminishes
when the plates are moved in the contrary direction. A scale and a vernier
follow the plates in their motion, and measure the thickness of the compen-
sator. This scale, represented with its vernier in fig. 624, has two divisions
with a common zero, one from left to right for right-handed liquids, and
another from right to left for left-handed.

When the vernier is at zero of the scale, the sum of the thicknesses of
the plates NN' is exactly equal to that of the plate /, and as the rotation of
the latter is opposed to that of the compensator, the effect is zero. But by

646 On Light. [677-

moving the plates of the compensator in one or the other direction either
the compensator or the quartz, /, preponderates, and there is a rotation from
left to right.

Behind the compensator is a double-refracting prism, c (fig. 622), serving
as analyser to observe the polarised ray which has traversed the liquid and
the various quartz plates. In order to understand more easily the object or
the prism c^ we will neglect for a moment the crystals and the lenses on the
left of the drawing. If at first the zero of the vernier v coincides with that
of the scale, and if the liquid in the tube is inactive, the actions of the com-
pensator, and of the plate z, neutralise each other ; and, the liquid having no
action, the two halves of the plate ^, seen through the prism r, give exactly
the same tint as has been observed above. But if the tube filled with inac-
tive liquid be replaced by one full of solution of sugar, the rotary power of
this solution is added to that of one of the halves {a or b) of the plate q (viz.
that half which tends to turn the plane of polarisation in the same direction
as the solution), and subtracted from that of the other. Hence the two
halves of the plate q no longer show the same tint ; the half <■;, for instance,
is red, while the half b is blue. The prisms of the compensator are then
moved by turning the milled head b, either to the right or to the left, until
the difference of action of the compensator and of the plate i compensates
the rotary power of the solution, which takes place when the two halves
of the plate ^, with double rotation, revert to their original tint.

The direction of the deviation and the thickness of the compensator are
measured by the relative displacement of the scale r, and of the vernier v.
Ten of the divisions on the scale correspond to a difference of i millimetre
in the thickness of the compensator ; and as the vernier gives itself tenths
of these divisions, it therefore measures differences of j^^ in the thickness of
the compensator.

When once the tints of the two halves of the plate are exactly the same,
and therefore the same as before interposing the solution of sugar, the
division on the scale corresponding to the vernier is read off, and the cor-
responding number gives the strength of the solution. This depends on the
experimental fact that 16-471 grains of pure and well-dried sugar-candy being-
dissolved in water, and the solution diluted to the volume of 100 cubic cen-
timetres, and obsei-ved in a tube of 20 centimetres in length, the deviation
produced is the same as that effected by a quartz plate a millimetre thick.
In making the analysis of raw sugar, a weight of 16-471 grains of sugar is
taken, dissolved in water, and the solution made up to 100 cubic centimetres,
with which a tube 20 centimetres in length is filled, and the number indicated
by the vernier read off, when the primitive tint has l:)cen obtained. This
number being 42, for example, it is concluded that the amount of ciystallisable
sugar in the solution is 42 per cent, of that which the solution of sugar-candy
contained, and, therefore, 16-471 grains >; j'Ja, or 6-91 8 grains. This result
is only valid when the sugar is not mixed with uncrystallisable sugar or
some other left-handed substance. In that case the crystallisable sugar,
which is right-hantlcil, must be, by means of hydrochloric acid, converted
into uncrystallisable sugar, which is left-handed ; and a new determination
is made, which, together with the first, gives tin- quantity of crystallisable
sugar.

-679] Polarisation of Heat. 647

The arrangement of crystals and lenses, o,g,f, and a, placed behind the
prism t-, forms what Soleil calls the producer of sensible tints. For the
most delicate tint — that by which a very feeble difference in the coloration
of the two halves of the rotation plate can be distinguished — is not the same
for all eyes ; for most people it is of a vioIet-bluc tint, like flax blossom ; and
it is important either to produce this tint, or some other equally sensible to
the eye of the observer. This is effected by placing in front of the prism, c,
at tirst a quartz plate, 0, cut perpendicular to the axis, then a small Galileo's
telescope consisting of a double convex glass, ^, and a double concave glass,
f, which can be approximated or removed from each other according to the
distance of distinct vision of each observer. Lastly, there is a double-
refracting prism, f, acting as polariser in reference to the quartz, and the prism
a as analyser ; and hence, when the latter is turned either right or left, the
light which has traversed the prism t, and the plate <?, changes its tint, and
finally gives that which is the most delicate for the experimenter.

678. Analysis of diabetic urine. — In the disease diabetes, the urine
contains a large quantity of fermentable sugar, called diabetic sugar, which
in the natural condition of the urine turns the plane of polarisation to the
right. To estimate the quantity of this sugar, the urine is first clarified by
heating it with acetate of lead and filtering ; the tube is filled with the clear
liquid thus obtained ; and the milled head b turned until, by means of the
double-rotating- plate, the same tint is obtained as before the interposition of
the urine. Experiment has shown that 100 parts of the saccharimetric scale
represent the displacement which the quartz compensators must have when
there are 225"6 grains of sugar in a litre ; hence each division of the scale
represents 2-256 of sugar. Accordingly, to obtain the quantity of sugar in a
given urine, the number indicated by the vernier, at the moment at which
the primitive tint reappears, must be multiplied by 2-256.

679. Polarisation of beat. — The rays of heat, like those of light, may
become polarised by reflection and by refraction. The experiments on this
subject are difficult of execution ; they were first made by Malus and
Berard, in 1810 ; after the death of Malus they were continued by the latter
philosopher.

In his experiments, the heat rays reflected from one mirror were re-
ceived upon a second, just as in Norremberg's apparatus ; from the second
they fell upon a small metallic reflector, which concentrated them upon the
bulb of a differential thermometer. Berard observed that heat was not
reflected when the plane of reflection of the second mirror was at right angles
to that of the first. As this phenomenon is the same as that presented by
light under the same circumstances, Berard concluded that heat became
polarised in being reflected.

The double refraction of heat may be shown by concentrating the sun's
rays by means of a heliostat on a prism of Iceland spar, and investigating
the resultant pencil by means of a thermopile, which must have a sharp
narrow edge. In this case also there is an ordinary and an extraordinary
ray, which follow the same laws as those of light. In the optic axis of the
calcspar, heat is not doubly refracted. A Nicol's prism can be used for the
polarisation of heat as well as for that of light : a polarised ray does not
traverse the second Nicol if the plane of its principal section is perpendicular

648 On Light. [679-

to the vibrations of the ray. The phenomena of the polarisation of heat
may also be studied by means of plates of tourmaline and of mica. The
angle of polarisation is virtually the same for heat as fof light. In all these
experiments the prisms must be very near each other.

The diffraction, and therefore the interference, of rays of heat has recently
been established by the experiments of Knoblauch and others. And Forbes,
who has repeated Fresnel's experiment with a rhombohedron of rock salt,
has found that by two total internal reflections, heat is circularly polarised,
just as is the case with light.

-681] 649

BOOK VIII.
ON MAGNETISM.

CHAPTER I.
PROPERTIES OF MAGNETS,

680. STatural and artificial magnets.— Afa£ne/s are substances which
have the property of attracting iron, and the term inagnetisin is applied to
the cause of this attraction and to the resulting phenomena.

This property was known to the ancients ; it exists in the highest degree
in an ore of iron which is known in chemistry as the magnetic oxide of iron.
Its composition is represented by the formula Fe.,04.

This magnetic oxide of iron, or lodestone, as it is called, was first found
at Magnesia, in Asia Minor, the name magnet being derived from this cir-
cumstance. The name lodestone, which is applied to this natural magnet,
was given on account of its being used when suspended as a guiding or lead-
ing stone, from the Saxon ladan^ to lead ; so also the word lodestar. Lode-
stone is very abundant in nature : it is met with in the older geological forma-
tions, especially in Sweden and Norway, where it is worked as an iron ore,
and furnishes the best quality of iron.

When a bar or needle of steel is rubbed with a magnet, it acquires
magnetic properties without the magnet losing anything of its own force.
Such bars are called artificial magnets : they are more powerful than natural
magnets, and, as they are also more convenient, they will be exclusively
referred to in describing the phenomena of magnetism. The best modes of
preparing them will be explained in a subsequent article.

681. Poles and neutral lines. — When a small piece of soft iron is sus-
pended by a thread and a magnet is approached to it, the iron is attracted
towards the magnet, and some force is required for its removal. The force
of the attraction varies in different parts of the magnet ; it is strongest at the
two ends, and is totally wanting in the middle.

This variation may also be seen very clearly when a bar magnet is
placed in iron filings ; these become arranged round the ends of the bar
in feathery tufts, which decrease towards the middle of the bar, where there
are none. That part of the surface of the bar where there is no visible
magnetic force is called the ticutral line ; and the parts near the ends of the
bar where the attraction is greatest are called the poles. Every magnet,

650

On Magnetism.

[681-

whether natural or artificial, has two poles and a neutral line : sometimes,
however, in magnetising bars and needles, poles are produced lying between
the extreme points. Such magnets are abnormal, and these points are called
intermediate or consequent poles. The shortest line joining the two poles is
termed the axis of the magnet ; in a horseshoe magnet the axis is in the
direction of the keeper. The plane at right angles to the axis of a bar
magnet and passing through the neutral line is sometimes called the equator
of the magnet, and the length of a magnet, as far as magnetic actions are
concerned, is the distance of the poles.

We shall presently see that a freely suspended magnet always sets with
one pole pointing towards the north, and the other towards the south. The

end pointing towards the
ji^t^^Hj^ north is called in this
country the north pole.,
and the other end is
the south pole. The end
of the magnetic needle
pointing to the north is

Pf71»'

'|illl'fl'IPiillHill|iillillli|iiilllHilHMi

Fig. 626.

also sometimes called the marked end of the needle. Sometimes also the
end pointing to the north is called the red pole, and that to the south the
blue pole ; the corresponding terms red and blue magnetisms are also some-
times used.

682. Reciprocal action of two poles. — The two poles of a magnet appear
identical when they are brought in contact
with iron filings (fig. 626), but this identity
is only apparent, for when a small mag-
netic needle, ab (fig. 627), is suspended by
a fine thread, and the north pole, A, of
another needle is brought near its north
pole, a, a repulsion takes place. If, on
the contrary, A is brought near the south
pole, (5, of the movable needle, the latter
is strongly attracted. Hence these two
poles, a and b., are not identical, for one
is repelled, and the other attracted, by the
same pole of the magnet A. It may be
shown in the same manner that the two
poles of the latter are also different, by
successively presenting them to the same
pole, a, of the movable needle. In one
in the other attraction. Hence the following law

Fig. 627.

case there is repulsion,
may be enunciated :—

I^oles of tiic same name repel, and poles of contrary naiiie attract, one
another.

The opposite actions of the north and south polos may be shown by the
following experiment : — A piece of iron, a key for example, is supported
by a bar magnet. A second bar magnet of the same dimensions is then
moved along the first, so that their poles are contrary (fig. 628). The key
remains suspended so long as the two poles are at some distance, but when

Fig. 628.

-684] Precise Definition of Poles. 65 r

they are sufficiently near, the key drops, just as if the bar which supported

it had lost its magnetism. This, however, is not the case, for the key would

be again supported if the

first magnet were presented \<>H.

to it after the removal of ^^C/*""--^^

The attraction which a ■'■'■ii^^^^^^gj^^^^^^^^^^^^^^p>
magnet exerts upon iron is " ^"^^^^ 'i,"^^'^ '^

reciprocal, which is indeed ^^ ^

a general principle of all
attractions. It is easily veri-
fied by presenting a mass of
iron to a movable magnet, when the latter is attracted.

683. Hypothesis of two mag-netic fluids. — In order to explain the phe-
nomena of magnetism, the existence of two hypothetical magnetic fluids has
been assumed, each of which acts repulsively on itself, but attracts the other
fluid. The fluid whose action predominates at the north pole of the magnet
is called the north fluid or red magnetism ; and that at the south pole the
south fluid, or bltie magnetism. It is usual also to speak of north magnetism
as positive and of south as negative., or + and — respectively. The term
' fluid ' is apt to puzzle beginners, from its ambiguity. Ordinarily the idea
o a liquid is associated with the term 'a fluid;' hence the use of this term
to explain the phenomena of magnetism and electricity has produced a
widely prevailing impression of the material nature of these two forces. The
word 'fluid,' it must be remembered, embraces gases as well as liquids, and
here it must be pictured to the mind as representing an invisible, elastic,
gaseous atmosphere or shell surrounding the particles of all magnetic sub-
stances.

It is assumed that, before magnetisation, these fluids are combined round
each molecule, and mutually neutralise each other ; they can be separated
by the influence of a force greater than that of their mutual attraction, and
can arrange themselves round the molecules to which they are attached, but
cannot be removed from them.

The hypothesis of the two fluids is convenient in explaining magnetic
phenomena, and will be adhered to in what follows. But it must not be re-
garded as anything more than a provisional hypothesis, and it will afterwards
be shown (879) that magnetic phenomena appear to result from electrical
currents, circulating in the molecules of magnetic bodies ; a mode of view
which connects the theory of magnetism with that of electricity.

684. Precise definition of poles. — By aid of the preceding hypothesis
we are enabled to obtain a clear idea of the distribution of the magnetism
in a magnetised bar, and to account for the circumstance that there is no
free magnetism in the middle of the bar, and that it is strongest at the poles.
If AB (fig. 629) represent a magnet, then the alternate black and white
spaces may be taken to represent the position of the magnetisms in a series
of particles after magnetisation : the black spaces, representing the south
magnetism, all point in one direction, and the white ones the north in the
opposite direction. The last half of the terminal molecule at one end would
have north polarity, and at the other south polarity. Let N represent the

652 Ofi Magnetism. [684-

north pole of a magnetic needle placed near the magnet AH ; then the south
magnetism s in the terminal molecule would tend to attract N, and the
north magnetism ;/ would tend to repel it ; but as the molecule of south
magnetism s is nearer N than the molecule of the north magnetism /?, the
attraction between s and N would be greater than the repulsion between n
and X. Similarly the attraction between s' and N would be greater than
the repulsion between n' and N, and so on with the following s" and //", &c.
And all these forces would give a resultant tending to attract X, whose

//" s" >i' s' 11 s

CHO

Fig. 629.

point of application would have a certain fixed position, which would be the
south pole of AB. In like manner it might be shown that the resultant of
the forces acting at the other end of the bar would form a north pole, and
would hence repel the north pole of the needle, but would attract its south
pole.

That such a series of polarised particles really acts like an ordinary
magnet may be shown by partly filling a glass tube with steel filings, and
passing the pole of a strong magnet several times along the outside in one
constant direction, taking care not to shake the tube. The individual filings
will thus be magnetised, and the whole column of them presented to a mag-
netic needle will attract and repel its poles just like an ordinary bar magnet,
exhibiting a north pole at one end, a south pole at the other, and no polarity
in the middle ; but on shaking the tube, or turning out the filings, and put-
ting them in again so as to destroy the regularity, every trace of polarity will
disappear. It appears hence that the polarity at each end of a magnet is
caused by the fact that the resultant action on a magnetic body is strongest
near the ends, and does not arise from any accumulation of magnetisms at
the ends.

The same point may be illustrated by the following experiment, which is
due to Sir W. Grove : — In a glass tube with flat glass ends is placed water in
which is diffused magnetic oxide of iron. Round the outside of the tube is
coiled some insulated wire. On looking at a light through the tube the
liquid appears dark and muddy, but on passing a current of electricity through
the wire it becomes clearer (879). This is due to the fact that by the mag-
uftising action of the current, the particles, becoming magnetised, set with
their longest dimension parallel to the axis of the tube, in which position
they obstruct the passage of light to a less extent.

685. Experiments wltb broken magnets.— That the two magnetisms
arc present in all parts of the bar, and arc not simply accumulated at the
ends, is also evident from the following experiment : — A steel knitting-
needle (fig. 630) is magnetised by rubbing it with one of the poles of a mag-
net, and then, the existence of the two poles .\l'> and of the neutral line \

-686] Magnetic Induction. 653

having- been ascertained by means of iron filings, it is broken in the middle.
But now, on presenting successively the two halves to a magnet, each will be
found to possess two opposite poles AB' and A'B with a neutral line N, and
in fact is a perfect magnet. If these new magnets are broken in turn into
two halves, each will be a complete magnet AB" and A"B with its two poles
and neutral line, and so on, as far as the division can be continued. It is,

therefore, concluded by analogy that the smallest parts of a magnet, the
ultimate molecules, contain the two magnetisms ; that magnetism, in short,
is a phenomenon the cause of which resides in the elementary particle or
molecule itself. Each molecule is a magnet. It follows also from this ex-
periment that it is impossible to obtain an independent positive or negative
mass of magnetism which is not associated with an equal mass of the
opposite sign, in other words that unipolar magnets have no existence.

686. Magnetic induction. — When a magnetic substance is placed in
contact w ith a magnet, the two magnetisms of the former become separated ;
and so long as the contact remains, it is a complete magnet, having its two
poles and its neutral line. For instance, if a small cylinder of soft iron, ab
(fig. 631), be placed in contact with one of the poles of a magnet, the cylinder
can in turn support a second cylinder ; this in turn a third, and so on, to as

many as seven or eight, according to the power of the magnet. Each of these
little cylinders is a magnet ; if it be the north pole of the magnet to which
the cylinders are attached, the part a will have south, and b north magnetism ;
b will in like manner develop in the nearest end of the next cylinder south
magnetism, and so on. But these cylinders are only magnets so long as the
influence of a magnetised bar continues. For, if the first cylinder be re-
moved from the magnet, the other cylinders immediately drop, and retain no
trace of magnetism. The separation of the two magnetisms is only moment-
ary, which proves that the magnet yields nothing to the iron. Hence we
may have temporary magnets as well as permanent magnets ; the former of
iron and nickel, the latter of steel and cobalt (688).

This action, in virtue of which a magnet can develop magnetisation in

654 On Magnetism. [686-

iron, is called magnetic induction or influence^ and it can take place witliout
actual contact between the magnet and the iron, as is seen in the following
experiment :— A bar of soft iron is held with one end near a magnetic needle.
If now the north pole of a magnet be approached to the iron without touch-
ing it, the needle will be attracted or repelled, according as its south or
north pole is near the bar. For the north pole of the magnet will develop
south magnetism in the end of the bar nearest it, and therefore north mag-
netism at the other end, which would thus attract the south, but repel the
north end of the needle. Obviously, if the other end of the magnet were
brought near the iron, the opposite effects would be produced on the needle;
or if the opposite pole of a second magnet of equal strength simultaneously
be brought near the iron, the needle would be unaffected, as one magnet
would undo the work of the other.

Among other things, magnetic induction explains the formation of the
tufts of iron filings which become attached to the poles of magnets (fig. 626).
The parts in contact with the magnet are converted into magnets ; these
act inductively on the adjacent parts, these again on the following ones, and
so on, producing a filamentary arrangement of the filings. The bush-like
appearance of these filaments is due to the repulsive action which the
free poles exert upon each other. Any piece of soft iron while being
attracted by a magnet is for the time being converted into a magnet ;
hence is explained the paradoxical statement that ' magnets only attract
magnets.'

6S7. Coercive force. — We have seen from the above experiments that
soft iron becomes instantaneously magnetised under the influence of a
magnet, but that this magnetism is not permanent, and ceases when the
magnet is removed. Steel likewise becomes magnetised by contact with a
magnet ; but the operation is effected with difficulty, and in general the
more so as the steel is more highly tempered. Placed in contact with a
magnet, a steel bar accjuires magnetic properties very slowly ; and, to make
the magnetism complete, the steel must be rubbed with one of the poles.
But this magnetism, once evoked in steel, is permanent, and does not dis-
appear when the inducing force is removed.

These different effects in soft iron and steel arc ascribed to a kind of
resistance analogous to friction which is often called coercive force, and which,
in a magnetic substance, offers a hindrance to the separation of the two
magnetisms, but which also prevents their recombination w^hen once sepa-
rated. In steel this coercive force is very great ; in soft iron it is very small
or almost absent. By oxidation, stretching, pressure, torsion, or hammering,
etc., a certain amount of coercive force may be imparted to soft iron ; and
by heat the coercive force may be lessened, as will be afterwards seen.

688. Difference bet\ireen magrnets and magnetic substances. — JLn^-
nctic substatiics arc sul)slanccs which, like iron, steel, and nickel, arc attracted
l)y the magnet, 'ihey contain the two magnetisms, but in a state of neu-
tralisation. Compounds containing iron are usually magnetic, and the more
so in proportion as they contain a larger quantity of iron. Some, however
like iron pyrites, are not attracted by the magnet.

A magnetic substance is readily distinguished from a magnet. The
former has no poles ; if successively presented to the two ends of a magnetic

-688] Difference between Magnets and Magnetic Substances. 655

needle, ab (fig. 627), it will attract both ends equally, while with one and the
same end a ma^'^net would attract the one end of the needle, but repel the
other. Magnetic substances also have no action on each other; while mag-
nets attract or repel each other, according as unlike or like poles are pre-
sented. Attraction is no proof that a body is a magnet ; repulsion is.

Iron is not the only substance which possesses magnetic properties ;
nickel has considerable magnetic power, but far less than that of iron ; cobalt
is less magnetic than nickel ; while to even a slighter extent chromium and
manganese are magnetic. Further, we shall see that powerful magnets exert
a peculiar influence on all substances.

In the magnetic but unmagnetised condition the molecular magnets are
arranged quite irregularly, and their mutual action neutralises one another,
so that there is no action on an external body. But if they are acted on by
any magnetising power, a magnet, for example, the effect is to give the
molecular magnets a direction parallel to those of the magnet, and as soon
as more molecular magnets set in one certain direction than in another, the
magnet shows polarity ; this polarity increases the more any one direction
preponderates, and reaches a maximum when all the molecular magnets set
in one direction.

656 On Magnetism. [689-

CHAPTER II.

TERRESTRIAL MAGNETISM. COMPASSES.

689. Directive action of the earth on magnets.— When a magnetic

needle is suspended by a thread, as represented in fig. 628, or is placed

on a pivot on which it can move freely (fig. 632), it ultimately sets in a

position which is more or less north and

.^ south. If removed from this position it

always returns to it after making a certain

number of oscillations.

Analogous observations have been made
in different parts of the globe, from which the
earth has been compared to an immense mag-
net, whose poles are very near the terrestrial
poles, and whose neutral line virtually coin-
cides with the equator.

The polarity in the northern hemisphere
is called the norf/tcrn or boreal polarity, and
that in the southern hemisphere the southern
'^' ^^" ox austral Yio\?ix\\.y. In French works the end

of the needle pointing north is called the austral or southern pole, and that
pointing to the south the boreal or northern pole ; a designation based on
this hypothesis of a terrestrial magnet, and on the law that unlike magnet-
isms attract each other. In practice it will be found more convenient to
use the English names, and call that end of the magnet which points to the
north the north pole., and that which points to the south the south pole ; the
north pole of a magnet is a 7iorth-seeking pole, and a south pole a south-seek-
ing pole. Tc avoid ambiguity, that end of the needle pointing north is in
England sometimes spoken of as the jnarked end of the needle (68 1 ).

690. Terrestrial mag-netlc couple. — From what has been stated, it is
clear that the magnetic action of the earth on a magnetised needle may be
compared to a couple ; that is, to a system of two c(|ual forces, parallel, but
acting in contrary directions.

For let ab (fig. 633) be a movable magnetic needle making an angle with
the magnetic meridian M'M (6gi). The earth's north pole acts attractively
on the marked pole, «, and repulsively on the other pole, b., and two contrary
forces are produced, an and bn\ which are equal and parallel : for the
terrestrial pole is so distant, and the needle so small, as to justify the assump-
tion tliat the two directions an and bn' are parallel, and that the two poles
arc e(|uidistant from the earth's north pole. Ihit the earth's south pole acts
similarly on the jjoles of the needle, and produces two other forces, ^/j and/'.y,
whii h arc also e(|ual and parallel ; but the two forces an and as may be re-

Fig. 633.

-691] Magnetic Eieinents. Declination. 657

duced to a single resultant ^N {t,^), and the forces bn' and bs' to a resultant
/'S ; the two forces aN and bS are equal, parallel, and act in opposite direc-
tions, and they constitute the terrestrial magnetic couple ; it is this couple
which makes

the needle set „ _, ^ . ,

ultimately in

the magnetic ^r!_

meridian— a po- ------.v.-^v^pg^— :.-;-;=.. j^

sition in which ,.----

the two forces -r-

N and S are in
equilibrium.

The force which determines the direction of the needle thus is neither
attractive nor repulsive, but simply directive. It has no horizontal com-
ponent. If a small magnet be placed on a cork floating in water, it will at
first oscillate, and then gradually set in a line which is virtually north and
south. But if the surface of the water be quite smooth, the needle will not
move either towards the north or towards the south.

If, however, a magnet be approached to a floating needle, attraction or
repulsion ensues, according as one or the other of the poles is presented.
The reason of the different actions exerted by the earth and by a magnet on
a floating needle is as follows : — When the north pole, for instance, of the
magnet is presented to the south pole of the needle, the latter is attracted ;
it is, however, repelled by the south pole of the magnet. Now the force of
magnetic attraction or repulsion decreases with the distance ; and, as the dis-
tance between the south pole of the needle and the north pole of the magnet
is less than the distance Ijetween the south pole of the needle and the south
pole of the magnet, the attraction predominates over the repulsion, and the
needle moves towards the magnet. But the earth's magnetic north pole is
so distant from the floating needle that its length may be considered in-
finitely small in comparison, and one pole of the needle is just as strongly
repelled as the other is attracted.

The action of the earth on a magnet has also no component which is
directed vertically ; for if a steel bar be carefully equipoised and then
magnetised there is not the least alteration in the weight.

691. Magnetic elements. Declination, — In order to obtain a full
knowledge of the earth's magnetism at any place, three essentials are re-
quisite ; these are — i. Declination ; ii. Inclination ; iii. Force or Intensity.
These three are termed the magnetic elements of the place We shall explain
them in the order in which they stand.

The geographical meridian of a place is the imaginary plane passing
through this place and through the two terrestrial poles, and the meridian
is the outline of this plane upon the surface of the globe. Similarly the
magnetic meridian of a place is the vertical plane passing at this place
through the two poles of a movable magnetic needle in equilibrium about its
vertical axis.

In general the magnetic meridian does not coincide with the geogra-
phical meridian, and the angle which the magnetic makes with the geogra-
phical meridian— that is to say, the angle which the direction of the needle

U U

658

On Magnetism.

[691-

makes with the meridian — is called the declination or variation of the mag-
netic needle. The declination is said to be east or ivest^ according as the
north pole of the needle is to the east or west of the geographical meridian.

692. Variations in declination. — The declination of the magnetic
needle, which varies in different places, is at present west in Europe and in
Africa, but east in Asia and in the greater part of North and South America.
It shows further considerable variations even in the same place. These varia-
tions are of two kinds ; some are regular, and are either secular, annual,
or diurnal ; others, which are irregular, are called magnetic storms (694).

Secular variations. — In the same place the declination varies in the
course of time, and the needle appears to make oscillations to the east and
west of the meridian, the duration of which extends over centuries. The
declination has been known at Paris since 1580, and the following table
represents the variations which it has undergone : —

Year

Declination

Year

Declination

1580

ii°3o'E.

1835

22° 4'W.

1663

0°

1850

20° 30' W.

1700

8° 10' W.

1855

19° 57' W.

1780

i9°55'W.

i860

19° 32' w.

1785

22° 00' W.

1865

i8°44'W.

1805

22° 5'W.

1875

i7°2i'W. .

1814

22° 34' w.

1880

16° 53' w.

1825

22° 22' W.

1883

16° zi>' w.

1830

22° 12' W.

1888

i5°58'W.

This table shows that since 1580 the declination has varied at Paris as
much as 34°, and that the greatest westerly declination was attained in 1814,
since which time the needle has gradually tended towards the east.

At London the needle showed in 1580 an easterly declination of 1 1° 36' ;
in 1663 it was at zero ; from that time it gradually tended towards the west,
and reached its maximum declination of 24° 41' in 1818 ; since then it has
steadily diminished ; it was 22° 30' in 1850, 19° 32' in 1873, I9° 24' in 1874,
19° 16' in 1875, 19° 10' in 1876, 19° 3' in 1877, 18° 52' in 1878, 18° 40'in
1881, 18^ 15' in 1883, and is now (1889) 17° 42' W.

At Yarmouth and Dover the variation is about 40' less than at London ;
at Hull and Southampton about 20' greater ; at Newcastle and Swansea
about 1'^ 45,' and at Liverpool 2° o', at Edinburgh 3° o', and at Glasgow and
Dublin about 3° 50' greater than at London.

The following are the observations of the magnetic elements at Kew
extending over twenty years : —

■ Year

Declination

Inclination

Horizontal
force

1865
1869
1872
1875
1878

20° 59'

20° 32,'
20° 0'
19° 41'
19° 14'

68° 7'
68° 2'
67° 54'
67° 48'
67° 44'

3-829
3-848
3-869
3-885

3-895 1

693]

A nnual Variations.

659

Year

Declination

Inclination

HorizoBtal
force

1879
1880
1881
1882
1883
1884
1885

19° 6'
i8° 59'

18° 50'

18° 45'
18° 41'
18° 32'
18° 26'

67° 42'
67" 42'
67° 41'
67° 41'
67° 41'

67° 39'
67° 38'

3-900
3-899
3-903
3-904
3-909
3-916
3-917

In certain parts of the earth the magnet coincides with the geographical
meridian. These points are connected by an irregularly curved imaginary
line, called a line of tio vatiation or agofiic line. Such a line cuts the east
of South America, and, passing east of the West Indies, enters North
America near Philadelphia, and traverses Hudson's Bay ; thence it passes
through the North Pole, entering the Old World east of the White Sea,
traverses the Caspian, cuts the east of Arabia, turns then towards Australia,
and passes through the South Pole, to join itself again.

hogonic lines are lines connecting those places on the earth's surface in
which the declination is the same. The first of the kind was constructed in
1700 by Halley ; as the elements of the earth's magnetism are continually
changing, the course of such a line can only be determined for a certain time.
Maps on which such isogenic lines are depicted are called declination
or variation maps \ and a comparison of these in various years is well fitted
to show the variation which this magnetic element undergoes. Plate III.
represents a map on Mercator's projection giving these lines for the year 1882,
It will be seen that the surface of the globe is divided by these lines into two
regions : one, the smaller, in which the variation is westerly, as indicated by
the continuous lines ; the other, in which the variation is easterly, as indicated
by the dotted lines. This chart is useful to the mariner as not only giving
him the declination in any place, but also as showing him the places on the
globe where the declination changes most rapidly. Of these the most
remarkable are the coast of Newfoundland, the Gulf of St. Lawrence, the
seaboard of North America, and the English Channel and its approaches.

693. Annual variations. — Cassini first discovered in 1780 that the
declination is subject to small annual variations. At Paris and London it is
greatest about the vernal equinox, diminishes from that time to the summer
solstice, and increases again during the nine following months. It does not
exceed from 15' to 18', and it varies somewhat at different epochs.

The diurnal variatio7is were first discovered by Graham in 1722 ; they
can only be observed by means of long needles or delicate indicators such
as the reflection of a ray of light (522) and very sensitive instruments (702).
In this country the north pole moves ever)' day from east to west from sun-
rise until one or two o'clock ; it then tends towards the east, and at about
ten o'clock regains its original position. During the night the needle is
almost stationary. Thus the westerly declination is greatest during the
warmest part of the day.

At Paris the mean amplitude of the diurnal variation from April to

u u 2

66o

0)1 Mao;netisni.

[693

September is from 13' to 15', and for the other months from 8' to 10'. On
some days it amounts to 25', and on others does not exceed 5'. The greatest
variation is not always at the same time. The ampHtude of the daily varia-
tions decreases from the poles towards the equator, where it is very feeble.
Thus in the island of Rewak it never exceeds 3' to 4'.

694. Accidental variations and perturbations. — The declination is
accidentally disturbed in its daily variations by many causes, such as earth-
quakes, the aurora borealzs, and volcanic eruptions. The effect of the aurora
is felt at great distances. Auroras, which are only visible in the most northerly
parts of Europe, act on the needle even in these latitudes, where accidental
variations of 1° or 2° have been observed. In polar regions the needle fre-
quently oscillates several degrees ; its irregularity on the day before the aurora
borealis is a presage of the occurrence of this phenomenon.

Another remarkable phenomenon is the simultaneous occurrence of
magnetic perturbations in very distant countries. Thus Sabine mentions
a magnetic disturbance which was felt simultaneously at Toronto, the Cape,
Prague, and Van Diemen's Land. Such simultaneous perturbations have
received the name of magnetic storms (702).

695. Declination compass. — The declination compass is an instrument
by which the magnetic declination of any place may be determined when

its astronomical meridian is
known. The form repre-
sented in fig. 634 consists of
a brass box, AB, in the bot-
tom of which is a graduated
circle, M. In the centre is a
pivot on which oscillates a
very light lozenge-shaped
magnetic needle, ah. To the
box are attached two uprights
supporting a horizontal axis,
X, on which is fixed an
astronomical telescope, L,
movable in a vertical plane.
The box rests on a foot, P,
about which it can turn in a
horizontal plane, taking with
it the telescope. A fixed
circle, QR, which is called
the azimuthal circle, mea-

T sures the number of degrees
through which the telescope
has been turned, by means
of a vernier, V, fixed to the
box. The inclination of the
telescope, in reference to the
horizon, maybe measured liy

ixis of the telescope, and is read

^^^►:lv» vt,r

Fig. 634.

another vernier, K, which moves
off on a fixed graduated arc, jr.

itii the

-697]

Mariners Compass.

66 1

The first thing in determining the declination is to adjust the compass
horizontally by means of the screws SS, and the level n. The astronomical
meridian is then foimd, either by an observation of the sun at noon exactly,
or by any of the ready methods known to astronomers. The box AB is
then turned until the telescope is in the plane of the astronomical meridian.
The angle made by the magnetic needle with the diameter N, which corre-
sponds with the zero of the scale, and is exactly in the plane of the telescope,
is then read off on the graduated limb, and this is east or west, according as
the pole a of the needle stops at the east or west of the diameter N.

696. Correction of errors. — These indications of the compass are only
correct when the magnetic axis of the needle — that is, the right line passing
through the two poles — coincides with its axis of figure, or the line connect-
ing its two ends. This
is not usually the case,
and a correction must
therefore be made,
which is done by the
nietJiod of reversion.
For this purpose the
needle is not fixed in
the cap, but merely
rests on it, so that it
can be removed and
its position reversed ;
thus what was before
the lower is now the
upper face. The mean between the observations made in the two cases
gives the true declination.

For, let NS be the astronomical meridian, ab the axis of figure of the
needle, and inn its magnetic axis (fig. 635). The true declination is not the
arc Nrt:, but the arc N;//, which is greater. If now the needle be turned, the
line inn makes the same angle with the meridian NS ; but the north end of
the needle, which was on the right of w;?, is now on the left (fig. 636), so that
the declination, which was previously too small by a certain amount, is now
too large by the same amount. Hence the true declination is given by the
mean of these two observations.

697. Mariner's compass.^ — The magnetic action of the earth has received
its most important application in the mariner's compass. This is a declina-
tion compass used in guiding the course of a ship. Fig. 637 represents a
view of the whole, and fig. 638 a vertical section. It consists of a cylindrical
case, BB', which to keep the compass in a horizontal position in spite of the
rolling of the vessel, is supported on gimbals. These are two concentric
rings, one of which, attached to the case itself, moves about the axis xd which
plays m the outer ring AB, and this moves in the supports PQ, about the
axis w;/, at right angles to the first.

In the bottom of the box is a pivot, on which is placed by means of an
agate cap, a magnetic bar, ab, which is the needle of the compass. On this
is fixed a disc of mica, a little larger than the length of the needle, on which
is traced a star or 7-ose., with thirty-two branches, making the eight points or

Fig. 636.

66:

On Alagnetism.

[697-

rhiimbs of the wind, the demi-rhumbs, and the quarters. The branch ending
in a small star, and called N, corresponds to the bar ab, which is underneath
the disc.

The compass is placed near the stem of the vessel in the binnacle.
Knowing the direction of the compass in which the ship is to be steered, the
pilot has the rudder turned till the direction coincides with the sight-vane

passing through a line d marked on the inside of the box, and parallel with
the keel of the vessel.

The prisniaiic compass is greatly used for surA'eying and more especially
for military purposes ; it differs from the mariner's compass mainly in its
dimensions, and in the Avayin which observations are made. It consists of a
shallow metal box about 2h inches in diameter (fig. 639) ; the needle, which is
fixed below the compass card, plays on a pivot much as in fig. 638. A is a metal
frame across which is stretched a horse-hair, forming a sight-vane. Exactly op-
posite this is a right-angled prism P enclosed ^
in a metal case, with an eyehole and a slit as
represented at the side of the figure (fig. 639).
In order to make an observation the
compass is held horizontally, and so that

•■■';;• f'jS. Kig. 639.

the slit in the prism, the hair of the sight-vanc, antl the distant object are
seen to be in the same line ; looking through the eyehole, the angle which
the needle makes is then noted ; a similar observation is made with another
object, and thus the angle between them, or their bearing, is given.

The sight-vane is connected with a Itvcr, and can l)c turned down when

-698] hidiuation. Magnetic Eqitator. 663

it presses the magnet on the pivot, thus keeping it rigid, so that the compass
can be transported in any position.

As the image is seen through the convex face of the prism it is magnified,
and as it is seen by reflection it is reversed, so that in order to read the figures
correctly they must be reversed on the card ; the reflection being total there
is little loss of light.

698. Inclination. Mag-netlc equator. — It might be supposed from the
northerly direction which the magnet needle takes, that the force actin ^
upon it is situated in a point of the horizon. This is not the case, for if the
needle be so arranged that it can move freely in a vertical plane about a hori-
zontal axis, it will be seen that, although the centre of gravity of the needle
coincides with the centre of suspension, the north pole in our hemisphere dips
downwards. In the other hemisphere the south pole is inclined downwards.
The angle which the magnetic needle makes with the horizon, when the
vertical plane, in which it moves, coincides with the magnetic meridian, is
called the inclination or dip of the needle. In any other plane than the
magnetic meridian the inclination increases^ and is 90° in a plane at right
angles to the magnetic meridian. For the magnetic inclination represents
the direction of the total magnetic force, and may be resolved into two
forces, one acting in a horizontal and the other in a vertical plane. When
the needle is moved so that it is at right angles to the magnetic meridian,
the horizontal component can only act in the direction of the axis of suspen-
sion, and therefore cannot affect the needle, which is then solely influenced
by the vertical component, and stands vertically. The following considera-
tions will make this clearer : —

Let NS (fig. 640) represent a magnetic needle capable of moving in a
vertical plane. Let NT represent, in direction and intensity, the entire
force of the earth's magnetism acting
on the pole N. Then NT can be re-
solved into the forces N/; and N V ; TNA
being^ the angle of inclination or dip.

NT is termed the total force M ; and
its components are N/;, or the horizontal
force H, and NV, or the vertical force Z. Fig. 640.

Now, it is clear that the greater the angle of dip, TN/:, the less becomes
N//, or the horizontal force, and the greater NV, or the vertical force.
Hence, in high latitudes the directive force of a compass, which depends on
the horizontal force, is less than in low latitudes. At the magnetic poles the
horizontal force will be «//, and the vertical force a maximum ; here, there-
fore, the needle will be vertical. At the magnetic equator the reverse is the
case, and the needle will be horizontal. Hence, the oscillations of a compass
needle, by which, as will presently be explained, the strength of the earth's
magnetism is measured, become fewer and fewer in a given time as the
magnetic poles are approached, although there is really an increase in the
total force of the earth.

Again, the reason why a dip needle stands vertical when placed E.
and W. is clearly because in those positions the horizontal force now acting
at right angles to the plane of motion of the needle is ineffectual to move it,
and therefore merely produces a pressure on the pivot which supports the
needle. But the vertical component of the total force remains unaffected

664

On Alairnetisni.

[698

by the new position of the needle. Acting, therefore, entirely alone when
the dip needle is exactly E. and W., this vertical component drags the
needle into a line with itself ; that is, 90° from the horizontal plane.

The value of the dip, like that of the declination, differs in different
localities. It is greatest in the polar regions, and decreases with the latitude
to the equator, where it is approximately zero. In London at the present tmie
(1889) the dip is 67° 26', reckoning from the horizontal line. In the southern
hemisphere the inclination is again seen, but in a contrary direction ; that is,
the south pole of the needle clips below the horizontal line.

The magnetic poles are those places in which the dipping-needle stands
vertical ; that is, where the inclination is 90°. In 1830 the first of these, the
terrestrial north pole, was found by Sir James Ross in 96° 43' west longitude
of 70° north latitude. The same observer found in the South Sea, in 76°
south latitude and 168° east longitude, that the inclmation was 88° 2,1'- From
this and other observations, it has been calculated that the position of the
magnetic south pole was at that time in about 1 54° east longitude and 75^°
south latitude. The line of no declination passes through these poles, and
the lines of equal declination converge towards them.

The niagnetic equator, or aclinic line, is the line which joins all those
places on the earth where there is no dip ; that is, all those in which the
dipping-needle is quite horizontal. It is a somewhat sinuous line, not differ-
ing much from a great circle inclined to the equator at an angle of 12°, and
cutting it on two points almost exactly opposite each other — one in the
Atlantic, and one in the Pacific. These points appear to be gradually moving
their position, and travelling from east to west.

Lines connecting places in which the dipping-needle makes equal angles
are called isoclinic lines. They have a certain analogy and parallelism with
the parallels of latitude, and the term niagnetic latitude is sometimes used to
denote positions on the earth with reference to the magnetic dip. Plate IV.
is an inclination map for the year 1882, the construction of which is quite
analogous to that of the map of declination.

The inclination is subject to secular variations, like the declination, as is
readily seen from a comparison of maps of inclination for different epochs.
At Paris, in 1671, the inclination was 75° ; since then it has been continually
decreasing : in 1835 it was 67° 24'; in 1849, 67° ; in 1859, 66° 16' ; in 1869,
65° 43' ; in 1879, 65° 32' ; in 1883, 65° 17' ; and in 1888, 65° 14'.

The following table gives the alterations in the inclination at London,
from which it will be seen that since 1723, in which it was at its maximum, it
has continually diminished by something more than two minutes in each year.

Year
1576

Iiicliiiatioii

Veiir

Inclination

7.° 50'

1828

69° 47' ,

1600

72°

1838

69° 17'

1676

If 30'

1854

68° 31'

^T-l

74° 42'

1859

68° 21'

1773

72° 19'

IS74

67° 43'

1780

72° 8'

1876

67° 39'

1790

71° 33'

1878

67° 36'

1800

70° 35'

1880

67' 35'

1821

70° 31'

I88I

67° 35'

-699] Inclhiatioft CoDipass. 665

699. Inclination compass. — An inclination compass, or dip 7iecdlc, is an
instrument for measuring the magnetic inclination or dip. One form, repre-
sented in fig. 641, though not best adapted for the most accurate measure-
ments, is well suited for illustrating the principle. It consists of a graduated
horizontal brass circle w, supported on three legs, provided with levelling
screws. Above this circle there is a plate A, movable about a vertical axis,
and supporting, by means of two columns, a second graduated circle M, which
measures the inclination. The needle rests on a frame r, and the diameter
passing through the two zeros of the circle N can be ascertained to be
perfectly horizontal by means of the spirit-level /i.

To observe the inclination, the magnetic meridian must first be deter-
mined, which is effected by turning the plate A on the circle ;«, until the
needle is vertical, which is the case when it is in a plane at right angles to
the magnetic meridian (698). The plate A is then turned 90° on the circle
in, by which the ^•ertical circle M is brought into the magnetic meridian.
The angle dca, which the magnetic needle makes with the horizontal dia-
meter, is the angle of inclination.

There are here several sources of error, which must be allowed for. The
most important are these : — i. The magnetic a.xis of the needle may not
coincide with its axis of figure :
hence an error which is cor-
rected by a method of reversion
analogous to that already de-
scribed (696). ii. The centre of
gravity of the needle, may not
coincide with the axis of suspen-
sion, and then the angle dca is
too great or too small, according
as the centre of gravity is below
or above the centre of suspen-
sion ; for in the first case the
action of gravity is in the same
direction as that of magnetism,
and in the second it is in the
opposite direction. To correct
this error, the poles of the
needle must be reversed by first
demagnetising it, and then im-
parting a contrary magnetism
to what it had at first. The
inclination is now re-determined,
and the mean taken of the re- ^...^ ^ ^

suits obtained in the two groups

of operations, iii. The plane of the ring may not coincide with the true mag-
netic meridian. It should be in that plane when the needle has its minimum
deviation ; an observation of this kind should therefore be taken along with
that previously described, by which the needle is moved 90° from its maxi-
mum deviation.

The dip needle may be used to determine the inclination in another

666

On Magnetism.

[699-

way. It is first allowed to oscillate in the magnetic meridian, and then in
a plane at right angles to it. If the number of oscillations m a given time
in the first position be 7i, and in the second position «,, then in the first position
the whole force of the earth's magnetism E acts, and in the second posi-
tion only the vertical component, which is E sin x, x being the angle of dip.
Now, since the forces acting on the needle are, from the laws of the pendulum
(55), as the squares of the number of oscillations in a given time, we have

■ ; = — . from which sin x= -^.

E sm X n~ n-

700. Astatic needle and astatic system. — An astatic needle is one
which is uninfluenced by the earth's magnetism. A needle movable about
an axis in the plane of the magnetic meridian and parallel to the inclination
would be one of this kind ; for the terrestrial magnetic couple, acting then
in the direction of the axis, cannot impart to the needle any determinate
direction.

An astatic system is a combination of two needles of the same force
joined parallel to each other with the poles in contrary directions, as shown
in fig. 642. If the two needles have exactly the
same magnetic force, the opposite actions of the
earth's magnetism on the poles a' and b and on
the poles a and b' counterbalance each other ; the
system is then completely astatic, and sets at right
angles to the magnetic meridian.

A single magnetic needle may also be rendered
astatic by placing a large magnet near it. By
repeated trials a certain position and distance can
be found at which the action of the magnet on the
needle just neutralises that of the earth's magnetism,
and the needle is free to obey any third force ; in
other words, the field due to the magnet just neutralises the earth's field.

701. Force of the earth's magnetism. — If a magnetic needle be
moved from its position of equilibrium, it will revert to it after a series of
oscillations, which follow laws analogous to those of the pendulum (80). If
the magnet be removed to another place, and caused to oscillate during
the same length of time as the first, a different number of oscillations
will be observed. And the earth's magnetic force in the two places will be
respectively proportional to the squares of the number of oscillations.

If at M the number of oscillations in a minute had been 35 =;;, and at
another place M', 24 = ;/', we should have —

Fig. 642.

1-085.

Force of the earth's magnetism at M _ «^ _ 625
Force of the earth's magnetism at M' »/ 576

That is, if the force of the magnetism at the second place is taken as unity,
that of the first is 1*085. ^f the magnetic condition of the needle had not
changed in the inter\al between the two obscr\ations, this method would
give the relation of the force at the two places.

In these determinations of the force, it would be necessary to have the
oscillations of the dip-needle, which are produced by the total force of
the earth's magnetism. These, however, are difiicult to obtain with

-702] Magnetic Observatories. 66y

accuracy, and therefore those of the declination needle are usually taken.
The force which makes the declination needle oscillate is only a portion
of the total magnetic force, and is smaller in proportion as the inclination
is greater. If a line nc=M (fig. 643) represent the total force, the angle i
the inclination, then the horizontal component ab = H is M cos i. Hence, to
express the total force in the two places by the oscillations of the declina-
tion needle, we must substitute the values M cos i and M' cos i' for M and
IVr in the preceding equation, and we have — t

M cos t n- ■, M «^ cos z 177

TTTT •/=,-.; hence =_— . . NX

M' cos t n- M' n~ cos z . \.

That is 'to say, having obsei-ved in two different places the; \

number of oscillations, 71 and «', that the same needle makes in I \

the same time, the ratio of the magnetic force in the two places j \

will be found by multiplying the ratio of the square of the 1

number of oscillations by the inverse ratio of the cosine of the ~

angle of dip. ^'^•^+3.

Plate V. is a chart representing the horizontal component of the earth's
force. Knowing the angle of dip z, the total force M, or the vertical force Z,
in any place, may be obtained from the values in the chart by the formula
M = H sec i ; and Z = H tan z.

The total force is least near the magnetic equator, and, increasing with
the latitude, is greatest near, but not quite at, the magnetic poles ; the places
of maximum intensity are conveniently named the magiietic foci. The chart
shows that the horizontal force diminishes as we go towards the poles : this
is not inconsistent with the above statement if we take the dip into account
(698).

The lines connecting places of equal force are called isodynamic lines.
They are not parallel to the magnetic equator, but seem to have about the
same direction as the isothermal lines. According to Kuppfer, the force
appears to diminish as the height of the place is greater ; a needle which
made one oscillation in 24" vibrated more slowly by o-oi" at a height of
1,000 feet : but, according to Forbes, the force is only ^~ less at a height
of 3,000 feet. There is, however, some doubt as to the accuracy of these
observations, owing to the uncertainty of the correction for temperature.

The intensity varies in the same place with the time of day : it attains its
maximum between 4 and 5 in the afternoon, and is at its minimum between
10 and II in the morning.

According to Gauss, the total magnetic action of the earth is the same as
that which would be exerted if in each cubic yard there were eight steel
bar magnets each weighing a pound.

It is probable, though it has not yet been ascertained with certainty, that
the force undergoes secular variations. From measurements made at Kew,
it appears that on the whole, the total force experiences a very slight annual
increase (692).

702. ivxagrnetic observatories.^ — During the last few years great atten-
tion has been devoted to the observation of the magnetic elements, and obser-
vatories for this purpose have been fitted up in different parts of the globe.
These observations have led to the discovery that the magnetism of the earth
is in a state of constant fluctuation, like the waves of the sea. And in study-
ing the variations of the declination, (S:c., the mean of a great number of

668 On Magnetism. [702-

observations must be taken, so as to eliminate the irregular disturbances,
and bring out the general laws.

The principle on which magnetic observations are automatically recorded
is as follows : — Suppose that in a dark room a bar magnet is suspended
horizontally, and at its centre is a small mirror ; suppose further that a lamp
sends a ray of light to this mirror, the inclination of which is such that the ray
is reflected, and is received on a horizontal drum placed underneath the lamp.
The axis of the drum is at right angles to the axis of the magnet ; it is covered
with sensitive photographic paper, and is rotated uniformly by clockwork.
If now the magnet is quite stationary, and the drum rotates, the reflected
spot of light will trace a straight line on the paper with which the revolving
drum is covered. But if, as is always the case, the position of the magnet
varies during the twenty-four hours, the effect will be to trace a sinuous line
on the paper. These lines can afterwards be fixed by ordinary photographic
methods. Knowing the distance of the mirror from the drum, and the length
of the paper band which comes under the influence of the spot of light in a
given time — twenty-four hours, for instance — the angular deflection at any
given moment may be deduced by a simple calculation (522).

The observations made in the English magnetic observatories were
reduced by Sabine, and revealed some curious facts in reference to mag-
netic storms (694). He found that there is a certain periodicity in their
appearance, and that they attain their greatest frequency about every ten
years. Independently of this, Schwabe, who for many years studied the- sub-
ject, found that the spots on the sun, seen on looking at it through a
coloured glass, vary in their number, size, and frequency, but attain their
maximum about every ten or eleven years. Now Sabine established the
interesting fact that the period of their greatest frequency coincides with the
period of greatest magnetic disturbance. Other remarkable connections
between the sun and terrestrial magnetism have been observed ; one,
especially, of recent occurrence has attracted considerable attention. It was
the flight of a large luminous mass across a vast sun-spot, while a simul-
taneous perturbation of the magnetic needle was observed in the observatory
at Kew : subsequent examination of magnetic observations in various parts
of the world showed that within a few hours one of the most violent magnetic
storms ever known had prevailed.

It seems, however, that these accidental variations in the declination can-
not be due to changes in any direct action of a possible magnetic condition
of either the sun or the moon. For it can be shown that if the magneti-
sation of the latter were as powerful as that of the earth, the deflection
which it could produce would not amount to the ?,^\\\ of a second, a quantity
which cannot be measured. In order to produce a variation of 10', such
as is frequently met with, the magnetisation of the sun or of the moon
must be 12,000 times that of the earth ; in other words, a more powerful de-
gree of magnetisation than that of powerfully magnetised steel bars.

Magnetic storms are nearly always accompanied by the exhibition of the
aurora borealis in high latitudes ; that this is not universal may be due to
the fact that many auroras escape notice. The converse of this is true, that
no great display of the aurora takes place without a violent magnetic storm.
The centre or focus towards which the rays of the aurora converge lies
approximately in tlic prolongation of the direction of the dipping-needle.

704]

669

CHAPTER III.

LAWS OF MAGNETIC ATTRACTION AND REPULSION.

703. law of decrease witb distance. — Coulomb discovered the remark-
able law in reference to magnetism, t]iat magnetic attractions and repulsions
are inversely as the squares of the distances. He proved this by means of
two methods : — (i.) that of the torsion balance, and (ii.) that of oscillations.

704. i. The torsion balance. — This apparatus depends on the principle
that, when a wire is twisted through a certain space, the angle of torsion is
proportional to the force of torsion
(89). It consists (fig. 644) of a
glass case closed by a glass top,
with an aperture near the edge,
to allow the introduction of a mag-
net, A. In another aperture in the
centre of the top a glass tube fits,
provided at its upper extremity
with a micrometer. This consists
of two circular pieces : f?, which is
fixed, is divided on the edge into
360^, while on one ^, which is mov-
able, there is a mark, ^, to indicate
its rotation. D and E represent
the two pieces of the micrometer
on a larger scale. On E there
are two uprights connected by a
horizontal axis, on which is a very
fine silver wire supporting a mag-
netic needle, ab. On the side of

Fig. 644.

the case there is a graduated scale, which indicates the angle of the needle
rt/5, and hence the torsion of the wire.

When the mark c of the disc E is at zero of the scale D, the case is so
arranged that the wire supporting the needle and the zero of the scale in the
case are in the magnetic meridian. The needle is then removed from its
stirrup, and replaced by an exactly similar one of copper, or any unmagnetic
substance ; the tube, and with it the pieces D and E,are then turned so that
the needle stops at zero of the graduation. The magnetic needle ab., being
now replaced, is exactly in the magnetic meridian, and the wire e.xerts no
torsion.

Before introducing the magnet A, it is necessary to investigate the action
of the earth's magnetism on the needle ab. when the latter is removed out of

6/0 On Magnetism. [704-

the magnetic meridian. This will vary with the dimensions and force of the
needle, with the dimensions and nature of the particular wire used, and with
the intensity of the earth's magnetism in the place of observation. Accord-
ingly, the piece E is turned until ab makes a certain angle with the magnetic
meridian. Coulomb found in his experiments that E had to be turned 36°
in order to move the needle through 1° ; that is, the earth's magnetism was
equal to a torsion of the wire corresponding to 35°. As the force of torsion
is proportional to the angle of torsion, when the needle is deflected from the
meridian by 2, 3 . . . degrees, the directive action of the earth's magnetism
is equal to 2, 3 . . . times 35°.

The action of the earth's magnetism having been determined, the magnet
A is placed in the case so that similar poles are opposite each other. In one
experiment Coulomb found that the pole a was repelled through 24°. Now
the force which tended to bring the needle into the magnetic meridian
was represented by 24° + 24 x 35 = 864, of which the part 24° was due to the
torsion of the wire, and 24 x 35° was the equivalent in torsion of the directive
force of the earth's magnetism. As the needle was in equilibrium, it is clear
that the repulsive force which counterbalanced those forces must be equal
to 864°. The disc was then turned until ab made an angle of 1 2°. To effect
this, eight complete rotations of the disc were necessary. The total force
which now tended to bring the needle into the magnetic meridian was com-
posed of: — 1st, the 12° of torsion by which the needle was distant from its
starting point ; 2nd, of 8 x 360° = 2880, the torsion of the wire ; and 3rd, the
force of the earth's magnetism, represented by a torsion of 12 x 35°. Hence
the forces of torsion which balance the repulsive forces exerted^at a distance
of 24° and of 1 2° are —

24° ... . 864

12° ... . 3312

Now, 3312 is very nearly four times 864 ; hence for half the distance the
repulsive force is four times as great.

705. ii, Metbod of oscillations. — A magnetic needle oscillating under
the influence of the earth's magnetism may be considered as a pendulum,
and the laws of pendulum motion apply to it (55). The method of oscilla-
tions consists in causing a magnetic needle to
oscillate first under the influence of the earth's
magnetism alone, and then successively under the
combined influence of the earth's magnetism and
of a magnet placed at unequal distances.
y The following determination by Coulomb will

I illustrate the use of the method. A magnetic needle

] was used which made 1 5 oscillations in a minute

_A \ under the influence of the earth's magnetism alone.

ji.ll '"■' A magnetic bar about 2 feet long was then placed

vertically in the plane of the magnetic meridian,

'*'■ '■''■■ so that its north ])ole was downwards and presented

to the south pole 0 of the oscillating needle (fig. 645), so as to concur in its

action with that of the earth. He found that at a distance of 4 inches the

needle made 41 oscillations in a minute, and at a distance of 8 inches 24

-706] Magnetic Curves. '671

oscillations. Now, from the laws of the pendulum (55), the intensities of the
forces are inversely as the squares of the times of oscillation. Hence, if
we call M the force of the earth's magnetism, ?n the attractive force of the
magnet at the distance of 4 inches, tii' at the distance of 8 inches, we have

M : M + w = 15* 141^ and
M : M + in' =15'^: 24',
eliminating I\I

»i : w' = 4i-- 15- : 24-- 15-= 1456 : 351 =4 : I nearly,

or ;// : m' = 4 : i.

In other words, the force acting at 4 inches is quadruple that which acts at
double the distance.

The above results do not quite agree with the numbers required by the
law of inverse squares. But this could only be expected to apply in the case
in which the repulsive or attractive force is exerted between two points, and
not, as is here the case, between the resultant of a system of points. And it
is to this fact that the discrepancy between the theoretical and observed
results is due.

When a magnet acts upon a mass of soft iron, the law of the variation
with the distance is modified. The attraction in this case is inversely pro-
portional to the distance between the magnet and the iron.

When the distance between the magnet and the iron is small, Tyndall
found that the attraction is directly proportional to the square of the strength
of the magnet ; but when the iron and the magnet are in contact, then the
attraction is directly proportional to the strength of the magnet.

706. Magnetic curves. — If a stout sheet of paper stretched on a frame
be held over ;i h ' .... ^ j^.^^^ filings be

Fig. 646.

strewn on the paper, on tapping the frame the filings will be found to arrange
themselves in thread-like curved lines, stretching from pole to pole (fig. 646).
These lines form what are called 7nagnetic curves. The direction of the
curve at any point represents the direction of the lines of magnetic force at
this point.

6/2 On Magnetism. [706-

To render these curves permanent, the paper on which they are formed
should be waxed ; if then a hot iron plate be held over them, this melts the
wax, which rises by capillary attraction (131) between the particles of filings,
and on subsequent cooling connects them together. They may also be fixed
by carefully placing on them a sheet of paper coated with paste, which is
then gently pressed and lifted off; it should be quickly dried to prevent the
iron from rusting.

These curves are a graphic representation of the law of magnetic attrac-
tion and repulsion with regard to distance ; for under the influence of the
two poles of the magnet, each particle becomes itself a minute magnet, the
poles of which arrange themselves in a position dependent on the resultant
of the forces exerted upon them by the two poles, and this resultant varies
with the distance of the two poles respectively. A small magnetic needle
placed in any position near the magnet will take a direction which is the
tangent to the curve at this place.

707. Magnetic definitions. — The space in the immediate neighbourhood
of any magnet undergoes some change in consequence of the presence of this
magnet, and such a space is spoken of as a magnetic field ; it is indeed the
sphere of action of the magnet ; the effect produced by the magnet itself is
often spoken of as due to the magnetic field. Magnets of different powers
produce magnetic fields of different intensities. The strength of the field
diminishes with the distance from the magnet.

The direction which represents the resultant of the magnetic forces at
any position in a magnetic field is spoken of as the direction of the lines of
force of this field. In fig. 646 the magnetic curves represent the direction of
the lines of force in the field due to the two opposite poles.

A uniform magnetic field is one in which the lines of force are parallel.
This is practically the case with a small portion of a field at some distance
from a long thin magnet of uniform magnetisation. The dipping-needle,
when free to oscillate in a vertical plane in the magnetic meridian, represents
the direction of the lines of force due to the terrestrial magnetic field. The
strength of the field due to this in any one place is uniform in much the
same sense in which gravity is uniform in any place. A field of unit strength
is one which acts on a unit pole with a force equal to that of a dyne (709).
The strength of any magnetic field is measured by the number of lines of
magnetic force present in the field.

The expression ' lines of force ' or ' lines of magnetic force ' is used in much
the same sense as that in which we speak of rays of light. And just as we
may express the illumination of a surface by the number of rays of light
which fall upon it, so also we may say that the strength of any magnetic
surface is proportional to the number of lines of force which it cuts.

We have seen that in speaking of the pendulum we distinguish between a
simple and a compound one (79). The laws of the pendulum apply in strict-
ness only to the former, which in practice cannot be realised, although we
])ossess arrangemenls which produce the same cfTcct as a simple pendulum,
and are equivalent to it. So too in magnetism we may discriminate between
an ideal and an actual magnet ; the former being considered as a long,
infinitely thin, bar of magnetised molecules, to which only do the laws of
magnetic action in strictness apply, although they can be realised with

-707J Magnetic Definitions. 6jt,

ordinary magnets with sufficient approximation. Thus in the action of
magnets at a distance we may assume that all the magnetism is concen-
trated in the poles, provided that the length is three to four hundred times
the diameter, or provided the fourth power of half the length of the magnet
may be disregarded in comparison with the distance at which it acts (708).

In a magnet the magnetic moment is the product of the length of the
magnet into the strength of one pole.

If a magnetic body be placed in a magnetic field, the intensity of the
magnetisation which it acquires will be proportional to the strength of the
field, and to a coefficient k, which depends on the material itself and which
is called the coefficient of magnetisation. Bodies such as soft iron, which are
readily magnetised, are said to have great susceptibility to magnetisation.

The magnetic moment of a bar divided by its mass represents the
specific magnetism.

The intensity of magnetisation in a bar, assumed to be uniformly
magnetised, is the magnetic moment divided by the volume, that is to say
the weight in grammes divided by the specific gravity.

The ratio of the total magnetic induction to the force producing it has
been called by Sir W. Thomson the magnetic perineability of a substance,
and is represented by the symbol /x. It represents in magnetism the specific
inductive capacity of dielectrics (745), and may be regarded as expressing
the magnetic inductive capacity, or magnetic conductivity for lines of force.

708. Total action of two magrnets on eacb other. — In the above case
of the torsion balance one pole of the magnet to be tested was at so great
a distance that it could not appreciably modify the influence of the other.
When, however, the conditions are such that both poles act, then they follow
a different law, as will now be demonstrated.

Let ns (fig. 647) be a small magnetic needle, free to move in a horizontal
plane, and let NS be a bar magnet placed at right angles to the magnetic
meridian, at a distance which is great compared
with its own dimensions, not less than ten times as
great, and so that the straight line drawn through
its middle point and that of the needle coincides
with the magnetic meridian. In this position the
magnet NS is said to be 'broadside on.' The two
poles S and s will repel each other in the direction
sa ; if mm^ is the repellent force which these two

poles would exert at the unit distance, then — ^' is

the force which they would exert at the distance
Sj- = r; let this force be represented in direction
and strength by the line sa. Similarly, the pole N
will act on j, with a force represented by the line
sc ; S and N being at the same distance r from j-,
sa and sc are equal, and their resultant may be
represented by the line sb. From the similarity of
the triangles (^i-^ and NSj- we have the proportion Sj : SN =rt5- : /;.? ; if
/ is the value of the resultant bs, that is the total action of the magnet
SX on the pole s., and if / be half the length of the magnet SX, we

X X

6/4 Oyt Magnetism. [708-

have r\zl= -"'^ : f, from which /=3^^^; that is, the total action of the

magnet NS upon another magnet is inversely as the cube of the distance r.

If the two magnets be placed 'end on' as represented in fig. 648, the

needle being in the magnetic meridian, and the deflecting magnet at right

71 angles thereto, and so that the pro-
longation of its axis bisects the needle,
then if nun, is the force with which the
pole N attracts the pole s at the unit
distance, 7/1 and ni, being the strength
^'S- 648. Qf |.j^g poles in the bar magnet and

the magnetic needle respectively, the attracting force at the distance Nj will

be "^"'^ , / being, as before, the half-length of the magnet, and ;- the distance

(r+/)-
of the pole J' from the middle of the magnet NS ; in like manner the repellent

force with which S acts upon s willl be -';,. If ns is small compared with

the distance of the bar magnet NS, the direction of these forces may be
assumed to be parallel, and at right angles to ns. Since S is nearer than N
the repulsion will predominate, and the total force with which the magnet
NS acts on the pole s is

F= —

in/n.

which, assuming that / is so small in comparison with r that its square and
higher powers may be neglected, gives approximately

y _4 nivi, I
so that compared with the first position of the magnet

F = 2/

709. Setermlnation of mag'netlsm in absolute measure. — The com-
parisons of the intensity of the earth's magnetism in different places (701)
are only relative. Of late years much attention has been devoted to the
method of expressing not only this, but all other magnetic forces in what is
called absolute measure. This term is used as opposed to relative, and does
not imply that the measure is absolutely accurate, or that the units of com-
parison employed are of perfect construction ; it means that the measure-
ments, instead of being a simple comparison with an arbitrary quantity of the
same kind as that measured, are referred to the fundamental units of time,
length, and mass (21).

The units originally adopted on the proi)osal of the liritish Association,
and now almost universally received, are the second as unit of time, the
centimetre as unit of length, and the gramme as unit of mass. This system
is called the ccntiinctrc-gravime-second, or CCS. system, and units referred
to this system are spoken of as C.G.S. units (61 a).

The manner in which this determination is made in the case of magnet-
ism, depends essentially on the observation of the oscillation of a horizontal

-709J Dctcrmhiatiofi of Magnetism in Absolntc Measure. 675

bar magnet under the influence of the earth's magnetism ; and in the second
place, on observing the deflection of a magnetic needle under the influence
of this same magnet.

When a bar magnet suspended by a thread without torsion, free to oscil-
late in a horizontal plane, is deflected from its position of equilibrium and
then left to itself, it vibrates backwards and forwards through its position of
equilibrium, making oscillations which, if small, are isochronous like those of
the pendulum. The number of these oscillations in a given time depends on the
mass and dimensions of the bar, on its magnetic power, and on the intensity of
the earth's magnetism in the place of obser\ation. The time, /, of a complete

oscillation of such a magnet is represented by the formula t^in xl

where k is the moment of inertia of the magnet ; that is, the mass which
must be concentrated at the unit of distance from the centre of suspension,
to present the same resistance to change of angular velocity, about this centre,
as the magnet itself actually does. The moment of inertia of a magnet may
be determined theoretically if it be homogeneous in structure, and of a
regular geometrical shape ; or it may be determined experimentally by first
observing the time of oscillation of the magnet under the influence of the
earth's magnetism, and then the time when it has been loaded with a mass
the inertia of which is knowTi, and which does not alter the magnetic moment
of the bar. M is the magnetic moment of the bar itself, and H is the force
of the earth's magnetism. Hence

HM^^';^ (I).

This expression gives the force which, applied in opposite directions at
the ends of a lever of unit length, placed at right angles to the direction of
this force, would have the same eftect in tending to turn the lever, as the
magnetic force of the earth has in tending to turn the magnet about a vertical
axis when it is set at right angles to the magnetic meridian.

Now the value of HM depends on the nature of the bar, and on the force
of the earth's magnetism in the place in question. If the bar were mag-
netised more or less strongly, or if the same bar were removed to a different
locality, the product would have a different value. We must, therefore, find
some independent relation between H and AI, which will give rise to a new
equation, and thus M, the magnetic moment of the bar, would be got rid of,
and an absolute value be obtained for H.

Such a relation exists in the deflection from the magnetic meridian, which
a bar magnet produces in a magnetic needle.

If, in the formula in the preceding article, we put M = 2w/, then— '^ =

the + or - force acting on either pole of the magnetic needle, and, as both
poles are acted on, the magnet will be subject to the action of a couple, the

moment of which will be expressed by — — -^ 2/, cos a ; where a is the angle

of deflection, / the half-length of the small magnetic needle ; let M, = 2m J.
In like manner the earth's magnetism will act upon the magnetic needle
with a couple, the moment of which is expressed by Hw, 2/ sin « = HM

X X J

6^6 On Magnetism. [709-

sin a. Now when the needle is in equihbrium these forces are equal ; that
is —

^il!^cosa = HM sina,

from which %— = r' tan a (2).

Combining (i) and (2) we get the expression

« = ?\/.

r^ tan a

an expression which involves no other physical units than those of length
(involved in k and r), mass (involved in y^), and time (involved in /), so that
the value of H can be expressed in absolute measure.

The value for H in this expression only gives the horizontal compo-
nent of the earth's magnetism ; the total force is obtained by dividing the
value of H by the cosine of the angle of dip for the place and time of ob-
servation. This varies on the earth's surface from 0-3 to 07.

The numerical value of H will depend, moreover, on the units taken.
On the C.G.S. system the unit of force is called a dyne. It is (as we have
seen, 61 a) the force which acting upon a gramme for a second g'enerates a
velocity of a centimetre per second. The value of H at Greenwich for the
year 1877, expressed in this unit, is 0-18079 of a dyne; that is, the horizontal
component of the earth's magnetism at this place acting on the unit of
magnetism, associated with one gramme of matter, would produce a velocity
of 0-18079 centimetre at the end of a second. The angle of dip at this
time and place being 67° y]'., we get the total force =0-4745 ""it. If
British units — namely, the foot, grain, second— be employed, the unit of
force is that which by acting for a second on a grain gives to it a velocity
of a foot per second, and the unit magnetic pole is such that if placed one
foot from a second equal pole it will repel it with a force equal to the unit
just defined. To convert the value of H, when expressed in centimetres,
grammes, and seconds, into the equivalent value referred to British units, we
must multiply by 21-69. In like manner, to convert magnetic forces referred
to British units into the corresponding values e.xpressed in centimetres,

grammes, and seconds we must multiply by 0-0461 = - ' -.

2 1 -69
If once the value of H in any locality has been determined it is easy to
determine the value of M for any magnet ; it is by experiments of this kind
that the magnetic movement of minerals is arrived at.

-713]

677

CHAPTER IV.

PROCESSES OF MAGNETISATION.

710. Magnetisation. — The various methods of magnetisation are the
influence of natural or artificial magnets, terrestrial magnetism, and elec-
tricity. This last method will be described under voltaic electricity. The
three principal methods of magnetisation by magnets are known by the
technical names of single toiic/t, sepa?'ate touch, and double touch.

711. Metbod of sing-le toucta. — This consists in moving the pole of a
powerful magnet from one end to the other of the bar to be magnetised, and
repeating this operation several times always in the same direction. The
neutral magnetism is thus gradually decomposed throughout all the length
of the bar, and that end of the bar which was touched last by the magnet is
of opposite polarity to the end of the magnet by which it has been touched.
This method only produces a feeble magnetic power, and is, accordingly,
only used for small magnets. It has further the disadvantage of frequently
developing consequent poles.

712. IKXetbod of separate toucb. — This method, which was first used
by Dr. Knight in 1745, consists in placing the two opposite poles of two
magnets of equal force in the middle of the bar to be magnetised, and in
moving each of them simultaneously towards the opposite ends of the bar.
Each magnet is then placed in its original position and the operation re-
peated. After several frictions on both faces of the bar it is magnetised.

In Knight's method the magnets are held vertically. Duhamel improved
the method by inclining the magnets, as represented in fig. 649 ; and still

Fig. 649.

more by placing the bar to be magnetised on the opposite poles of two fixed
magnets, the action of which strengthens that of the movable magnets. The
relative position of the poles of the magnets is indicated in the figure. This
method produces the most regular magnets.

713. Metbod of double toucb. — In this method, which was invented by
Mitchell, the two magnets are placed with their poles opposite each other
in the middle of the bar to be magnetised. But, instead of moving them in
opposite directions towards the two ends, as in the method of separate touch,

6/8 On Magnetism. [713-

they are kept at a fixed distance by means of a piece of wood placed between
them (fig. 649), and are simultaneously moved first towards one end, then
from this to the other end, repeating this operation several times, and finish-
ing in the middle, taking care that each half of the bar receives the same
number of frictions.

Epinus, in 1758, improved this method by supporting the bar to be mag-
netised, as in the method of separate touch, on the opposite poles of two
powerful magnets, and by inclining the bars at an angle of 15° to 20°. In
practice, instead of two bar magnets, it is usual to employ a horse-shoe
magnet which has its poles conveniently close together.

By this method of double touch, powerful magnets are obtained, but they
have frequently consequent poles. As this would be objectionable in com-
pass needles, these are best magnetised by separate touch.

714. Mag-netisatlon by the action of the earth. — The action of the
earth on magnetic substances resembles that of a magnet, and hence the
terrestrial magnetism is constantly tending to separate the two magnetisms
in soft iron and in steel. But as the coercive force is very considerable in
the latter substance, the action of the earth is inadequate to produce mag-
netisation, except when continued for a long time. This is not the case
with perfectly soft iron. When a bar of this metal is held in the magnetic
meridian parallel to the inclination, the bar becomes at once endowed with
feeble magnetic polarity. The lower extremity is a north pole, and if the
north pole of a small magnetic needle be approached, it will be repelled.
This magnetism is of course unstable, for if the bar be turned the poles are
inverted, as pure soft iron is destitute of coercive force.

While the bar is in this position, a certain amount of coercive force may
be imparted to it by giving it several smart blows with a hammer, and the
bar retains for a short time the magnetism which it has thus obtained. But
the coercive force thus developed is very small, and after a time the mag-
netism disappears.

If a bar of soft iron be twisted while held vertically, or, better, in the
plane of the dip, it acquires a feeble permanent magnetism.

It is this magnetising action of the earth which develops the magnetism
frequently observed in steel and iron instruments, such as fireirons, rifles,
lamp-posts, railings, gates, lightning conductors, &;c., which remain for some
time in a more or less inclined position. They become magnetised with their
north pole downwards, just as if placed over the pole of a powerful magnet.
The magnetism of native black oxide of iron (680) has doubtless been pro-
duced by the same causes ; the very dififcrent magnetic power of different
specimens being partly attributable to the ditiferent positions of the veins of
ore with regard to the line of dip. The ordinary irons of commerce are not
quite pure, and possess a feeble coercive force ; hence a feeble magnetic
polarity is generally found to be possessed by the tools in a smith's shop.
Cast-iron, too, has usually a great coercive force, and can be permanently
magnetised. The turnings, also, of wrought iron and of steel produced by
the powerful lathes of our ironworks are found to be magnetised.

7 1 5. Magrnetlsxn of Iron ships. — The inductive action of terrestrial mag-
netism upon the masses of iron always found in ships exerts a disturbing
action upon the compass needle. The local attraction, as it is called, may

-715] Magnetism of Iron Ships. 679

be so considerable as to render the indications of the needle almost useless
if it be not guarded against. A full account of the manner in which local
attraction is produced, and in which it is compensated, is inconsistent with
the limits of this book, but the most important points are the following : —

i. A vertical mass of soft iron in the vessel, say in the bows, would
become magnetised under the influence of the earth ; in the northern hemi-
sphere, the lower end would be a north pole, and the upper end a south
pole ; and as the latter may be assumed to be nearer the north pole of the
compass needle, its action would preponderate. So long as the vessel was
sailing in the magnetic meridian this would have no effect ; but in any other
direction the needle would be drawn out of the magnetic meridian, and a little
consideration will show that when the ship was at right angles to the magnetic
meridian the effect would be greatest. This vertical uiduction would disap-
pear twice in swinging the ship round, and would be at its maximum twice ;
hence the deviation due to this cause is knowai as semicircular deviation.

ii. Horizontal masses again, such as deck beams, are also acted upon
inductively by the earth's magnetism, and their induced magnetism exerts
a disturbing influence upon the magnetic needle. The effect of this hori-
zontal induction will disappear when the ship is in the magnetic meridian
and also when it is at right angles thereto. In positions intermediate to the
above the disturbing influence will attain its maximum. Hence in swinging
a ship round there would be four positions of the ship's head in which the
influence would be at a maximum, and four in which it would be at a mini-
mum. The effect of horizontal induction is accordingly spoken of as quad-
7-antal dei'iatioti.

The influence of both these causes, vertical and horizontal induction,
may be remedied in the process of ' swinging the ship.' This consists in
comparing the indications of the ship's compass with those of a standard
compass placed on shore. The ship is then swung round in various posi-
tions, and by arranging small vertical and horizontal masses of soft iron in
proximity to the steering compass, positions are found for them in which the
inductive action of the earth upon them quite neutralises the influence of the
earth's magnetism upon the ship ; and in all positions of the ship, the com-
pass points in the same direction as the one on shore.

iii. The extended use of iron in ship-building, more especially when the
frames are entirely of iron, has increased the difficulty. In the process of
building a ship, the hammering and other mechanical operations to which
it is subject, while under the influence of the earth's magnetism, will cause
it to become to a certain extent permanently magnetised. The distribution
of the magnetism, the direction of its magnetic axis, will depend on the
position in which it has been built ; it may or may not coincide with the
direction of the keel. The vessel becomes, in short, a huge magnet, and
will exert an influence of its own upon the compass quite independently of
vertical or horizontal induction. The influence is semicircular ; that is, it
•disappears when the magnetic axis of the ship is in the magnetic meridian,
and is greatest at right angles to it. It may be compensated by two permanent
magnets placed near the compass in suitable positions found by trial during
the process of swinging the ship. Supposing the inherent magnetism of the
ship to have the power of drawing the compass a point to the east, the com-

68o On Magnetism. [715-

pensating magnets may be so arranged as to tend to draw it a point to the
west, and thus keep it in the magnetic meridian. If, however, the inherent
magnetism be destroyed, from whatever cause, it is clear that the magnets
will now draw it aside a point too much to the west. This is the source of a
new difficulty. It has been found that a ship which at the time of sailing
was properly compensated, would, on returning from a long voyage, have its
compasses over-compensated. The buffeting which the ship had experienced
had destroyed its inherent magnetism, and numerous instances are known
where the loss of a vessel can be directly traced to this cause. Fortunately,
it has been found that after some time a ship's magnetic condition is virtu-
ally permanent, and is unaltered by any further wear and tear. The mag-
netism which it then retains is called its ^^r;/zrt;;z^;// magnetism, in opposition
to the siib-perina7ient which it loses.

The difficulty of adequately compensating compasses, which is greatly
increased by the armour-plated and turret ships now in use, has induced one
school to throw over any attempt at correction ; but by careful observation
of the magnetic condition of a ship, and tabulating the errors to construct a
table, and comparing this with the indications of the compass at any one
time, the true course can be made out.

In the Royal Navy, the plan now adopted is to combine both methods :
compensate the errors to a considerable extent, and then construct a table
of the residual errors.

716. Mag-netic saturation. — Experiment has shown that with feeble
magnetising power the magnetic force which can be imparted to a steel bar
increases with the magnetising force used. It depends also on the number of
strokes or movements of the magnetismg magnets or coils : on the form and
dimensions of the bar, on its density, on the quantity of carbon it contains, on
its hardness, and on the manner in which it is tempered. Yet there is a limit
to the magnetic force which can be imparted to iron or steel, and when this
is attained, the bar is said to be saturated or magnetised to saturatiojj. A
bar may indeed be magnetised beyond this point, but this excess is tem-
porary ; it gradually diminishes until the magnet has sunk to its point of
saturation.

This is intelligible, for the magnetisms once separated tend to reunite,
and when their attractive force is equal to that which opposes their separa-
tion—that is, the coercive force of the metal — equilibrium is attained, and
tlie magnet is saturated. Hence, more magnetism ought to be developed
in bars than they can retain, in order that they may decline to their perma-
nent state of saturation. To increase the magnetism of an unsaturated bar,
a less feeble magnet must not be used than that by which it was originally
magnetised.

In order to attain a stationary condition, the magnet should be heated to
boiling for some time after being magnetised ; it should then be remagnetised
and again heated to boiling, and so forth ; and after the last magnetisation
it sliould be Ijoiled for six hours or more. Such magnets are far more durable
than ordinary ones.

717. Mag-netlc battery. — A magnetic battery or maga::ine consists of
a number of magnets joined together by their similar poles. Sometimes
they have the form of a horse-shoe, and sometimes a rectilinear form. The

-718] Armatures. 68 1

battery represented in fig. 650 consists of five superposed steel plates. That
in fig. 651 consists of twelve plates, arranged in three layers of four each.
The horse-shoe form is best adapted for supporting a weight, for then both
poles are used at once. In both the bars are magnetised separately, and
then fixed by screws.

The force of a magnetic battery consisting of ;/ similar plates equally
magnetised, is not n times as great as that of a single one, but is somewhat
smaller. These magnets mutually en-
feeble each other ; manifestly because,
for instance, each north pole evokes
south magnetism in the adjacent north
pole, and thereby diminishes some of its
north polarity. At the same time the
strength is greater than if the steel is in
one coherent mass ; the reason doubtless
is that thin plates of steel are more easily
magnetised to saturation than thick ones,
as the inducing action does not extend
deep. The separate plates should not
be in contact, as the enfeeblement of the
magnetism is thereby less. It is also ad-
visable to connect the pieces by a mass
of soft iron as shown in fig. 651. The
magnetism of a plate which has formed
part of such a batterj' will be found to
be materially less than it was originally.
Thus Jamin found that six equal plates
which separately had each the portative
force 18 kilos, only lifted 64 kilos when
arranged as a battery, instead of 108 ; and when removed from the battery,
each of them had only the portative force 9 to 10 kilos. The force is in-
creased by making the lateral plates i or 2 centimetres shorter than the one
in the middle (fig. 650).

718. Armatures. — When even a steel bar is at its limit of saturation, it
gradually loses its magnetism. To prevent this, armatures or keepers are
used ; these are pieces of soft iron, A and B (fig. 651), which are placed in
contact with the poles. Acted on inductively, they become powerful tem-
porary magnets, possessing
opposite polarity to that of
the inducing pole ; they thus
react in turn on the perma-
nent magnetism of the bars,
preserving and even increas-
ing it.

\Mien the magnets are in
the form of bars, they are

arranged in pairs, as shown ^^' ^"

in fig. 652, with opposite poles in juxtaposition, and the circuit is com])leted
by two small bars of soft iron, AB. Movable magnetic needles, if not clamped

Fig. 650.

682

Oft Magnetism. [718-

down, set spontaneously towards the magnetic poles of the earth, the influ-
ence of which acts as a keeper.

A horse-shoe magnet has a keeper attached to it, which is usually
arranged so as to support a weight. The keeper becomes magnetised under
the influence of the two poles, and adheres with great force : the weight
which it can support being more than double that which a single pole would
hold.

In respect to this weight, a singular and hitherto inexplicable pheno-
menon has been observed. When contact is once made, and the keeper is
charged with its maximum weight, any further addition
would detach it : but if left in contact for a day, an
additional weight may be added without detaching
it, and by slightly increasing the weight every day it
may ultimately be brought to support a far greater
load than it would originally. But if contact be once
broken, the weight it can now support does not much
exceed its original charge.

It is advantageous that the surface of the magnet
and armatures which are in contact should not be
plane but slightly cylindrical, so that they touch along
a line.

In providing a natural magnet with a keeper, the
line joining the two poles may first be approximateh^
determined by means of iron filings ; it may also be
determined by bringing it near a magnetic needle, and
ascertaining the positions in which its action is greatest
(708). Two poles of soft iron (fig. 653), each terminating in a massive shoe,
are then applied to the faces corresponding to the poles. Under the in-
fluence of the natural magnet, these plates become magnetised, and if the
letters A and B represent the position of the poles of the natural magnet,
the poles of the armature are a and b.

719. Portative force. Power of mag-nets. — The poj'tative force is
the greatest weight which a magnet can support. Hacker found that the
portative force of a saturated horse-shoe magnet, which, by repeatedly de-
taching the keeper, had become constant, may be represented by the formula

in which P is the portative force of the magnet, j?^ its own weight, and a a
coefficient which varies with the nature of the steel and the mode of mag-
netising. Hence a magnet which weighs 1000 ounces only supports 25
times as much as one weighing 8 ounces or ^.^^ as heavy, and 25 such bars
would support as much as a single one which is as heavy as 125 of them.
It appears immaterial whether the section of the bar is quadratic or circular,
and the distance of the legs is of inconsiderable moment ; it is important
however, that the magnet be suspended vertically, and that the load be
exactly in the middle. In Hacker's magnets the value o{ a was 10-33, while
in Logemann's it was 23. By arranging together several thin magnetised
j)latcs Jamin constructed bar magnets which sujiport 15 times their own
wciiiht.

Fig. 653'

-720] Circumstances ivhicJi influence the Power of Magnets. 683

The strength of two bar magnets may be compared by the following
simple method, which is known as Kiilp's compensation method : — A small
magnetic compass needle is placed in the magnetic meridian. One pole
of one of the magnets to be tested is then placed at right angles to the
magnetic meridian in the same plane as the needle, and so that its axis pro-
longed would bisect the needle. The compass needle is thereby deflected
through a certain angle. The similar pole of the other magnet is then
placed similarly on the other side of the needle, and a position found for
it in which it exactly neutralises the action of the first magnet ; that is,
when the needle is again in the magnetic meridian. If the magnets are not
too long, compared with their distance from the needle, their strengths are
approximately as the cubes of the distance of the acting poles from the
magnetic needle.

720. Circumstances which influence the power of mag'nets. — All bars
do not attain the same state of saturation, for their coercive force varies.
Twisting or hammering imparts to iron or steel a considerable coercive force.
But the most powerful of these influences is the operation of tempering (94).
Coulomb found that a steel bar tempered at dull redness, and magnetised to
saturation, made ten oscillations in 93 seconds. The same bar tempered at
a cheny-red heat, and similarly magnetised to saturation, only took 63
seconds to make ten oscillations.

Hence it would seem that the harder the steel the greater is its coercive
force ; it undergoes magnetisation with much greater difficulty, but retains
it more effectually. It appears, however, from Jamin's experiments that no
such general rule of this kind can be laid down ; for each specimen of steel
there seems, according to the proportion of carbon which it contains, to be
a certain degree of tempering which is most favourable for the development
of permanent magnetisation.

\'ery hard steel bars have the disadvantage of being very brittle, and in
the case of long thin bars a hard tempering is apt to produce consequent
poles. Compass needles are usually tempered at the blue heat— that is,
about 300° C— by which a high coercive force is obtained without great
fragility. Steel is magnetised with difficulty even when placed for some
time in a coil through which a powerful current is passing ; soft iron under
these circumstances is magnetised at once. If a short coil covering only a
portion of the steel bars be moved backwards and forwards the magnetisa-
tion is more complete.

The hardness of steel, and the proportion of carbon which it contains,
exert an important influence on the degree to which it can be magnetised.
For the same degree of hardness, the magnetisation increases with the pro-
portion of carbon in the steel, and more markedly the smaller this propor-
tion ; with the same proportion of carbon it increases with the hardness of
the steel. It appears probable that the compound of iron and carbon in
steel is the carrier of the permanent magnetisation, and the interjacent
particles of iron the carriers of the temporary magnetisation. Holtz mag-
netised plates of English corset steel to saturation and determined their
magnetic moment ; they were then placed in dilute hydrochloric acid, by
which the iron was eaten away, and the magnetic moment determined when
the plate had been magnetised to saturation after each such treatment. It

684 On Magnetism. [720-

was thus found that, with a diminution in the proportion of iron, there was
an increase in the magnetic moment for the unit of weight. HoUz found,
however, that perfectly pure iron prepared by electrolysis can acquire per-
manent magnetism.

In ordinary bar magnets the intensity of magnetisation (707) varies from
200 to 400 C.G.S. units, and in very thin long ones may attain 800, or about
half the maximum of soft iron. Taking the specific gravity of steel at 7-8,
the specific magnetism is 25 to 50 for the ordinary magnets. It is here
supposed that the magnetisation is uniform, which is not the case.

Jamin investigated the distribution of force in magnets by suspending
from one arm of a delicate balance a small iron ball, and then ascertain-
ing what force, applied at the other arm, was required to detach the
ball when placed in contact with various positions of the magnet to be
investigated.

Taking thus a thin plate magnetised to saturation, it was found that the
magnetisation increased with the thickness, but did not materially vary
with the breadth of the plate. The magnetic force was developed almost
exclusively at the ends. The curve representing the magnetic force (721)
was convex towards the poles at the ends. If now several similar plates are
superposed, the corresponding curves become steeper and prolonged towards
the middle ; the magnetic force thus becomes increased. When the curves
run into each other in the middle the maximum of the combination is reached ;
any additional plates produce no increase in the strength. Steel bars may
also be magnetised so as to show the same curves, and such bars and com-
binations of plates are called by Jamin notvfial magnets.

Jamin found that magnetisation extends deeper in a bar than has been
usually supposed ; in soft and annealed steel it penetrates deeply. The
depth diminishes with the hardness of the steel and the proportion of carbon
it contains. If plates of varying thickness are so thin that the magnetisation
can entirely penetrate them, the thicker of these plates are more strongly mag-
netised by the same force, for the magnetisation extends through a thicker
layer than the thinner ones ; if, however, the plates are very thick, they are
magnetised to the same extent by one and the same force. With equal bars
the thickness of the magnetic layer varies with the strength of the magnetising
force. Jamin proved this by placing the plates in dilute sulphuric acid ; he
found magnetisation in bars which had been exposed to the stronger force,
while those which had been more feebly magnetised showed none when
they had been eaten away by the acid to the same extent. He also showed
that the magnetisation which had penetrated was as strong as that on the
surface.

Holtzhas made some experiments on the influence of solid bars as against
hollow tubes in the construction of permanent steel magnets. The latter are
to be preferred ; they are decidedly cheaper, as they need not be bored, but
may be bent from steel plates. A bar and a tube of the same steel, 125 mm.
in length by 13 mm. diameter, the tube being 175 mm. thick, were magnetised
to saturation, and their magnetic moments determined by the method of
oscillations (705), the tube being loaded with c(>p])cr. The magnetism of the
tube was to that of the bar as i-6 : 1. The tul)cs also retained their mag-
netisation better. After the lapse of six months the ratio of the magnetisation

-720] Circiii)ista)iccs tc/iich iftflncmc the Poiucr of Magnets. 685

of the tube was to that of the bar as 27 : i. A magnetised steel tube filled
with a soft iron core has scarcely any directive force. Holtz considers that
it acts as a keeper.

Temperature.— \\icxQ-\SQ of temperature always produces a diminution of
magnetisation. If the changes of temperature are small — those of the at-
mosphere, for instance — the magnet is not permanently altered. Kuppfer
allowed a magnet to oscillate at different temperatures, and found a definite
decrease in its power with increased temperature, as indicated by its slower
oscillations. In the case of a magnet 2^ inches in length, he observed that
with an increase of each degree of temperature the duration of 800 oscillations
was 0-4" longer. If ;/ be the number of oscillations at zero, and n^ the
number at /, then

« = ;/, ( I - f/),

where c is a constant depending in each case on the magnet used. This
formula has an important application in the correction of the observations
of magnetic force which are made at different places and at different
temperatures, and which, in order to be comparable, must first be reduced
to a uniform temperature.

When a magnet has been more strongly heated, it does not regain its
original force on cooling to its original temperature ; and when it has been
heated to redness, it is demagnetised. This was first shown by Coulomb,
who took a saturated magnet, heated it to progressively higher temperatures,
and noted the number of oscillations after each heating. The higher the
temperature to which it had been heated the slower its oscillations.

A magnet heated to bright redness loses its magnetism so completely
that it is quite indifferent, not only towards iron, but also towards another
magnet, and this holds so long as this high temperature continues. Incan-
descent iron also does not possess the property of being attracted by the
magnet. Hence there is in the case of iron a magnetic limit., beyond which
it is unaffected by magnetism. Such a magnetic limit exists in the case of
other magnetic metals. With cobalt., for instance, it is far beyond a white
heat, for at the highest temperatures hitherto examined it is still magnetic ;
the magnetic limit of chromium is somewhat below red heat ; that of tiickel
at about 350' C, and oi ma?iganese at about 15° to 20° C.

A change of temperature, whether from 16° to 100° or from 100° to 16°,
increases the strength of temporary or induced magnetism both in the case
of iron and of steel.

Percussion and Torsion. — When a steel bar is hammered while beino-
magnetised it acquires a much higher degree of magnetisation than it would
without this treatment. Conversely when a magnet is let fall, or is otherwise
violently disturbed, it loses much of its magnetisation. Wiedemann has inves-
tigated in a very complete manner the relations of torsion and magnetisation.
Torsion exerts a great influence on the magnetisation of a bar, and the inter-
esting phenomenon has been observed that torsion influences magnetism in
the same manner as magnetism does torsion. Thus the permanent mag-
netisation of a steel bar is diminished by torsion, but not proportionally to
the increase of torsion. In like manner the torsion of twisted iron wires is
diminished by their being magnetised, though less so than in proportion to

686

Oji Magnetism.
Repeated torsions in the

[721-

their magnetisation. Repeated torsions in the same direction scarcely
diminish magnetisation, but a torsion in the opposite direction produces a
new diminution of the magnetism. In a perfectly analogous manner, re-
peated magnetisations in the same direction scarcely diminish torsion, but a
renewed magnetisation in the opposite direction does so.

721. Bistribution of free mag-netism.— Coulomb investigated the dis-
tribution of magnetic force by placing a large magnet in a vertical position
in the magnetic meridian ; he then took a small magnetic
needle suspended by a cocoon thread, and fixed at right
angles to a stout copper wire so as to retard the oscillations
(fig. 654) ; and having ascertained the number of its oscilla-
tions under the influence of the earth's magnetism alone, he
presented it to different parts of the magnet. The oscilla-
tions were fewer as the needle was nearer the middle of the
bar, and when they had reached that position their number
was the same as under the influence of the earth's magnetism
alone. For saturated bars of more than 7 inches in length
*^ . the distribution could always be expressed by a curve whose

"' ^"*' abscissae were the distances from the ends of the magnet,

and whose ordinates were the force of magnetism at these points. With
magnets of the above dimensions the poles are at the same distance from
the end ; Coulomb found tlie distance to be r6 inch in a bar 8 inches long.
He also found that, with shorter bars, the distance of the poles from the
end is \ of the length ; thus with a bar of three inches it would be half an
inch. These results presuppose that the other dimensions of the bar are
very small as compared with its length, that it has a regular shape, and is
uniformly magnetised. When these conditions are not fulfilled, the positions
of the poles can only be determined by direct trials with a magnetic
needle. With lozenge-shaped magnets the poles are nearer the middle.
Coulomb found that these lozenge-shaped bars have a -gxtTsX&x dinxti-ue force
than rectangular bars of the same weight, thickness, and hardness.

p- •, .*■ r.

* *■■ r •».

Fig. 655.

A short magnet is defined by Coulomb as one whose length is less than
50 times its diameter.

-722] Mayers F/oatnig Magucts. 687

Kohlrausch found that the pole of a magnet, as far as its action at a
distance is concerned, is j',; from the end.

722. Mayer's floating- magrnets. — The reciprocal action of magnetic
poles may be conveniently illustrated by an elegant method devised by
Prof A. M. Mayer. Steel sewing-needles are magnetised so that their
points are north poles, and their eyes, which are thus south poles, just pro-
ject through minute cork discs, so that when placed in water the magnets
float in a vertical position. If the north pole of a strong magnet is brought
near a number of these floating magnets they are attracted by it, and take up
definite positions, forming figures which depend on the reciprocal repulsion
of the floating magnets, and on their number. Some of them are repre-
sented in fig. 655. The more complex produce more than one arrangement
which are not equally stable, the letters a, b, and c indicating the decreasing
order of stability. A slight shock often causes one form to pass into another
and more stable form.

These figures not only illustrate magnetic actions, but they suggest an
image of the manner in which alteration of molecular groupings may give
rise to physical phenomena, such as those of superfusion (345).

Such floating magnets as are here described are delicate tests of mag-
netisation, and are convenient for investigating the distribution of the poles
in bodies of irregular shape.

688 Frict tonal Electricity. [723-

BOOK IX.

FRICTION AL ELECTRICITY

CHAPTER I.

FUNDAMENTAL PRINCIPLES.

723. Electricity. Its nature. — Electricity is a powerful physical agent
which manifests itself mainly by attractions and repulsions, but also by
luminous and heating effects, by violent shocks, by chemical decomposition,
and many other phenomena. Unlike gravity, it is not inherent in bodies,
but it is evoked in them by a variety of causes, among which are friction,
pressure, chemical action, heat, and magnetism.

Thales, 600 B.C., knew that when amber was rubbed with silk it acquired
the property of attracting light bodies ; and from the Greek form of this
word {fjX(KTpov) the term electricity has been derived. This is nearly all
the knowledge left by the ancients ; it was not until towards the end of the
sixteenth century that Dr. (Gilbert, physician to Queen Elizabeth, showed
that this property was not limited to amber, but that other bodies, such as
sulphur, wax, glass, &c., also possessed it in a greater or less degree.

724. Development of electricity by friction. — When a glass rod, or a
stick of sealing-wax, or shellac, is held in the hand, and is rubbed with a
piece of flannel, or with the skin of a cat, the parts rubbed will be found to
have the property of attracting light bodies, such as pieces of silk, wool,
feathers, paper, bran, gold leaf, &c., which, after remaining a short time in
contact, are again repelled. They are then said to have become electrified.
In order to ascertain whether bodies are electrified or not, instruments called
electroscopes are used. The simplest of these, the electric pendulum (fig.
656), consists of a pith ball attached by means of a silk thread to a glass
support. When an electrified body is brought near the pith ball, the latter
is instantly attracted, iDut after momentary contact is again repelled (fig.
657).

A solid l)ocly may also be electrified by friction with a liquid or with a
gas. In the Torricellian vacuum a mo\eniL"nt of the mercury against the
sides of the glass jiroduces a disengagement of electric light visible in the
dark ; a tube exhausted of air, but containing a few drops of mercury, be-
comes also luminous when agitated in the dark.

If a quantity of mercury in a dry glass vessel be connected with a gold-
leaf electroscope by a wire, and a dry glass rod be immersed in it, no indica-

-725]

Conductors and Notnwiductors.

689

tions are observed during the immersion, but on smartly withdrawinj^ the
rod, the leaves increasingly diverge, attaining their maximum when the lod
lea\es the mercury.

Some substances, particularly metals, do not seem capable of receiving
the electric excitement. When a rod of metal is held in the hand, and
rubbed with silk or flannel, no electrical eftects are produced in it ; and bodies

Fig. 656.

Fig. 657.

were divided by Gilbert into ideoelectrics, or those which become electrical
by friction ; and anelectrics, or those which do not possess this property.
These distinctions no longer obtain in any absolute sense ; under appropriate
conditions, all bodies may be electrified by friction (726).

725. Conductors and nonconductors. — When a diy glass rod, rubbed
at one end, is brought near an electroscope, that part only will be electrified
which has been rubbed ; the other end will produce neither attraction nor
repulsion. The same is the case with a rod of shellac or of sealing-wax.
In these bodies electricity does not pass from one part to another — they do
not conduct electricity. Experiment shows that, when a metal has received
electricity in any of its parts, the electricity instantly spreads over its entire
surfl\ce. Metals are hence said to be good conductors of electricity.

Bodies have, accordingly, been divided into conductors and nonconductors
or insulators. This distinction is not absolute, and we may advantageously
consider bodies as offering a resistance to the passage of electricity which
varies with the nature of the substance. Those bodies which offer little
resistance are thus conductors, and those which offer great resistance are
nonconductors or insulators : electrical r^«<^«f//7///y is accordingly the inverse
of electrical resistance. There is no such thing as an absolute nonconductor
of electricity, any more than there is an absolute nonconductor of heat.
We are to consider that between conductors and nonconductors there is a
quantitative and not a qualitative difference ; there is no conductor so good

Y Y

690

Frictional Electricity.

[725-

but that it offers some resistance to the passage of electricity, nor is there any
substance which insulates so completely but that it allows some electricity
to pass. The transition from conductors to nonconductors is gradual, and no
line of sharp demarcation can be drawn between them.

In this sense we are to understand the following table, in which bodies
are classed as cofiductors, semiconductors, and nonco?tductors ; those bodies
being conveniently designated as conductors which, when applied to a
charged electroscope, discharge it almost instantaneously ; semiconductors
being those which discharge it in a short but measurable time — a few seconds,
for instance ; while nonconductors effect no perceptible discharge in the
course of a minute.

Conductors.

Metals.

Well-burnt charcoal.

Graphite.

Acids.

Aqueous solutions.

Water.

Snow.

Vegetables.

Animals.

Soluble salts.

Linen.

Cotton.

Seiniconductors.
Alcohol and ether.
Powdered glass.
Flour of sulphur.
Dry wood.
Paper.
Ice at 0°.

Nonconductors.
Dry oxides.
Ice at —25° C.
Lime.

Caoutchouc.
Air and dry gases.
Dry paper.
Silk.
Diamonds and precious

stones.
Glass.
Wax.
Sulphur.
Resins.
Amber.
Shellac.

This list is arranged in the order of decreasing conductivity, or, what is the
same thing, of increasing resistance. The arrangement, however, is not in-
variable. Conductivity depends on many physical conditions. Glass, for
example, which does not conduct at ordinary temperatures, does so at 200°
to 300° C. To show this, platinum wire is coiled on a glass rod to within a
couple of inches from the end. If the coiled part is held in the hand and
the free end when at the ordinary temperature is applied to a charged
electroscope it does not affect it ; but if the free end be heated by placing it
in a Bunsen's flame, it will now be found to discharge the electroscope.
Shellac and resin do not insulate so well when they are heated. Water,
which is a good conductor, conducts but little in the state of ice at 0°, and
very badly at -25°. Powdered glass and flour of sulphur conduct veiy
well, while in large masses they are nonconductors ; probably because in a
state of powder each particle becomes covered \\\\\\ a film of moisture that
acts as a conductor. The nonconducting power of glass is also greatly
influenced by its chemical composition. Some specimens have an appreci-
al)lc conductivity even if dry and at the ordinary temperature.

Heat acts indirectly by drying, Ijy which many bodies lose their conduc-
tivity either partially or wholly.

According to Said Effendi, if the conducting power of water be taken at

-727] Distinction of the Two Kinds of Electricity. 691

1,000, the conducting power of petroleum is 72 ; alcohol 49 ; ether 40 ;
turpentine 23 ; and benzole 16. Domalip obtained the following-- numbers
for the respective conductivities: Water 144; ether 6-3; turpentine 1-9;
and benzole i.

726. Insulating- bodies. Common reservoir. — Bad conductors are
called ifisidators, for they arc used as supports for bodies in which electricity
is to be retained. A conductor remains electrified only so long as it is sur-
rounded by insulators. If this were not the case, as soon as the electrified
body came in contact with the earth, which is a good conductor, the electri-
city would pass into the earth, and diffuse itself through its whole extent,
On this account, the earth has been named the common reservoir. A body
is insulated, by being placed on a support with glass feet, or on a resinous
cake, or by being suspended by silk threads. No bodies, however, insulate
perfecdy ; all electrified bodies lose their electricity more or less rapidly
by means of the supports on which they rest. Glass is always somewhat
hygroscopic, and the aqueous vapour which condenses on it affords a
passage for the electricity ; the insulating power of glass is materially im-
proved by coating it with shellac or copal varnish. Dry air is a good insu-
lator ; but when the air contains moisture it conducts electricity, and this is
the principal source of the loss of electricity. Hence it is necessary, in
electrical experiments, to rub the supports with cloths dried at the fire, and
to surround electrified bodies by glass vessels, containing substances which
absorb moisture, such as chloride of calcium, or pumice soaked with sul-
phuric acid.

From their great conductivity metals do not seem to become electrified
by friction. But if they are insulated, by being held in the hand by an india-
rubber glove or a silk handkerchief and then rubbed, they give good indi-
cations. This may also be seen by the

following experiment (fig. 658). A brass ^ ~^^^ '— - --^1=^=^

tube is provided with a glass handle by

which it is held, and then rubbed with ' • :> •

silk or flannel. On approaching the metal to an electrical pendulum (fig
656), the pith ball will be attracted. If the metal is held in the hand electri-
city is indeed produced by friction — but it immediately passes through the
body into the ground.

If, too, the cap of a gold-leaf electroscope be briskly flapped with a dry
silk handkerchief, the gold leaves will diverge.

727. Distinction of the two kinds of electricity. — If electricity be
developed on a glass rod by friction with silk, and the rod be brought near
an electrical pendulum, the ball will be attracted to the glass, and after
momentary contact will be again repelled. By this contact the ball beconies
electrified, and so long as the two bodies retain their electricity, repulsion
follows whenever they are brought near each other. If a stick of sealing-wax,
electrified by friction with flannel or silk, be approached to another electrical
pendulum, the same effects will be produced — the ball will fly towards the
wax, and after contact will be repelled. Two bodies, which have been
charged with electricity, repel one another. But the electricities respectively
developed in the preceding cases are not the same. If, after the pith ball
had been touched with an electrified glass rod, an electrified stick of sealing-

Y V 2

692 Frictional Electricity. [727-

wax, and then an electrified glass rod, be alternately approached to it, the
pith ball will be attfacted by the former and repelled by the latter. Simi-
larly, if the pendulum be charged by contact with the electrified sealing-
wax, it will be repelled when this is approached to it, but attracted by the
approach of the excited glass rod.

On experiments of this nature, Dufay first made the observation that
there are two different electricities : the one developed by the friction of
glass under certain circumstances, the other by the friction of resin or
shellac. To the first the name vitreous electricity is given ; to the second
the name resinous electricity.

728. Theories of electricity. — Two theories have been proposed to
account for the different effects of electricity. Franklin supposed that there
exists a peculiar, subtle, imponderable fluid, which acts by repulsion on its
own particles, and pervades all matter. This fluid is present in every sub-
stance in a quantity peculiar to it, and when it contains this quantity it is in
the natural state, or in a state of equilibrium. By friction certain bodies
acquire an additional quantity of the fluid, and are said to be positively
electrified ; others by friction lose a portion, and are said to be tiegatively
electrified. The former state corresponds to vitreous electricity, and the
latter to resi?ious electricity. Positive electricity is represented by the
sign + , and negative electricity by the sign - ; a designation based on
the algebraical principle, that when a plus quantity is added to an equal
minus quantity zero is produced. So when a body containing a quantity of
positive electricity is touched with a body possessing an equivalent cjuantity
of negative electricity, a neutral or zero state is produced.

The theory of Syjnmer ?i?.?,nmQ:?, that every substance contains an inde-
finite quantity of a subtle, imponderable matter, which is called the electric
fluid. This fluid is formed by the union of two fluids — the positive and the
negative. When they are combined they neutralise one another, and the
body is then in the natural or neutral state. By friction, and by several
other means, the two fluids may be separated, but one of them can never be
excited without a simultaneous production of the other. There may, how-
ever, be a greater or less excess of the one or the other in any body, and it
is then said to be electrified positively or negatively. As in Franklin's
theory, vitreous corresponds to positive and resinous to negative electricity.
Thi§ distinction is merely conventional : it is adopted for the sake of conve-
nience, and there is no other reason why resinous electricity should not be
called positive electricity.

Electricities of the same name repel one another, and electricities of
opposite kinds attract each other. The electricities can circulate freely on
the surface of certain bodies, which are called conductors, but remain con-
fined to certain parts of others, which are called nonconductors.

It must be added that this theory is quite hypothetical ; but for purposes
of instruction its general adoption is justified by the convenient explanation
which it gives of electrical phenomena.

729. Action of electrilied bodies on each other. — Admitting the two-
fluid hypothesis, the phenomena of attraction a\u\ repulsion may be enun-
ciated in the following law :—

-730] Lazv of the Development of Electricity by Friction. 693

Two bodies charged with the same electricity repel each other ; two bodies
charged with opposite electricities attract each other.

These attractions and repulsions take place in \irtue of the action which
the two electricities exert on themselves, and not in virtue of their action on
the particles of matter.

730. Iiaw of the development of electricity by friction. — Whenever
two bodies are rubbed together, the neutral electricity is decomposed. Two
electricities are developed at the same time and in ecjual quantities— one
body takes positive and the other negative electricity. This may be proved
by the following experiment devised by Faraday : — A small flannel cap
provided with a silk thread (fig. 659) is fitted on the end of a stout rod of
shellac, and rubbed round a few times. When the cap is removed by means
of the silk thread, and presented to a pith ball pendulum charged with positive
electricity, the latter will be repelled, proving that the
flannel is charged with positive electricity ; while if the
shellac is presented to the pith ball, it will be attracted,
showing that the shellac is charged with negative
electricity. Both electricities are present in equal
quantities ; for if the rod be presented to the electro-
scopes before removing the cap, no action is observed.

The electricity developed on a body by friction
depends on the rubber as well as the body rubbed.
Thus glass becomes negatively electrified when rubbed Fig. 65q.

with catskin, but positively when rubbed with silk.

In the following list, which is mainly due to Faraday, the substances are
arranged in such an order that each becomes positively electrified when
rubbed with any of the bodies following, but negatively when rubbed with
any of those which precede it : —

1. Catskin.

2. Flannel.

3. Ivoiy.

4. Rock crystal.

The nature of the electricity set free by friction depends also on the
degree of polish, the direction of the friction, and the temperature. If two
glass discs of dififerent degrees of polish are rubbed against each other, that
w^hich is most polished is positively, and that which is least polished is
negatively, electrified. If two silk ribbons of the same kind are rubbed
across each other, that which is transversely rubbed is negatively and the
other positively electrified. If two bodies of the same substance, of the same
polish, but of different temperatures, are rubbed together, that which is most
heated is negatively electrified. Generally speaking, the particles which are
most readily displaced are negatively electrified.

Poggendorff has observed that many substances which have hitherto been
regarded as highly negative, such as gun-paper, gun-cotton, and ebonite, yield
positive electricity when rubbed with leather coated with amalgam. It
must be added that the results of experiments on the kind of electricity pro-
duced by rubbing bodies together are somewhat uncertain, as slight differences
in the surfaces of the bodies rubbed may completely alter their deportment.

Glass.

W^ood.

13-

Resin.

Cotton.

10.

Metals.

14.

Sulphur.

Silk.

II.

Caoutchouc.

15-

Guttapercha.

The hand.

12.

Sealing-wax.

16.

Gun-cotton.

694 Frictional Electricity. [730-

A valuable source of negative electricity is a strip of pyroxyline or gunpaper
drawn through the fingers.

731. Development of electricity by pressure and cleavagre. —

Electrical excitement may be produced by other causes than friction. If a
disc of wood, covered with silk, on which some amalgam has been rubbed,
and a metal disc, each provided with an insulating handle, be placed in con-
tact, and then suddenly separated, the metal disc is negatively electrified.
A crystal of Iceland spar pressed between the fingers becomes positively
electrified, and retains this state for some time. The same property is
observed in several other minerals, even though conductors, provided they
be insulated. If cork and caoutchouc be pressed together, the first becomes
positively, and the latter negatively electrified. A disc of wood pressed on
an orange and separated carries away a good charge of electricity if the
contact be rapidly interrupted. But if the disc is slowly removed the quan-
tity is smaller, for the two fluids recombine at the moment of their separation.
For this reason there is no apparent effect when the two bodies pressed
together are good conductors.

The contact of heterogeneous bodies is no doubt the source of electricity.
Pressure and friction are but particular cases ; in the former case the con-
tact is closer, and in the latter case the surfaces are being continually renewed,
and the effect is the same as if there were a series of rapidly succeeding
contacts.

Cleavage also is a source of electricity. If a plate of mica be rapidly
split in the dark, a slight phosphorescent light is perceived. Becquerel
fixed glass handles to each side of a plate of mica, and then rapidly separated
them. On presenting each of the plates thus separated to an electroscope,
he found that one was negatively and the other positively electrified. If a
stick of sealing-wax be broken, the ends exhibit different electricities.

All badly conducting crystalline substances exhibit electrical indications
by cleavage. The separated plates are always in opposite electrical condi-
tions, provided they are not good conductors : for if they were, the separa-
tion would not be sufficiently rapid to prevent the recombination of the two
electricities. To the phenomena here described is due the luminous appear-
ance seen in the dark when sugar is broken. If sulphur or resin be melted
in glass vessels and a glass rod be placed in the melted mass, on cooling
the solid mass can be lifted out, and will be found to be negatively electrified.

732. Pyroelectrlclty.— Certain minerals, when warmed, acquire electri-
cal properties ; a phenomenon to which the name pyroelectricity is given.
It is best studied in tourmaline^ in which it was first disco\ered from the
fact that this mineral has the power of first attracting and then repelling
hot ashes when placed among them.

To observe this phenomenon, a crystal of tourmaline (fig. 660) is sus-
pended horizontally by a silk thread, in a glass cylinder placed on a heated
metal plate, or in an ordinary hot-air bath. On subsequently investigating
the electric condition of the ends by approaching to them successively an
electrified glass rod, one end will be found to be positively electrified, and
the other end negatively electrified, and each end shows this polarity as
long as the tcmiicrature rises. The arrangement of the electricity is thus
like that of the magnetism in a magnet. The points at which the intensity

-732]

Pyroelectricity,

695

Fig. 660.

of free electricity is greatest are called the poles^ and the line connecting
them is the electric axis. When a tourmaline, while thus electrified, is broken
in the middle, each of the pieces has its two poles, and the polarity of the
broken ends is opposite, resembling thus the experiment of the broken
magnets (6S5). The quantities of electricity produced when
tourmaline is heated are equal as well as opposite, for if a
heated crystal be suspended by an insulating support inside an
insulated metal cylinder, the outside of which is connected with
an electroscope (745), no divergence in its leaves is produced.

These polar properties depend on the change of tempera-
ture. When a tourmaline, which has become electrical by being
warmed, is allowed to cool slowly, it first loses electricity, and
then its polarity becomes reversed ; that is, the end which was
positive now becomes negative, and that which was negative
becomes positive, and the position of the poles now remains
unchanged so long as the temperature sinks. Tourmaline only
becomes pyroelectric within certain limits of temperature ; these
var)' somewhat with the length, but are usually between 10° and
1 50" C. Below and above these temperatures it behaves like
any other body, and shows no polarity.

Tourmaline belongs to the hexagonal system, and usually crystallises in
hemihedral forms ; those, that is to say, which are differently modified at the
ends of their crystallographical principal axis. The name analogous pole is
given to that end A of the crystal which shows positive electricity when the
temperature is rising, and negative electricity when it is sinking ; antilogous
pole to the end B which becomes negative by being heated, and positive by
being cooled.

Besides tourmaline the following minerals are found to be pyroelectric,
though not so markedly — boracite, topaz, prehnite, silicate of zinc, scolezite,
axenite. And the following organic bodies are pyroelectric : cane-sugar,
Pasteur's salt (racemate of sodium and ammonium), tartrate of potassium, &c.

Sir W. Thomson supposes that every portion of tourmaline and other
hemihedral crystals possesses a definite electrical polarity, the intensity of
which depends on the temperature. When the surface is passed through a
flame every part becomes electrified to such an extent as to exactly neutralise,
for all external points, the effect of the internal polarity. The ciystal thus has
no external action, nor any tendency to change its mode of electrification.
But if it be heated or cooled the internal polarisation of each particle of the
crystal is altered, and can no longer be balanced by the superficial electrifi-
cation, so that there is a resultant external action.

A very convenient, and at the same time sensitive, means of investigating
the action of heat on crystals is to sift on these, after having been warmed, a
mixture of flour of sulphur and red lead through a small cotton sieve. By
the friction in sifting the sulphur acquires negative and the red lead positive
electricity, and the powders thus charged attach themselves to those parts of
the crystal which have the opposite electricity, and thus by their difterent
colours give at once an image of its distribution.

Crystals of fluor-spar are not only electrified by heat, but also when
they are exposed to radiation from the sun and from the electric light. This
phenomenon is known ^s photo-electricity.

696

Frictional Electricity.

[733-

CHAPTER II.

QUANTITATIVE LAWS OF ELECTRICAL ACTIOX.

733. Electrical quantity. — In the experiment with the flannel cap,
described above (730), each time the experiment is made, the quantity of
positive electricity produced, which remains on the flannel, is equal to that
of the negative electricity, which remains on the sealing-wax. The flannel,
with its charge of positive electricity, may be detached, and if we work
under precisely uniform conditions, equal quantities of electricity can thus
be separated.

If we fill a cask with water by means of a measure, the quantity added
would be directly proportional to the number of such measures. Now,
although in the above experiment the quantities of electricity produced each
time are equal, yet when the flannel cap is applied each time to an insulated
conductor it does not necessarily follow that the quantity of electricity imparted

is directly proportional to the number of
such applications.

On the C.G.S. system the unit quantity
of electricity is that amount which, acting,
at a distance of one centimetre across air,
on a quantity of electricity of the same
kind equal to itself, would repel it with a
force equal to one dyne (709), and is called
a Coulomb.

734. Iiaws of electrical attraction
and repulsion. — The laws which regu-
late the attraction and repulsion of elec-
trified bodies may be thus stated : —

I. TJic repulsions or attractions be-
tween tioo electrified bodies are in ttie

J; - f ^ ^_.^ [|ii invetse ratio of the squares of tJieir dis-

","'^j',i^iiiifnii«iiiiia'=»™';^ '„ ''•• *y|^^ tance.

II. The distance remaining the same.,
the force of attraction or repulsion between
two electt ified bodies is directly as the pro-
duct of the quantities of electricity with
which they are char<^ed.

These laws were established by Cou-
lomb, by means of llie torsion balance, used in determining the laws of mag-
netic attractions and repulsions (704), modified in accordance with the re-
(luirements of the case. The wire, on the torsion of which the method

-734] Lazes of Electrical Attraction atid Repulsion. 697

depends, is so fine that a foot weighs only /„ of a grain. At its lower ex-
tremity there is a fine shellac rod, np (fig. 661), at one end of which is a
small disc of copper-foil, n. Instead of the vertical magnetic needle, there
is a glass rod, i, terminated by a gilt pith ball, ;«, which passes through the
aperture r. The scale oc is fixed round the sides of the vessel, and during
the experiment the ball, ;«, is opposite the zero point 0. The micrometer
consists of a small graduated disc, e, movable independently of the tube d,
and of affixed index, a, which shows by how many degrees the disc is turned.
In the centre of the disc there is a small button, /, to which is fixed the wire
which supports np.

i. The micrometer is turned until the zero point is opposite the index,
and the tube d is turned until the knob n is opposite zero of the graduated
circle ; the knob m is in the same position, and thus presses against 71. The
knob in is then removed and electrified, and replaced in the apparatus,
through the aperture r. As soon as the electrified knob m touches «, the
latter becomes electrified, and is repelled, and after a few oscillations re-
mains constant at a distance at which the force of repulsion is equal to the
force of torsion. In a special experiment Coulomb found the angle of tor-
sion between the two to be 36° ; and as the force of torsion is proportional
to the angle of torsion, this angle represents the repulsive force between m
and n. In order to reduce the angle to 18° it was necessary to turn the disc
through 126°. The wire was twisted 126° in the direction of the arrow at
its upper extremity, and 18° in the opposite direction at its lower extremity,
and hence there was a total torsion of 144°. On turning the micrometer in
the same direction, until the angle of deviation was 8^°, 567° of torsion was
necessary. Hence the whole torsion was 575^. Without sensible error
these angles of deviation may be taken at 36°, 18°, and 9° ; and on comparing
them with the corresponding angles of torsion, 36°, 144°, and 576°, we see
that while the first are as

I : A : i,
the latter are as

I : 4 : 16 ;

that is, that for a distance \ as great Llie angle of torsion is 4 times as great,
and that for a distance \ as great the repulsive force is 16 times as great.

In experimenting with this apparatus the air must be thoroughly dry, in
order to diminish, as far as possible, loss of electricity. This is effected by
placing in it a small dish containing chloride of calcium.

The experiments by which the law of attraction is proved are made in
much the same manner, but the two balls are charged with opposite electri-
cities. A certain quantity of electricity is imparted to the movable ball, by
means of an insulated pin, and the micrometer moved until there is a certain
angle below. A charge of electricity of the opposite kind is then imparted
to the fixed ball. The two balls tend to move towards each other, but are
prevented by the torsion of the wire, and the movable ball remains at a
distance at which there is equilibrium between the force of attraction, which
draws the balls together, and that of torsion, which tends to separate them.
The micrometer screw is then turned to a greater extent, by which more
torsion and a greater angle between the two balls are produced. And it is

698

Frictiojial Electricity.

[734-

from the relation which exists between the angle of deflection on the one
hand and the angle which expresses the force of torsion on the other, that
the law of attraction has been deduced.

ii. To prove the second law let a charge be imparted \.o m ; n being in
contact with it becomes charged, and is repelled to a certain distance. The
angle of deflection being noted, let the ball ;« be touched by an insulated
but unelectrified ball of exactly the same size and kind. If in this way half
the charge on one of the balls is removed it will be found that the amount
of torsion necessary to maintain the balls at their original angular distance
is half what it was before.

The two laws are included in the formula F = ,.,, where F is the force,

e and e' the quantities of electricity on any two surfaces, and d the distance
between them. If e and e' are of opposite electricities the action is one of
attraction, while if they are the same it is a repulsive action.

Coulomb also established the law by the method of oscillations which is
particularly applicable to the case of attraction, as there are difficulties in ex-
perimenting with the torsion balance. An apparatus for this purpose consists

•ig. 662

of an insulated metal sphere (fig. 662), and at a little distance a short thin rod
of shellac hung by a silk thread and with a disc of metal foil at one end, the
whole being enclosed in a glass cylinder which rests on an insulating plate.
If now the disc is charged with the opposite electricity to that of the sphere,
and is removed from its position of equilibrium, it will make a series of
oscillations before coming to rest. It can be proved that the charge on the
sphere acts as if it were concentrated at the centre, and if the needle is short,
the distance at which the force acts will be that from the centre of the sphere
to the thread of suspension. As in the case of magnetic oscillations we may
use a formula for the time of a single oscillation analogous to that of the

-735]

pendulum (55)

Distribution of Electricity.

699

■'^Jl\^ in

that is t^Tvx/ ''' , in which M is the moment of inertia

of the needle, L its length, and F the force of attraction. Now, all other
things being the same, it is found that when the sphere is placed at varying
distances, d and d^, the times of oscillations, / and /„ vary, and therefore
the force varies, and the relation is established that F : F^ = d'\ : d'K

7j'^. Distribution of electricity. — When an insulated sphere of conduct-
ing material is charged with electricity, the electricity passes to the surface
of the sphere, and forms there an extremely thin layer. If, in Coulomb's
balance, the fixed ball be replaced by another electrified sphere, a certain
repulsion will be observed. If then this sphere be touched with an insulated
sphere identical with the first, but in the neutral state, the first ball will be
found to have lost half its electricity, and only half the repulsion will be
observed. By repeating this experiment with spheres of various substances
solid and hollow, but all having the same superficies, the result will be the
same, excepting that, with imperfectly conducting materials, the time required
for the distribution will be greater. From this it is concluded that the dis-
tribution of electricity depends on the extent of the surface, and not on the
mass, and, therefore, that electricity does not penetrate into the interior, but
is confined to the surface. This conclusion is further established by the
following experiments : —

i. A thin hollow copper sphere provided with an aperture of about an inch
in diameter (fig. 663), and placed on an insulating support, is charged in the
interior with electricity. When the carrier or proof plane (a small disc of
copper-foil at the end of a slender glass or shellac rod) is applied to the in-
terior, and is then brought near an electroscope, no electrical indications
are produced. But if the proof plane is
applied to the electroscope after having
been in contact with the exterior, a con-
siderable divergence ensues.

The action of the proof plane as a
measure of the quantity of electricity is
as follows : — When it touches any surface
the proof plane becomes confounded with
the element touched ; it takes in some
sense its place relatively to the electricity,
or rather, it becomes itself the element
on which the electricity is diffused. Thus
when the proof plane is removed from
contact we have in effect cut away from
the surface an element of the same
thickness and the same extent as its own,
and have transferred it to the balance
without its losing any of the electricity
which covered it.

ii. A hollow globe, fixed on an insu- ''' ' "*'

lating support, is provided with two hemispherical envelopes which fit closely
and can be separated by glass handles. The interior is now electrified and
the two hemispheres brought in contact. On then rapidly removing them

700

Frictional Electricity.

[735-

ffig. 664), the coverings will be found to be electrified, while the sphere is in
its natural condition.

^ 'Mill

lllllllllllllllllll III!

— t=r

I iiiiiriii'iiiiir 'iiiiiiiiiiiiili

This may also be illustrated by the experiment represented in fig. 665, in
which A is a hollow brass hemisphere resting on a support of ebonite, and is
electrified by striking it with silk ; a similar
hemisphere B provided with a glass handle G is
placed over it. A metal spring on the inside of
1! is brought in contact with A by pressing the
ebonite button E, and on afterwards examining
the two hemispheres all the electricity is found
on the outer one B.

iii. The distribution of electricity on the sur-
face may also be shown by means of the follow-
ing apparatus : — It consists of a metal cylinder
on insulating supports, on which is fixed a long
strip of tinfoil which can be rolled up by means
of a small insulating handle (fig. 666). A quad-
rant electrometer is fitted in metallic communi-
cation with the cylinder. When the sphere is rolled up, a charge is imparted
to the cylinder, by which a certain divergence is produced. On unrolling the
tinfoil this divergence gradually diminishes, and increases as it is again rolled
up. The quantity of electricity remaining the same, the electrical force, on
each unit of surface, is therefore less as the surface is greater.

iv. The following ingenious experiment by Faraday further illustrates
this law : — A metal ring is fitted on an insulated support, and a conical
gauze bag, such as is used for catching butterflies, is fitted to it (fig. 667).

By means of a silk thread, the bag can be drawn inside out. After
electrifying the bag, it is seen by means of a jiroof plane that the electricity
is on the exterior ; but if the positions are reversed by drawing the bag
inside out, so that the interior has now become the exterior, the electricity
will still be found on the exterior.

-736j

Distribution of Electricity.

701

V. The same point may be further illustrated by an experiment due to
Terquem. A bird-cage, preferably of metal wire, is suspended by insulators,
and contains either a gold-leaf electroscope or pieces of Dutch metal, feathers,

pith balls, &c. When
the cage is connected
with an electrical ma-
chine, the articles in
the interior are quite
unaffected, although
strong sparks may be
taken from the outside.

Fig. 666.

Bands of paper may be fixed to the inside ; while those fixed to the outside
diverge widely. A bird in the inside is quite unaffected by the charge or
discharge of the electricity of the cage.

The property of electricity, of accumulating on the outside of bodies,
is ascribed to the repulsion which the particles exert on each other. Elec-
tricity tends constantly to pass to the surface of bodies, whence it continually
tends to escape, but is prevented by the resistance of the feebly conducting
atmosphere.

To the statement that electricity resides on the surface of bodies, two
exceptions may be noted. When two opposite electricities are discharged
through a wure— a phenomenon which, when continuous, forms an electrical
current — the discharge is effected throughout the whole mass of the con-
ductor. Also a body placed inside another may, if insulated from it, receive
charges of electricity. On this depends the possibility of electrical experi-
ments in ordinary rooms.

736. Electric density. — On a metal sphere the distribution of the
electricity is everywhere the same, simply from its symmetry. This can be
demonstrated by means of the proof plane and the torsion balance. A metal
sphere placed on an insulating support is electrified, and touched at different
parts of its surface with the proof plane, which each time is applied to the
movable needle of the torsion balance. As in all cases the torsion observed

702

Frictional Electricity.

[736-

is sensibly the same, it is concluded that the proof plane each time receives
the same quantity of electricity. In the case of an elongated ellipsoid (fig.
668) it is found that the distribution of electricity is different at different
points of the surface. The electricity accumulates at the most acute points.
This is demonstrated by successively touching the ellipsoid at different parts
with the proof plane, and then bringing this into the torsion balance. By
this means Coulomb found that the greatest deflection was produced when
the proof plane had been in contact with the point a^ and the least by con-
tact with the middle space c.

The elect} ic density or electric thickness is the term used to express
the quantity of electricity found at any moment on a given surface. If

S represents the
surface and Q the
quantity of elec-
tricity on that sur-
face, then, assuming
that the electricity
is equally distri-
buted, its electrical
density is equal

-I

Coulomb found
.by quantitative ex-
periments, that in
an ellipsoid the
density of the elec-
tricity, at the equa-
tor of the ellipsoid, is to that at the ends in the same ratio as the length of
the minor to the major axis. On an insulated cylinder, terminated by two
hemispheres, the density of the electrical layer at the ends is greater than
in the middle. In one case, the ratio of the two densities was found to be
as 2-3 : I. On a circular disc the density is greatest at the edges.

"J-^J. Force outside an electrified body. — The force F which a sphere,
charged with a quantity of electricity Q, exerts on a point at a distance d

from its centre, is -^ ; this is equal to '^, if S is the area of the sphere, and
d- d~

p the density of electricity on the unit of surface.
Now the area of the sphere is 47rR- ; and if the dis-
tance d is equal to the radius R, then the force at the
47rpR2 .

Fig.

surface S = -

This holds also if the point considered is at a very

small distance just outside the sphere. Let a small

segment at> be cut in a sphere (fig. 669). Then its

Fie 66q. action on a point/^ just inside the sphere will be exactly

neutralised by the action of the rest of the sphere ncd

on this point, since there is no electrical force inside a sphere (735) ; that

is, the action of the two portions is equal, but in opposite directions. Now

-738] Potential. 703

for a point^', just outside the sphere, the actions will also be equal, but in
the same directions. Ikit the total action of the whole sphere is 47r/) : hence
the action of each portion is half of this ; that is, Znp.

It may be shown in like manner that the whole force of any closed con-
ductor is 47rp per unit area.

On an insulated conductor, where the electricity is in ecjuilibrium, a
particle of electricity will have no tendency to move along the surface, for
otherwise there would be no equilibrium. But the electricity does exert a
pressure on the external non-conducting medium, which is always directed
outwards, and is called the elect7-ostatic teiision or pressure.

The amount of this pressure is i-jvp" for unit area, p being the electrical
density at the point considered. It is therefore proportional to the square of
the density. The effect of this on a soap-bubble, for instance, if electrified
with either kind of electricity, is to enlarge it. In any case the electrification
constitutes a deduction from the amount of atmospheric pressure which the
body experiences when unelectrified.

The term electric density and electrical tension are often confounded.
The latter ought rather to be restricted, as Maxwell proposed, to express the
state of strain or pressure exerted upon a dielectric in the neighbourhood of
an electrified body ; a strain which, if continually mcreased, tends to disrup-
tive discharge. Electric tension may thus be compared to the strain on a
rope which supports a weight ; and the dielectric medium which can support
a certain tension and no more is said to have a certain electrical strength in
the same sense as a rope which bears a certain weight without breaking is
said to have a certain strength.

738. Potential.— In the experiment (fig. 669), instead of applying the
test sphere directly to the large sphere, let the two be placed at a consider-
able distance from each other, and let them be connected by a long thin wire,
and then, detaching the small sphere, let the quantity upon it be measured
by the torsion balance: the angle of deflection will show that this quantity
is the same whatever part of the large sphere be touched, as must indeed be
the case, owing to symmetry ; but the amount of this charge will be mate-
rially difterent from the amount when the small sphere is placed in direct
contact with the larger one. Hence the quantity of electricity removed
differs according to the mode in which connection is made.

If now this experiment be repeated with the ellipsoid, it will be found
that whatever point of this is put in distant connection with the proof sphere
by the long wire, the charge which the small sphere acquires is always the
same ; although, as we have seen, the proof sphere would remove very dif-
ferent quantities of electricity according to the part where it touches.

Here, then, we are dealing with experimental facts which our previous
notions are insufficient to explain. It is manifest that the difference in the
results depends neither on the total charge nor on the density. We require
the introduction of a new conception, which is that of electrical potential.
Introduced originally into electrical science by Green, out of considerations
arising from the mathematical treatment of the subject, the use of the term
potential is justified and recommended by the clearness with which it brings
out the relations of electricity to work.

We have already seen, that in order to lift a certain mass against the

704 Frictional Electricity. [738-

attraction of gravitation (59-62) there must be a definite expenditure of work,
and the equivalent of this work is met with in the energy which the lifted
mass retains, or what is called the potential energy of position.

Let us now suppose that we have a large insulated metal sphere charged
with positive electricity, and that, at a distance which is very great in com-
parison with the size of the sphere, there is a small insulated sphere charged
with the same kind of electricity. If now we move the small sphere to any
given point nearer the larger one, we must do a certain amount of work upon
it to overcome the repulsion of the two electricities.

The work required to be done against electrical forces, in order to move
the unit of positive electricity from an infinite distance to a given point in
the neighbourhood of an electrified conductor, is called XS\q potential 2X this
point. If, in the above case, the larger sphere were charged with negative
electricity, then instead of its being needful to do work in order to bring a
unit of positive electricity towards it, work would be done by electrical
attraction, and the potential of the point near the charged sphere would thus
be negative.

The potential at any point may also be said to be the work done against
electrical force, in moving unit charge of negative electricity from that point
to an infinite distance.

• The amount of work required to move the unit of positive electricity
against electrical force, from any one position to any other, is equal to the
excess of the electrical potential of the second position over the electrical
potential of the first. This is, in effect, the same as what has been said
above, for at an infinite distance the potential is zero.

We cannot speak of potential in the abstract, any more than we can
speak of any particular height, without at least some tacit reference to a
standard of level. Thus, if we say that such and such a place is 300 feet
high, we usually imply that this height is measured in reference to the level
of the sea. So, too, we refer the longitude of a place to some definite
meridian, such as that of Greenwich, either expressly or by implication.

In like manner we cannot speak of the potential of a mass of electricity
without, at least, an implied reference to a standard of potential. This
standard is usually the earth, which is taken as being zero potential. If we
speak of the potential at a given point, the difference between the potential
at this point and the earth is referred to.

If, in the imaginary experiment described above, we move the small
sphere round the large electrified one always at the same distance, no work
is done by or against it for the purpose of overcoming or of yielding to
electrical attractions or repulsions, just as if we move a body at a certain
constant level above the earth's surface, no work is done upon it as respects
gravitation. An imaginary surface drawn in the neighbourhood of an elec-
trified body, such that a given charge of electricity can be moved from any
one point of it to any other without any work being done either by or against
electrical force, is said to be an cquipotential sur/ncc. Such a surface may
be described as ha\ing e\-cryvvhcre the sai/w electrical level ; and the notion
of bodies at different electrical levels, in reference to a particular standard,
is analogous to that of bodies at diflferent potentials. In the case of an
insulated electrified sphere the successive equipolential surfaces would be

-739] Electrical Capacity. 705

successive shells of gradually increasing radii, like the coats of an onion.
The space about an electrified body or electrified system is called the elec-
trical field. The fall of potential from one equipotential surface to another
is most rapid in the direction of the perpendiculars to the two surfaces.
These perpendiculars represent the lines of electrical force, the 'lines of
force' of Faraday, or the 'lines of induction' of Ma.xwcll. On the surface
of an insulated electrified sphere at a distance from other conductors, these
lines of force are perpendicular to the surface of the sphere. The lines of
electrical force may be made visible in the dark by placing two small balls
at a distance from each other in conducting communication with an elec-
trical machine at work, and then sifting lycopodium powder through a fine
sieve while the space is simultaneously illuminated by the lime or the electric
light.

As water only flows from places at a higher level to places at a lower
level, so also electricity only passes from places at a higher to places at a
lower potential. If an electrified body is placed in conducting communica-
tion with the earth, electricity will flow from the body to the earth, if the
body is at a higher potential than the earth ; and from the earth to the
body, if the body is at a lower potential, and its flow will be proportional to
the difference of potential. If the potential of a body is higher than that
of the earth, it is said to have a positive potential ; and if at a lower poten-
tial, a negative potential. A body charged with free negative electricity is
one at lower potential than the earth ; one charged with free positive elec-
tricity is at a higher potential.

739. Electrical capacity. — The capacity of any conductor may be
measured by the quantity of electricity which it can acquire when placed
in contact with a body which charges it to unit electrical potential.

We may illustrate the relation between capacity and potential by refer-
ence to the analogous phenomenon of heat. In the interchange of heat
between bodies of different temperatures the final result is that heat only
passes from bodies of higher to bodies of lower temperature. So also elec-
tricity only passes from bodies of higher to bodies of lower potential.
Potential is as regards electricity what temperature is as regards heat, and
might indeed be called electrical temperature. We may have a small
quantity of heat at a very high temperature. Thus a short thin wire heated
to incandescence has a far higher heat potential, or temperature, than a
bucket of warm water. But the latter will have a far larger quantity. A
flash of lightning represents electricity at a very high potential, but the
quantity is small.

The relation between electrical potential and density may be further
illustrated by reference to the head of water in a reservoir. The pressure
is proportional to the depth ; the potential is everywhere the same. For
suppose we want to introduce an additional pound of water into the reser-
voir, the same amount of work is recjuired whether the water be forced in
at the bottom or be poured in at the top.

If a hole be made very near the top of the reservoir, a quantity of water
in falling to the ground would generate an amount of heat proportional to
the fall. If the same quantity escaped through a hole near the bottom, it
would not produce so much heat by direct fall ; but it will possess a certain

z 7.

7o6 Frictional Electricity. [739-

velocity, the destruction of which will produce a quantity of heat which,
added to that produced by the fall, will give exactly as much as the
other.

When the charge or quantity of electricity imparted to a body increases,
the potential increases in the same ratio; so that, calling Q the quantity of
electricity, C the capacity, and V the potential, we have Q = CV ; that is to
say, that the charge, or quantity of electricity, that any body possesses, is
the product of the potential into the capacity.

Now for a sphere whose radius is R the potential V = -^-, from which

we get C = R ; that is, that the capacity of a spliere is equal to its radius.

While there is a close analogy between heat and electricity, as regards
capacity, there are important differences ; thus the capacity of a body for
heat is influenced by the temperature (457), being greater at higher tem-
peratures, while the capacity of a body for electricity does not depend on
the potential. Again, the calorific capacity depends solely on the mass of
a body, and in bodies of the same material and shape is proportional to
the cube of homologous dimensions ; the capacity for electricity is directly
proportional to such dimensions, and not to the weight or volume. Calorific
capacity is proportional to a specific coefficient, which varies with the mate-
rial, but is independent of its shape ; while electrical capacity varies with
the shape of a body, but not with its material, provided the electricity can
move freely upon it. Calorific capacity is unaffected by the proximity of
other bodies, while the electrical capacity depends on the position and shape
of all the adjacent conductors.

If we have a series of bodies at a considerable distance from each other,

whose capacities and potentials are respectively c, c\ c'\ &c., and v, v\ v' \

&c., then, if they are all connected by fine wires of no capacity, they all

instantly acquire the same potential V, which is determined by the equation

Y _cv -^ c'v' + c"v"

c -fC' + c"

The analogy of this to the equalisation of temperature which takes place
when bodies at different temperatures are mixed together is directly
apparent (449). It may be further illustrated by supposing a series of
tubes of different diameters, and connected by very narrow tubes, but in
which are stopcocks to cut off communication. If, while in this state, water
be poured into the tubes to different heights, it will be manifest that they
will hold very various quantities of water. If, however, the stopcocks are
opened, the tubes will still contain quantities of water proportional to their
capacities, Ijut the level or potential in all will be the same.

740. IVXeasurement of capacity and potential. — We may use Coulomb's
balance for the purpose of measuring the capacity C, or the potential V, of
a body charged with electricity. For this purpose the body in question is
placed, by means of a long fine wire of no capacity, in distant contact with
a small neutral insulated sphere of known radius r. This small sphere is
then applied to the torsion balance, and its charge q = )■%> is measured. Now
since the original charge on the si)here is Q = C\', after contact with the
small sphere, which is neutral, the system will have a new potential or
electrical level, ?', such that CV = (C + r) 7>. Restoring now tlie small sphere

-741] Potential of a Sphere. 707

to the neutral state, and repeating the experiment and the measurement,
we shall then get a second value n>\ from which we have the equation

C7/ = (C + r) v'. Combining and reducing, we get the ratio V= ^", which,

v'
seeing that 7-7' and rv' are numerical values, leads directly to the desired
result.

In like manner it is easy to determine the capacity by obvious transfor-
mations of these equations.

It will thus be seen that this process of determining potential is analo-
gous to that of determining temperature by means of a thermometer ; and
the proof sphere plays the part, as it were, of an electrical tJiermometer. It
may be observed that in the case of heat we pass from the conception of
temperature to that of qiiatitity of heat, while with electricity, starting with
the fact of quantity, or charge of electricity, we arrive at the conception of
potential of electricity.

741. Potential of a sphere. — \iq^ q\ and q" are any masses of electri-
city on the surface of an insulated conducting sphere, and d d' and d" their

respective distances from any point of the interior of the sphere, then f' ^,

d d'

and ^,^ are the values of the potentials v, v\ and v" wjiich they would

severally produce at this point. Let the point in question be the centre,
and let Q be the sum of the whole quantities ; then V, the potential of the

sphere, equals l^, R being the radius.

If there be a sphere, or uniform spheroidal shell of matter, which acts
according to the inverse square of the distance, then the total action of this
sphere is the same as if the whole matter were concentrated at the centre.
This was first proved by Newton in the case of gravitation ; but it also
applies to electricity, and hence, in calculating the potential at any point out-
side a sphere possessing a uniform charge, we need only consider its dis-
tance from the centre, and for such a case we may write the value of the

potential V = >.

If a charge of electricity, Q, be imparted to two insulated conducting
spheres whose radii are respectively r and r', and which are connected by
a long fine wire, the quantity of which may be neglected, the electricity
will distribute itself over the two spheres, which will possess the charges
q and q' ; that \%^ q -^^ q' = <^. (i) The whole system will be at the same

potential V, such that V = ? = f,. (2) Combining these two equations and
reducing, we get for the quantities q and q' on each sphere q = -^^ , and

r + r

r ■
Qr'

Now, since the diameter of any sphere with which we can experiment is
infinitely small compared with that of the earth, it follows that when a sphere
is connected with the earth by a fine wire the quantity of electricity which
it retains is infinitely small.

z z 2

7o8 Frictional Electricity. [741-

For the densities on the two spheres we have d= ^ - and</' = ^ , from

47T-r- 47rr

which by equation (2) it is readily deduced that d : d' = r' \ r ; that is, that
the electrical densities on two spheres in distant connection are inversely as
the radii. If, for instance, a fine wire be connected with a charged insulated
sphere, the distant pointed end of the wire may be regarded as a sphere
with an infinitely small radius, and thus the density upon it would be in-
finitely great.

742. Action of points. — We have just seen that on a point in connection
with a conductor charged with electricity the density may be considered to
be infinitely great, but the greater the density the greater will be the tendency
of electricity to overcome the resistance of the air, and escape, for the electro-
static pressure is proportional to the square of the density (J37)- If the hand
be brought near a point on an electrified conductor a slight wind is felt ; and
if the disengagement of electricity takes place in the dark a luminous brush
is seen. If an electrified conductor is to retain its electricity all sharp points
and edges must be avoided ; on the other hand, to facilitate the outflow of
electricity in apparatus and experiments (764), frequent use is made of this
action of points. A flame acts like a very fine point in diffusing electricity.

743. Jtoss of electricity. — Experience shows that electrified bodies
gradually lose their electricity, even when placed on insulating supports.
This loss is mainly due to the insulating supports. The charge is gradually
dissipated in consequence of the electricity either passing through the sup-
ports or creeping over the surface. All substances conduct electricity in
some degree ; those which are termed insulators are simply very bad con-
ductors. An electrified conductor resting on supports must therefore lose a
certain quantity of electricity — either by penetration into its mass or along

the surface. This loss of electricity is a main cause

of difficulty in experiments on the quantitative laws

of electricity ; it varies with the electric density,

and increases with the hygrometric state of the air,

though it does not seem that the loss from this

cause is due to a direct conductivity by moist air.

Sir W. Thomson ascribes the greater part of the loss

to the conducting layer of moisture which covers the

supports ; and he finds that in comparison with this,

the direct loss by even moist air is inconsiderable.

Brown shellac or ebonite is the best insulator ;

- ^ glass is a hygroscopic substance, and must be

dried with great care. It is best covered with a thin

'^' ^'^' layer of shellac varnish, as has already been stated.

Mascart's i77sulator is admirably adapted for supporting bodies charged

with electricity. It consists of a glass vessel of special shape (fig. 67o\ to

the glass vase of which is fused the stem. This passes through the neck

and supports the palate, P ; the neck is closed by an ebonite stopper, and

inside the vessel is sulphuric acid, so that the slcm A is always dry.

-744]

709

CHAPTEl

III.

ACTION OF ELECTRIFIED BODIES ON BODIES IN THE NATURAL STATE.
INDUCED ELECTRICITY. ELECTRICAL MACHINES.

744. Electricity by influence or induction. — An insulated conductor,
cliarged with either kind of electricity, acts on bodies in a neutral state
placed near it in a manner analogous to that of the action of a magnet on
soft iron ; that is, it decomposes the neutral electricity, attracting the oppo-

tig 67

site and repelling the like kind of electricity. The action thus exerted is
said to take place by injlucncc or induction.

The phenomena of induction may be demonstrated by means of a brass
cylinder placed on an insulating support, and provided at its extremities
with two small electric pendulums, which consist of pith balls suspended by
linen threads (fig. 671). If this apparatus is placed near an insulated con-
ductor ;//, charged with either kind of electricity— for instance, the conductor
of an electrical machine, which is charged with positive electricity— the
natural electricity of the cylinder is decomposed, free electricity will be
developed at each end, and both pendulums will diverge. If, while they still
diverge, a stick of sealing-wax, excited by friction with flannel, be approached
to that end of the cylinder nearest the conductor, the corresponding pith
ball will be repelled, indicating that it is charged with the same kind of
electricity as the sealing-wax — that is, with negative electricity ; while if the
excited sealing-wax is brought near the other ball it will be attracted, showing
that it is charged with positive electricity. If, further, a glass rod excited

710 Frictional Electricity. [744-

by friction with silk, and therefore charged with positive electricity, be ap-
proached to the end nearest the conductor, the pendulum will be attracted :
while if brought near the other end, the corresponding pendulum will be re-
pelled. If the influence of the charged conductor be suppressed, either by
removing it, or placing it in communication with the ground, the separated
electricities will recombine, and the pendulums exhibit no divergence.

The cause of this phenomenon is obviously a decomposition of the neutral
electricity of the cylinder, by the free positive electricity of the conductor ;
the opposite or negative electricity being attracted to that end of the cylinder
nearest the conductor, while the similar electricity is repelled to the other
end. Between these two extremities there is a space destitute of free
electricity. This is seen by arranging on the cylinders a series of pairs of
pith balls suspended by threads. The divergence is greatest at each
extremity, and there is a line at which there is no divergence at all, which is
called the neutral line. The two electricities, although equal in quantity, are
not distributed over the cylinder in a symmetrical manner ; the attraction
which accumulates the negative electricity at one end is, in consequence of
the greater nearness, greater than the repulsion which drives the positive
electricity to the other end, and hence the neutral line is nearer one end than
the other. Nor is the electricity induced at the two ends of the cylinder
under the same conditions. That which is repelled to the distant extremity
is free to escape if a communication be made with the ground ; whilst, on
the other hand, the unlike electricity which is attracted is held bound or
captive by the inducing action of the electrified body. Even if contact be
made with the ground on the face of the cylinder adjacent to the inducing
body, the electricity induced on that face will not escape. The repelled
electricity, however, on the distant surface is not thus bound ; it is free to
escape by any conducting channel, and hence will immediately disappear
wherever contact be made between the ground and the cylinder. Both the
pith balls will collapse, and all signs of electricity on the cylinder depart with
the escape of the repelled or free electricity. But now, if communication with
the ground be broken, and the inducing body be discharged or removed to a
considerable distance, the attracted or bound electricity is itself set free, and
diffusing over the whole cylinder causes the pith balls again to diverge, but
now with the opposite electricity to that of the original inducing body. The
reason for the escape of the repelled electricity is as follows : — If the
cylinder be placed in connection with the ground, by metallic contact with
the posterior extremity, and the charged conductor be still placed near
the anterior extremity, the conductor will exert its inductive action as before.
But it is now no longer the cylinder alone which is influenced. It is a
conductor consisting of the cylinder itself, the wire, and the whole earth.
The neutral line will recede indefinitely, and, since the conductor has
become infinite, the quantity of neutral fluid decomposed will be increased.
Hence, when the posterior extremity is placed in contact with the ground,
the pendulum at the anterior extremity diverges more widely. If the con-
necting-rod be now removed, neither the quantity nor the distribution will
be altered ; and if the conductor be removed or be discharged, a charge
of negative electricity will be left on the cylinder. It will, in fact, remain
charged with electricity, the opposite of that of the charged conductor. Even

-745] Faraday s Experiments. 7 1 1

if, instead of connecting the posterior extremity of the cylinder with the
ground, any other part had been so connected, the general result would
have been the same. All the parts of the cylinder would be charged with
negative electricity, and, on breaking the connection with the earth, would
remain so charged.

Thus a body can be charged with electricity by induction as well as by
conduction. But, in the latter case, the charging body loses jjart of its
electricity, which remains unchanged in the former case. The electricity
imparted by conduction is of the same kind as that of the electrified
body, while that excited by induction is of the opposite kind. To impart
electricity by conduction, the body
must be quite insulated ; while in the
case of induction it must be in con-
nection with the earth — at all events
momentarily.

A body electrified by induction
acts in turn on bodies placed near
it, separating the two fluids in a
iTianner shown by the signs on the
sphere.

What has here been said has
reference to the inductive action
exerted on good conductors. Bad
conductors are not so easily acted
upon by induction, owing to the great
resistance they present to the circu-
lation of electricity ; but, when once
charged, the electric state is more
permanent.

This is analogous to what is met
with in magnetism ; a magnet in-
stantaneously magnetises a piece of
soft iron, but this is only temporary, and depends on the continuance of the
action of the magnet ; a magnet magnetises steel with far greater difficulty,
but this magnetisation is permanent.

The fundamental phenomena of induction may be conveniently investi-
gated and demonstrated by means of the apparatus represented in fig.
672, which consists of a narrow cylindrical brass tube BA, supported by an
insulating glass handle, and held over the excited cake of an electrophorus
(752).

745. Faraday's experiments. — The following experiments of P^araday,
which are often known as ' the ice-pail experiments,' from the vessels with
which they were originally made, are excellent illustrations of the operation
of induction, and are of great theoretical importance : —

A carefully insulated metal cylinder, A, fig. 673, is connected by a wire
with an electroscope E, at some distance. On slowly placing inside the
cylinder an insulated brass ball C, charged with positive electricity, which
is small in comparison with the size of the cylinder, the leaves of the electro-
scope diverge, and, as can be shown, with positive electricity, and the

Fig. 672.

712

Frictional Electricity.

[745-

'^^^ISUi^^J

divergence increases until a certain depth is attained, when there is no
further increase. The divergence now remains constant, whatever be the
position of the ball, and when the inside and outside are tested with the
proof plane they are found to be charged with negative and positive respec-
tively. If the ball is withdrawn the leaves of the electroscope collapse, and
there is no electrification on the cylinder ;
the quantities of negative and positive
electricity developed on the two surfaces
are accordingly equal to each other.

If now the ball, while still charged
with positive electricity, be brought as
before into the cylinder, and be allowed
to touch the inside, there is no alteration,
^9 i I not even a momentary one, in the diver-

gence of the leaves of the electroscope ;
but if the ball be withdrawn it will now be
found to be neutral, as is also the inside
of the cylinder, while the outside is charged
with positive electricity. When the ball
touches the interior, the system forms
only a single conductor, and all the elec-
tricity passes to the outside ; but since
Fig. 673. the charge as indicated by the electro-

scope does not alter, it follows that the
positive of the ball and the negative of the inside of the cylinder are equal
to each other.

If while the ball charged with positive electricity is inside the cylinder,
the latter is momentarily put to earth, the gold leaves collapse, and the proof
plane, if applied to the outside, removes no trace of electricity ; for all
external bodies the cylinder behaves as if it were neutral. The internal
surface is, however, covered with a layer of negative electricity, and this is
equivalent to the positive charge of the ball, for all trace of electricity dis-
appears if the ball is made to touch the side.

If the ball, after the cylinder has been momentarily connected to earth,
be removed without having touched the sides, the negative passes to the
outside and forms there a layer which is distributed as was the layer of
positive electricity before being connected with the ground. The cylinder
is thus finally charged with a quantity of electricity equal and of opposite
sign to the inducing body.

Four such cylinders (fig. 674) are placed concentrically within each other,
and are insulated from each other by discs of shellac, and tlie outer one is
connected with the electroscope. On introducing the charged ball into the
central cavity the leaves diverge just as if the intermediate ones did not
exist. Each of these is charged with equal quantities of opposite electricities,
all equal in value to that of the sphere. The internal charge of the cylinder
is the same as if all the intermediate cylinders were suppressed, and the
charge does not vary e\cn when the intermediate ones arc connected with
each other or are touched by the electrified ball C.

If, while C is in its original condition, the internal cylinder, 4, is con-

-746]

Limit to the Action of Induction.

713

Fig. 674.

nected with the ground, the leaves colhipse, and the other cyHnders are in
the neutral state ; the two layers which remain, positive on C, and negative
on the adjacent cylinder, are without action on an external point. If any
other cylinder be thus treated the external ones are reduced to the neutral
state.

With the aid of the cylinder (fig. 674) it is easy to demonstrate that by
friction both electricities are pro-
duced at the same time, and in l^^^Jt
equal quantities. For if the
flannel and sealing-wax in fig. 659
after being rubbed are placed
simultaneously in the cylinder
no divergence is produced, while
if each is introduced separately,
they produce equal divergence
but of opposite sign.

Whenever a charge of elec-
tricity exists there is somewhere a corresponding charge of electricity of
the opposite kind. This may seem inconsistent with the fact that an insu-
lated sphere may have a charge of one kind of electricity. But it is to be
remembered that this is the case of a Leyden jar (770) in which the
dielectric is the layer of air between the sphere and the sides of the room
which form the outer coating.

746. Iilmit to the action of induction. — The inductive action which an
electrified body exerts on an adjacent body in decomposing its neutral fluid
is limited. On the surface of the insulated cylinder, which we have con-
sidered in the pieceding paragraph, let there be at n any small quantity of
neutral electricity (fig. 675). The positive electricity of the source m first
decomposes by induction the neutral electricity in ;/, attracting its negative
towards A, and repelling its positive towards B ; but in the degree in which
the extremity A becomes charged with negative electricity, and the extre-
mity B with positive electricity, there are developed at A and B two forces,
/"and/', which act in the opposite direction to the original force. For the
forces/ and f concur in driving towards B the negative of n, and towards

r i\-_

Fig. 675.

A its positive. But as the inducing force F which is exerted at in is con-
stant, while the forces/ and / are increasing, a time arrives at which the
force F is balanced by the forces / and /. All decomposition of the
neutral condition then ceases ; the inducing action has attained its limit.

If the cylinder be removed from the source of electricity, as the inducing
action decreases, a portion of the free electricities at A and B recombine to
form the neutral fluid. If, on the other hand, they are brought nearer, as
the force F now exceeds the forces / and /, a new decomposition of the

714 Friclional Electricity. [746-

neutral fluid takes place, and fresh quantities of positive and negative elec-
tricities are respectively accumulated at A and B.

747. Faraday's theory of induction. — Hitherto any possible influence
of the medium which separates the electrified from the unelectrified body in
the case of induction has been disregarded. It has been tacitly assumed
that electrical actions are exerted at a distance, and the medium has been
looked upon as an inert mass through which the forces can act, but which
itself is destitute of any active properties. The researches of Faraday, how-
ever, prove that this is not the case ; that the medium is of fundamental im-
portance, and that the action is not an action at a distance, or at any rate
at no greater distance than that between any two molecules.

According to Faraday's views conductors are in a certain sense qualita-
tively different from non-conductors. He looked upon a non-conductor as
consisting of a number of molecules which may be spherical, and which are
absolute conductors, and are disseminated in a non-conducting medium.
The action of an electrified body is either to separate the electricities within
the molecule and arrange them in a polar chain, or to impart to the mole-
cules which are themselves polarised at the outset a definite polar arrange-
ment ; those ends of the molecule which face the inducing body having elec-
tricity of the opposite kind, and those which are turned away from it having
electricity of the same kind. In the interior of the medium, where succes-
sively the positive end of one molecule faces the negative end of the next,
the two electricities neutralise each other ; but where the non-conductor is
bounded by a conductor the free electrification is no longer neutralised, but
constitutes the charge which is perceived. The action is therefore analogous
to that of the pole of a magnet on a piece of soft iron ; and Faraday called
i t dielectric polarisation.

The following experiment was devised by Faraday to illustrate this
polarisation of the medium, as he called it. He placed small filaments of
silk in a vessel of turpentine (fig. 676), and, having plunged two conductors
in the liquid on opposite sides, he charged one and placed the other in con-
nection with the ground. The particles of silk immediately arranged them-
selves end to end, and adhered

closely together, forming a con- r ^_2!!!\ +e

tinuous chain between the two ^^ [fk^!fi^^^^^''^^^^^-^^^^^^^^?->')T. — /^'^

sides. An experiment by Mat- W'^W^'^' '^"Tf~|^'^^^%P

teucci also supports Faraday's 1^ J

theory. He placed several thin
plates of mica closely together,
and i)rovidcd the outside ones
with metallic coatings, like a
fulminating pane (769). Having electrified the system, the coatings were
removed by insulating handles, and on e.\amining the plates of mica succes-
sively, each was found charged with positive electricity on one side and
negative electricity on the other.

748. Specific inductive capacity. — Faraday named the property which
bodies have of transmitting electrical induction, the specific inductii^c capacity.,
or, as it is often called, the inductive power. If the dielectric does play the
essential part in the phenomena of induction it is not likely that all insu-

.170.

-748]

Specific Inductive Capacity.

715

lating bodies possess it in the same degree. This seems to have been known
to Cavendish. To determine and compare the inductive power Faraday
used the apparatus represented in fig. 677, and of which fig. 678 represents
a vertical section. It consists of a brass sphere made up of two halves, P
and Q, which fit accurately into each other, like the Magdeburg hemi-
spheres. In the interior of this spherical envelope there is a smaller brass
sphere C, connected with a metal rod, terminating in a ball B. The rod is
insulated' from the envelope PQ by a thick layer of shellac A. The space
7)in receives the substance whose inductive power is to be determined. The
foot of the appai^atus is provided with a screw and stopcock, so that it can
be screwed on the air-pump, and the air in imi either rarefied or exhausted.
Two such apparatus perfectly identical are used, and at first they only
contain air. The envelopes PQ are connected with the ground, and the
knob B of one of them receives a charge of electricity. The sphere C thus
becomes charged like the inner coating of a Leyden jar (770). The layer

I i,'. 077. Fig. 678.

mn represents the insulator which separates the two coatings. By touching
B with the proof plane, which is then applied to the torsion balance, the
quantity of free electricity is measured. In one experiment Faraday ob-
served a torsion of 250°, which represented the free electricity on B. The
knob B was then placed in metallic connection with the knob B' of the
other apparatus, and the torsion was now found to be 125°, showing that
the electricity had become equally distributed on the two spheres, as might
have been anticipated, since the pieces of apparatus were quite equal, and
each contained air in the space mn.

This experiment having been made, the space inn in the second appa-

yi6 Frictioiial Electricity. [748-

ratus was filled with the substance whose inductive power was to be deter-
mined : for example, shellac. The other apparatus, in which mn is filled
with air, having been charged, the density of the free electricity on C was
measured. Let it be taken at 290°, the number observed by Faraday in a
special case. When the knob B of the first apparatus was connected with
the knob B' of the second, the density was not found to be 145°, as would
be expected. The apparatus containing air exhibited a density of 1 14'', and
that with shellac of 1 13°. Hence the former had lost 176°, and had retained
114°, while the latter ought to have exhibited a density of 176° instead of
113°. The second apparatus had taken more than half the charge, and
hence a larger c^uantity of electricity had been condensed by the shellac.
Of the total quantity of electricity, the shellac had taken 176° and the air
114° ; hence the specific inductive capacity of air is to that of shellac as
114 : 176 ; or as i : 1-55. That is, the inductive power of shellac is more
than half as great again as air.

By the following simple experiment the influence of the dielectric may
be shown : — At a fixed distance above a gold-leaf electroscope let an elec-
trified sphere be placed, by which a certain divergence of the leaves is
produced. If, now, the charges remaining the same, a disc of sulphur or
of shellac be interposed, the divergence increases, showing that inductive
action takes place through the sulphur to a greater extent than through a
layer of air of the same thickness.

By various improved methods the following are the mean of the values
which have been obtained for the specific inductive capacity of diclecirics,
as they are called, in opposition to anelectrics^ or conductors : —

Air I -GO Shellac .... 3-04

Parafiine . . . 2-02 Sulphur .... 334

India-rubber . . . 2-22 Ebonite .... 3-42
Gutta-percha . . . 2-46 (jlass . . . . 5 to 6

These values are known as the dielectric constants ; and their determi-
nation presents considerable difficulty, owing to the occurrence of a pheno-
menon to which Faraday gave the name of electrical absorption, and which
is due to the same cause as the residual charge of condensers.

A condenser with a glass plate would thus have 5 or 6 times the capa-
city of an air condenser of the same dimensions, or the same capacity as an
air condenser of the same surface, but 5 or 6 times as thin.

Boltzmann divides dielectrics into two classes : to one of which belong
shellac, paraffine, sulphur and resin, which act like perfect insulators ; that
is, in using them the maximum charge is attained, if not instantaneously,
at all events after a very short time : in others, such as gutta-percha,
stearine, and glass, the chai'ge increases appreciably with the time.

A very interesting relation probably exists between the dielectric con-
stant and the refractive index of certain substances. Thus the following
numbers have been found : —

d s/d n

Sulphur .... 3-84 1-96 204

Resin .... 2-55 1-59 1-54

Paraffine .... 2-32 1-52 1-53

-750] Motion of Electrified Bodies. 7 1 7

where ;/ is the refractive index (538), and A^d the square root of the di-
electric constant.

Hopkinson found the following numbers for the dielectric constant of
certain liquids. Petroleum 2-10, oil of turpentine 2-23, olive oil 3-16, and
castor oil 47S.

Faraday was not able to detect any difference in the dielectric constants
of various gases. Boltzmann has shown, however, that there are differences
among them, and that there is a very close agreement between the square
root of their dielectric constants and their refractive indices, thus : —

Air .

. 1-00059

1-000295

I -000294

Carbonic acid .

. 1-00095

1-000473

I -000449

Hydrogen .

. I -00026

I -0001 32

I -000138

defiant gas

. 1-00131

1-000656

1-000678

The accurate determination of the dielectric constant is a matter of
great theoretical importance, especially from its bearing on Maxwell's
electro-magnetic theory of light. According to this theory, the medium in
which both electrical and luminous actions are transmitted is the same, and
is in fact the luminiferous ether (637), and it is a necessary consequence of
this theory that the above relation must exist between the refractive index
of a substance and its dielectric constant.

749. Communication of electricity at a distance.— In the experiment
represented in fig. 677 the opposite electricities of the conductor and the
separated cylinder tend to unite, but are prevented by the resistance of the
air. If the density is increased, or if the distance of the bodies be diminished,
the opposed electricities at length overcome this obstacle ; they rush toge-
ther and combine, producing a spark, accompanied by a sharp sound. The
negative electricity separated on the cylinder being thus neutralised by the
positive electricity of the charged body, a charge of positive electricity
remains on the cylinder. The same phenomenon is observed when a finger
is presented to a strongly electrified conductor. The latter decomposes by
induction the neutral electricity of the body, the opposite electricities com-
bine with the production of a spark, while the electricity of the same kind
as the electrified conductor, which is left on the body, passes off into the
ground.

The striking distance varies with the density, the shape of the bodies,
their conducting power, and with the resistance and pressure of the inter-
posed medium.

750. Motion of electrified bodies. — The various phenomena of attrac-
tion and repulsion, which are among the most frequent manifestations of
electrical action, may all be explained by means of ^
the laws of induction. If M (fig. 679) be a fixed
insulated conductor charged with positive electricity,
and N be a movable insulated body — for instance,
an electrical pendulum — there are three cases to be
considered :—

i. The movable body is iiiielect'fified and is a con-
ductor.— In this case M, acting inductively on N, '^' ^^'
attracts the negative and repels the positive electricity, so that the maxima of

/1 8 Frktional Electricity. [750-

density are respectively at the points a and b. Now a is nearer c than b
is ; and, since attractions and repulsions are inversely as the square of the
distance, the attraction between a and c is greater than the repulsion be-
tween b and c ; and, therefore, N will be attracted to M by a force equal
to the excess of the attractive over the repulsive force.

ii. The tnovable body is a conductor and is electrified. — If the electricity
of the movable body is different from that of the fixed body, there is always
attraction ; but if they are of the same kind, there is at first repulsion
and afterwards attraction. This anomaly may be thus explained : Besides
its charge of electricity, the neutral electricity is decomposed by the
induction of the positive electricity on M ; and consequently the hemisphere b
obtains an additional supply of positive electricity, while a becomes charged
with negative electricity. There is thus attraction and repulsion, as in
the foregoing case. The force of repulsion is at first greater, because the
quantity of positive electricity on N is greater than that of negative ;
but as the distance ac diminishes, the attractive force increases more rapidly
than the repulsive force, and finally exceeds it.

iii. Tlie movable body is a bad conductor. — If N is charged, repulsion
or attraction takes place, according as the electricity is of the same or
opposite kind to that of the fixed body. If it is in the natural state, the
body M will decompose the neutral electricity of N, and attraction will
take place as in the first case, since a powerful and permanent source of
electricity can more or less decompose the neutral electricity even of bad
conductors.

751. Gold-leaf electroscope. — The name electroscope is given to instru-
ments for detecting the presence and determining the kind of electricity in
any body. The original pith-ball pendulum is an electroscope ; but, though
sometimes convenient, it is not sufficiently delicate. Many successive im-
provements have been made in it, and have resulted in the form used, which
is due to Bennett.

Ben?tett^s, or the gold-leaf electroscope. — This consists of a tubulated glass
shape B (fig. 680), standing on a metal foot, which thus communicates with
the ground. A metal rod terminating at its upper extremity in a knob C,
and holding at its lower end two narrow strips of gold-leaf, n n, fits in the
tubulure of the shade, the neck of which is coated with an insulating
varnish. The air in the interior is dried by quicklime, or by chloride of
calcium, and on the insidcs of the shade there are two strips of gold-leaf
a, communicating with the ground. These, being charged by induction with
the opposite electricity to that of the gold lea\es, increase the divergence, and
therefore the delicacy of the apparatus. They also prevent the leaves when
diverging too suddenly from adhering to the sides, from which it is difficult
to detach them.

When the knob is touched with a body charged with either kind of
electricity, the leaves diverge ; usually, however, the apparatus is charged
by induction thus :—

If an electrified body — a stick of rubbed sculing-wax, for example— be
brought near the knoli, it will decompose the neutral electricity of the
system, attracting to the knob the electricity of the opposite kind, and
retaining it there, and roiiclling the electricity of tlu> same kiml Id thr gold

-751]

Gold Leaf Electroscope.

719

leaves, which consequently diverge. In this way the presence of an elec-
trical charge is. ascertained, but not its quality.

To ascertain ^&kind of electricity the following method is pursued : If,
while the instrument is under the influence of the body A, which we will
suppose has a negative charge, the
knob be touched by the finger, the
negative electricity produced by in-
duction pp.sses off into the ground, and
the previously divergent leaves will
collapse ; there only remains positive
electricity, retained in the knob by in-
duction from A. If now the finger be
first removed, and then the electrified
body, the positive electricity previously
retained by A will spread over the sys-
tem, and cause the leaves to diverge.
If now, while the system is charged
with positive electricity, a positively
electrified body — as, for example, an
excited glass rod — be approached, the
leaves will diverge more widely ; for
the electricity of the same kind will be repelled to the ends. If, on the
contrar}', an excited shellac rod be presented, the leaves will tend to collapse
the electricity with which they are charged being attracted by the opposite
electricity. Hence we may ascertain the kind of electricity, either by
imparting to the electroscope electricity from the body under examination,
and then bringing near it a rod charged with positive or negative electricity ;
or the electroscope maybe charged with a known kind of electricity, and the
electrified body in question brought near the electroscope.

The gold-leaf electroscope is sometimes used as an electrometer, or
measurer of electricity, by measuring the angle of divergence of the leaves ;
this is done by placing behind them a graduated scale ; for small angles the
quantity of electricity is nearly proportional to the sine of half the angle of
divergence.

Fig. 62o.

'20

Frictional Electricity

[752-

ELECTRICAL MACHINES.

752. Electrophorus. — It will now be convenient to describe the various
electrical machines, or apparatus for generating and collecting large supplies
of statical electricity. One of the most simple and inexpensive of these is
the electrophorus^ which was invented by Volta. It consists of a cake of
resin B (fig. 682), say about 12 inches in diameter, and an inch thick, which
is placed on a metal surface, or frequently fits into a wooden mould lined

Fig. 681. Fig. 682.

with tinfoil, which is called the form. Besides this there is a metal disc A
(fig. 682), of a diameter somewhat less than that of the cake, and provided
with an insulating glass handle ; this is the cover. The mode of working is
as follows : All the parts of the apparatus having been well dried, the
cake, which is placed in the form, or rests on a metal surface, is briskly
flapped with silk, or, better, with catskin, by which it becomes charged with
negative electricity. The cover is then placed on the cake. Owing, how-
ever, to the minute rugosities of the surface of the resin, the cover only
comes in contact with a few points, and, from the non-conductivity of the
resin, the negative electricity of the cake does not pass off to the cover. On
the contrary, it acts by induction on the neutral electricity of the cover, and
decomposes it, attracting the positive electricity to the under surface, and
repelling the negative electricity to the upi^er. If the upper surface be now
touched with the finger, the negative electricity, because repelled and free,
passes off, and the cover remains charged with positive electricity, held,
however, by the negative electricity of the cake ; the two electricities do
not unite, in consequence of the non-conductivity of the cake (fig. 681). If
now the cover be raised by its insulating handle, the charge diffuses itself
over the surface ; and if a conductor lie brought near it (fig. 6S2), a smart
spark passes.

The metal form on which the cake rests plays an important part in

-753J Plate Electrical MacJiine. 721

the action of the electrophorus, as it increases the quantity of electricity, and
makes it more permanent. For the negative electricity of the upper surface
of the resin, acting inductively on the neutral electricity of the lower, decom-
poses it, retaining on the under surface the positive electricity, while the
negative electricity passes otif into the ground. The positive electricity thus
developed on the under surface reacts on the negative electricity of the upper
surface, binding it, and causing it to penetrate into the badly conducting
mass, oji the surface of which fresh quantities of electricity can be excited
far beyond the limits possible without the action of the form. It is for this
reason that the electrophorus, once charged, retains its state for a consider-
able time, and sparks can be taken even after a long interval. If the form
be insulated, the charge obtained from it is far less than if it is on a con-
ducting support. For the negative electricity developed by induction on the
lower surface being now unable to escape, the condensing action referred to
cannot take place, and only a feeble charge can be given to the resin. The
retention of electricity is greatly promoted by keeping the cake on the form,
and placing the cover upon it, by which the access of air is hindered.
Instead of a cake of resin, a disc of gutta-percha, or vulcanised cloth, or
vulcanite, may be substituted ; and, of course, if glass, or any material which
is positively electrified by friction, be used, the cover acquires a negative
charge.

The electrophorus is a good instance of the conversion of work into
electropotential energy (63). When the cover is lifted from the excited cake
work must be expended in order to overcome the attraction of the electricity
in the cake for the opposite electricity developed by induction on the cover ;
and the ecjuivalent of this work appears in the form of the electricity thus
detached. Thus, when a Leyden jar is charged either by the machine or by
the electrophorus, the energy of the charge is a transformation of the work
of the operator.

753. Plate electrical macbine. — The first electrical machine was in-
vented by Otto von Guericke, the inventor also of the air-pump. It con-
sisted of a sphere of sulphur, which was turned on an axis by means of the
hand, while the other, pressing against it, served as a rubber. Resin was
afterwards substituted for the sulphur, which, in turn, Hawksbee replaced
by a glass cylinder. In all these cases the hand served as rubber ; and
Winckler, in 1740, first introduced cushions of horsehair, covered with silk,
as rubbers. At the same time Bose collected electricity, disengaged by
friction, on an insulated cylinder of tin plate. Lastly, Ramsden, in 1760,
replaced the glass cylinder by a circular glass plate, which was rubbed by
cushions. The form which the machine has now is but a modification of
Ramsden's original machine.

Between two wooden supports (fig. 683) a circular glass plate P is sus-
pended by an axis passing through the centre, and which is turned by means
of a handle M. The plate revolves between two sets oi cushions or rubbers,
F, of leather or of silk, one set above the axis and one below, which, by
means of screws, can be pressed as tightly against the glass as may be desired.
The plate also passes between two brass rods, shaped like a horse-shoe, and
provided with a series of points on the sides opposite the glass ; these rods
are fixed to larger metallic cylinders C C, which are called the prime cotiduc-

722

Frictional Electricity.

[753-

tors. The latter are insulated by being supported on glass feet, and are
connected with each other by a smaller rod ;-.

The action of the machine is thus explained. By friction with the rub-

bers the glass becomes positively and the rubbers negatively electrified.
If now the rubbers were insulated, they would receive a certain charge ot
negative electricity which it would be impossible to exceed, for the tendency
of the opposed electricities to reunite would be equal to the power of the
friction to decompose the neutral state. But the rubbers communicate with
the ground by means of a chain ; and, consequently, as fast as the negative
electricity is generated, it is continually reduced to zero by contact with the
ground. The positive electricity of the glass acts then by induction on the
conductor, attracting the negative electricity. This negative electricity
collects on the points opposite to the glass. Here its tendency to discharge
becomes so high that it passes across the intervening space of air, and
neutralises the positive electricity on the glass The conductors thus lose
their negative electricity and remain charged with positive electricity. The
plate accordingly gives up nothing to the prime conductors ; in fact, it only
abstracts from them their negative electricity.

-755] Maxim inn of Charge. 723

If the hand be brought near the conductor when charged, a spark
follows, which is renewed as the machine is turned. In this case the posi-
tive electricity decomposes the neutral electricity of the body, attracting its
negative electricity, and combining with it when the two have a sufificient
tension. Thus, with each spark, the conductor reverts to the neutral state,
but becomes again electrified as the plate is turned.

754. Precautions In reference to the machine. — The glass, of which
the plate is made, must be as little hygroscopic as possible. Of late ebonite
has been frequently substituted for glass ; it has the advantage of being
neither hygroscopic nor fragile, and of readily becoming electrified by
friction. It cannot, however, be relied on, as its surface in time undergoes a
change, especially if exposed to the light, whereby it becomes a conductor.
The plate is usually from ^V to \ of an inch in thickness, and from 20 to
30 inches in diameter, though these dimensions are not unfrequently ex-
ceeded.

The rubbers require great care, both in their construction and their pre-
servation. They are commonly made of leather, stuffed with horsehair.
Before use they are coated either with powdered aiiriim musivian (sulphuret
of tin), graphite, or amalgam. The action of these substances is not very
clearly understood. Some consider that it merely consists in promoting
friction. Others, agam, believe that a chemical action is produced, and
assign in support of this view the peculiar smell noticed near the rubbers
when the machine is worked. Amalgams, perhaps, promote most power-
fully the disengagement of electricity. Kienmayer's amalgam is the best
of them. It is prepared as follows : One part of zinc and one part of tin
are melted together and removed from the fire, and two parts of mercury
stirred in. The mass is transferred to a wooden box containing some chalk,
and then well shaken. The amalgam, before it is cold, is powdered in an
iron mortar, and preserved in a stoppered glass vessel. For use a little cacao
butter or lard is spread over the cushion, some of the powdered amalgam
sprinkled over it, and the surface smoothed by a ball of flattened leather.

In order to avoid a loss of electricity, two quadrant-shaped pieces of
oiled silk are fixed to the rubbers, so as to cover the plate on both sides :
one at the upper part from a to F, and the other in the corresponding part
of the lower rubbers. These flaps are not represented in the figure. Yellow
oiled silk is the best, and there must be perfect contact between the plate
and the cloth.

Ramsden's machine, as represented in fig. 683, only gives positive elec-
tricity. But it may be arranged so as to give negative electricity by placing
it on a table with insulating supports. The conductor is connected with
the ground by a chain, and the machine worked as before. The positive
electricity passes off by the chain into the ground, while the negative
electricity remains on the supports and on the insulated table. On bring-
ing the finger near the uprights, a sharper spark than the ordinaiy one is
obtained.

755. Maximum of ctaargre. — It is impossible to exceed a certain limit
of electrical charge with the machine, whatever precautions are taken, or
however rapidly the plate is turned. This limit is attained when the loss of
electricity equals its production. The loss depends on three causes : i. The

3 A2

724 Frictional Electricity. [755-

loss by the atmosphere, and the moisture it contains, ii. The loss by the sup-
ports, iii. The recombination of the electricities of the rubbers and the glass.
^^ The first two causes have been already mentioned.

H. L^^ With reference to the last, it must be noticed that the

^^ electrical charge increases with the rapidity of the rota-

tion, until it reaches a point at which it overcomes the
resistance presented by the non-conductivity of the
glass. At this point, a portion of the two electricities
separated on the rubbers and on the glass recombines,
and the charge remains constant. It is, therefore, ulti-
mately independent of the rapidity of rotation.

756. Quadrant electrometer. — The electrical
charge is roughly measured by the quadrant or
Henley's electrotneter, which is attached to the con-
ductor. This is a small electric pendulum, consisting
of a wooden rod d, to which is attached an ivorj' or
Fig. 684. cardboard scale (fig. 684). In the centre of this is a

small index of straw, movable on an axis, and terminating in a pith ball.
Being attached to the conductor, the index diverges as the machine is
charged, ceasing to rise when the limit is attained. When the rotation is
discontinued the index falls rapidly if the air is moist ; but in dry air it only
falls slowly, showing, therefore, that the loss of electricity in the latter case
is less than in the former.

757. Cylinder electrical macbine.- — The construction of the cylinder
machines, as ordinarily used in England, is due to Nairne. They are well
adapted for obtaining either kind of electricity. In Nairne's machine (fig.
685) the cylinder is rubbed by only one cushion C, which is made of leather

i.u- 685.

stuffed with horsehair, and is screwed to an insulated conductor A. On the
opposite side of the cylinder there is a similar insulated conductor 1>, pro-
vided with a series of points on the sides next the glass. To the lower part
of the cushion C is attached a piece of oiled silk, which extends over the

-758] Armstrongs Hydro-electric Machine. 725

cylinder to just above the points. This is not represented in the figure.
When the cylinder is turned, A becomes charged with negative and B with
positive electricity by the loss of its negative from the points P. The two
opposite electricities will now unite by a succession of sparks across D and
E. If use is to be made of the electricity, either the rubber or the prime
conductor must be connected with the ground. In the former case positive
electricity is obtained ; in the latter, negative.

758. Armstrong-'s hydro-electric maclilne. — In this machine electricity
is produced by the disengagement of aqueous vapour through narrow orifices.
The discovery of the machine was occasioned by an accident. A work-
man having accidentally held one hand in a jet of steam, which was issuing
from an orifice in a steam boiler at high pressure, while his other hand
grasped the safety-valve, was astonished at experiencing a smart shock.
Lord Armstrong (then Mr. Armstrong, of Newcastle), whose attention was
drawn to this phenomenon, ascertained that the steam was charged with
positive electricity, and, by repeating the e.xperiment with an insulated loco-
motive, he found that the boiler was negatively charged. Armstrong believed
that the electricity was due to a sudden expansion of the steam ; Faraday,
who afterwards examined the question, ascertained its true cause, which will
be best understood
after describing a
machine which

Armstrong devised
for reproducing the
phenomenon.

It consists of a
v.TOught-iron boiler
(fig. 686), with a
central fire, and
insulated on four
legs. It is about 5
feet long by 2 feet
in diameter, and
is provided at the
side with a gauge
O, to show the
height of the water
in the boiler. C is
the stopcock, which
is opened when the
steam has sufficient
pressure. Above
this is the box B, in
which are the tubes
through which the
steam is disen-
gaged. On these

Fig. 686.

are fitted jets of a peculiar construction, which will be understood from
the section of one of them, M, represented on a larger scale. They are

726

Frictional Electricity.

[758-

lined with hard wood in a manner represented by the diagram. The box
B contains cold water. Thus the steam, before escaping, undergoes partial
condensation, and becomes charged with vesicles of water — a necessary
condition, for Faraday found that no electricity is produced when the steam
is perfectly dry.

The development of electricity in the machine was at first attributed to
the condensation of the steam ; but Faraday found that it is solely due to
the friction of the globules of water against the jet. For if the little cylinders
which line the jets are changed, the kind of electricity is changed ; and if
ivory is substituted, little or no electricity is produced. The same effect is
produced if any fatty matter is introduced into the boiler. In this case the
linings are of no use. It is only in case the water is pure that electricity is
disengaged, and the addition of acid or saline solutions, even in minute
quantity, prevents any disengagement of electricity. If turpentine is added
to the boiler, the effect is reversed— the steam becomes negatively, and the
boiler positively, electrified.

With a current of moist air Faraday obtained effects similar to those of
this apparatus, but with dry air no effect is produced.

759. Holtz's electrical machine. — Before the end of last century elec-
trical machines were known in this country in which the electricity was not

developed by friction, Init by the continuous inductive action of a body
already electrified, as the electrophorus ; within the last few years such

-759]

Holtz's Electrical Machine.

727

machines have been re-invented and come into use. The form represented
in fig. 687 was invented by Holtz, of BerHn.

It consists of two circular plates of thin glass at a distance of 3 mm. from
each other ; the larger one, AA, which is 2 feet in diameter, is fixed by means
of 4 wooden rollers a, resting on glass axes and glass feet. The diameter of
the second plate, B B, is 2 inches less ; it turns on a horizontal glass axis,
which passes through a hole in the centre of the large fixed plate without
touching it. In the plate A, on the same diameter, are two large apertures,
or 7vi/idoius, Y ¥'. Along the lower edge of the window F, on the posterior
face of the plate, a band of paper, /, is glued, and on the anterior face a sort
oi tongue of thin cardboard, «, joined to/ by a thin strip of paper, and pro-
jecting into the wmdow. At the upper edge of the window, F', there are
corresponding parts,/' and ?t'. The papers/ and /' constitute the armatures.
The two plates, the armatures, and their tongues are covered with shellac
varnish, but more especially the edges of the tongues.

In front of the plate B, at the height of the armatures, are two brass
combs., O O', supported by two conductors of the same metal, C C. In the
front end of these conductors are two moderately large brass knobs, through
which pass two brass rods terminated by smaller knobs, r r\ and provided
with ebonite handles, K K'. These rods, besides moving with gentle friction
in the knobs, can also be turned so as to be more or less near and inclined
towards each other. The plate B B is turned by means of a winch M,and a
series of pulleys which transmit its motion to the axis ; the velocity which
it thus receives is 12 to 15 turns in a second, and the rotation should take
place in the direction indicated by the arrows — that is, towards the points of
the cardboard tongues 71 ?i'.

To work the machine, the armatures //' must be first primed — that is,
one of the armatures is positively and the other negatively electrified. This
is effected by means of a plate of ebonite, which is excited by striking it
with catskin ; the two knobs rr' having been connected so that the two
conductors C C only form one, as seen in fig. 688, which shows by a hori-

n- A

<»"*'«'«'«

Fig. 63S.

zontal section, through the axis of rotation, the relative arrangement of the
plates and of the conductors. The electrified ebonite is then brought near
one of them — •/, for instance — and the plate B is turned. The ebonite is
charged with negative electricity, and this withdraws the positive electricity
of the armature and charges it negatively. This latter acting by induction
through the plate B B, as it turns on the conductors OCC'O' (fig. 688), attracts
through the co>nl) O the positive electricity which collects on the front face of
the movable plate ; while at the same time negative electricity, repelled on
the comb O', collects, like the former, on the front face of the plate B.
Hence, the two electricities being carried along by the rotation, at the end

728

Frictional Electricity.

[759-

of half a turn all the lower half of the plate B, from/ to F' (fig. 689). is posi-
tively electrified, and its upper surface from p' to F negatively. But the two
opposite electricities above and below the window F' concur in decomposing
the electricity of the armature j!^';z' ; the partj?^ is positively electrified, while
negative electricity is liberated by the tongue n\ and is deposited on the
inner face of the plate B B, which from its thinness almost completely neu-
tralises the positive electricity on the anterior face.

The two armatures are then primed, and the same effect as at F' is
produced at F on the armature p n — that is, that the opposite electricities
above and below p n, decomposing a new quantity of neutral electricity,
the negative charge of the part/ increases, while the positive electricity which
is liberated by the tongue n neutralises the negative electricity which comes
from F' towards F ; and so forth, until, the machine having attained its

Fig. 689.

maximum charge, there is equilibrium in all its parts. From that point it
only keeps itself up, and in perfectly dry air it may work for a long time
without its l:)eing necessary to employ the ebonite plate. If this be removed,
and the knobs r and ;-' are moved apart (fig. 6S7) to a distance dependent
on the power of the machine, on continuing to turn, a torrent of sparks
strikes across from one knob to the other.

With plates of equal dimensions Holtz's machine is far more powerful
than the ordinary electrical machine (753). The power is still further increased
by suspending to the conductors C C two condensers, H H' (765), or small
Leyden jars, which consist of two glass tubes coated with tinfoil, inside and
out, to within a fifth of their height. Each of them is closed by a cork
through which passes a rod, communicating at one end with the inner coat-
ing, and suspended to one of the conductors by a crook at the other end-
The two external coatings are connected by a conductor, G. They are, in
fact, only two small Leyden jars (770), one of them, H, becoming charged
with positive electricity on the inside and negative on the outside ; the other,
ir, with negative electricity on the inside and positive on the outside,
becoming charged by the play of the machine, and being discharged at the

-760] WimsJmrsfs MacJiine. 729

same rate by the knoljs rr\ they strengthen the spark, which may attain a
length of 6 or 7 inches.

The current of the machine is utilised by placing in front of the frame
two brass uprights, ^(^' , with binding screws in which are copper wires ; then,
by means of the handles K K', the rods which support the knobs rr' are in-
clined, so that they are in contact with the uprights. The current being-
then directed by the wires, a battery of six jars can be charged in a few
minutes, water can be decomposed, a galvanometer deflected, and Geissler's
tubes illuminated as with the voltaic battery.

Kohlrausch found that a Holtz machine with a plate 16 inches in dia-
meter, and making 5 turns in three seconds, produced a constant current
capable of decomposing water at the rate of 3^ millionths of a milligramme
in a second. This is equal to the effect produced by a Grove's cell in a cir-
cuit of 45,000 ohms resistance.

Rossetti, who made a series of measurements with a Holtz machine,
found that the strength of the current is nearly proportional to the velocity
of the rotation ; it increases a little more rapidly than the rotation. The ratio
of the velocity of rotation to the strength of the current is greater when the
hygrometric state increases. The current produced by a Holtz machine is
quite comparable to that of a voltaic couple. Its electromotive force and
resistance are constant, provided the velocity of rotation and the hygrometric
state are constant.

The electromotive force is independent of the velocity of rotation, but
diminishes as the moisture increases ; it is nearly 52,000 times as great as
that of a Daniell's cell.

The internal resistance is independent of the moisture, but diminishes
rapidly with increased velocity of rotation. Thus with a velocity of 120 turns
in a minute it is represented by 2,810 million ohms (964), and with a velocity
of 450 turns it is 646 million ohms.

Holtz's machine is very much affected by the moisture of the air ; but
Ruhmkorfif found that by spreading on the table a few drops of petroleum,
the vapours which condense on the machine protect it against the moisture
of the atmosphere.

Holtz's machine alTords a means of making a curious experiment on
reversibility. If the two combs of a machine in the ordinary state are con-
nected with the poles of a second similar one, which is then set in action,
the combs of the first become luminous, and the plate begins to rotate, but
in the opposite direction to its ordinary course ; the electricity thus transmits
the motion of the second machine to the first ; the one expends what the
other produces. It may also be observed that the two machines are con-
nected by opposite poles, and the system constitutes a circuit which is tra-
versed in a definite direction by a continuous electrical current.

A ver)' simple and efficient machine of this kind is made by Voss of
Berlin. One with a plate of 10 inches diameter produces a spark of 4 to 5
inches.

760. 'Wimshurst'8 machine. — This is the simplest and most efficient of
all induction machines.

It consists (fig. 690) of two circular glass discs mounted on a fixed
horizontal spindle in such a way as to be rotated in opposite directions at a

730 Frictional Electricity. [760-

distance of not more than a quarter of an inch apart. Both discs are well
varpished, and attached to the outer surface of each are narrow radial
sections of tinfoil arranged at equal angular distances apart.

Fig. 690.

Attached to the fixed spindle on which the discs rotate is a bent conduct-
ing rod, at the ends of which are two fine wire brushes ; twice during each
revolution two diametrically opposite conductors are put in connection with
each other by means of this conductor, as they just graze the tips of the
brushes. At the back is a similar one at right angles to that in front, and
there is a position of maximum efficiency, which is when they make an angle
of 45° with the fixed collectors. There are two forks provided with combs
directed towards one another, and towards the t\\o discs which rotate between
them ; they are supported horizontally on glass Leyden jars, to which are
also attached the terminal electrodes or dischargers, the distance apart of
which can be varied by turning the Leyden jar from which they rise.

The machine is quite self-exciting, and requires neither friction, nor the
spark from any outside exciter, to start it. This is one of the most remark-
able features of this machine, that under ordinary conditions it attains its
full power after the second or third turn. The initial discharge is probably
obtained from the electricity of the air, or from the frictional resistance
against it.

-761] JVor/c Required for the Production of Electricity, 731

With a machine having plates 17 inches in diameter, a powerful spark
discharge passes between the two electrodes when they are 4 to 5 inches
apart, in regular succession, at the rate of 2 or 3 for every turn of the handle.
A machine with 12 plates, 30 inches in diameter, when driven at a speed of
200 turns per minute, produces sparks between the terminals of 13^ inches
in length ; and when the terminals are closed by a wire of 3,000 ohms
resistance (964) a current of § of a millampere is produced. With these
machines the increase of electricity has been found proportional to the
speed of rotation up to 5,000 turns in a minute.

It is not easy to give a satisfactory account of the theory of the machine.
Its inventor considers that the remarkable efficiency may be partly due
to the duplex action of the apparatus, both plates being active and con-
tributing electricity to the collecting combs, the sector-shaped plates of tin-
foil acting as inductors when in their position of lowest efficiency as carriers,
and as carriers when in the positions at which their inductive effect is at a
minimum, and vice versa, and as it follows from the construction of the
instrument that the inductors of the one disc are at a position of highest
efficiency when those of the other are at their lowest, and vice versa, and as
this applies with equal force to the sectors when considered as carriers, it
also follows that the charging of the electrodes, and therefore the discharge
between them, is by mutual compensation maintained constant.

761. Work required for the production of electricity.— In all electrical
machines electricity is only produced by the expenditure of a definite amount
of force, as will at once be seen by a perusal of the preceding descriptions.
The action of those machines, however, which work continuously, is some-
what complex. Not only is electricity produced, but heat also ; and it has
been hitherto impossible to estimate separately the work required for the
heat from that required for the electricity. This is easily done in theory, but
not in practice : it would be, for instance, difficult to determine the tem-
perature of the cushion, or of the plate of a Ramsden machine.

By means of a Lane electrometer (717) it was found that taking as unity
the quantity of electricity produced by one turn of a Ramsden machine with
a plate 39 inches in diameter, that produced by a Holtz machine with a
plate of 21 inches was o-86 ; but as for the same work the former made i
and the latter 10 turns in a second, it follows that the quantities produced
were as i : 8-6. Comparing the quantities per unit of surface, the yield of
the Holtz machine is more than 12 times that of the Ramsden.

In lifting the plate off a charged electrophorus a certairk expenditure of
force is needed, though it be too slight to be directly estimated (752). With
a Holtz machine it may be readily shown by experiment that there is a
definite expenditure of force in working it. If such a machine be turned
without having been charged, the work required is only that necessary to
overcome the passive resistances due to friction. If, however, a charged
ebonite plate is approached to one of the sectors, as soon as the peculiar
sound indicates that the machine is at work, it will be observed that there
must be a distinct increase in the mechanical effort necessary to work the
machine.

The work required to charge an unelectrified conductor to a given poten-
tial may be deduced from the following considerations : — To impart to a body

7^^

Frictional Electricity.

[761-

which is at potential V a quantity of electricity Q would require an amount
of work represented by QV (739). But in the case of an unelectrified body it
is neutral at the outset — that is, at zero potential ; and we may conceive the
electricity imparted to it in a series oi 11 very small charges of q each, such
that 71 q = Q ; and as the potential rises proportionally to the number of
charges, it may be assumed that the work done is equal to that required to
charge the body to an average potential of W ; hence the work in question
W = ^QV.

From the relation between the quantity of heat produced by the current
of a Holtz machine working under definite conditions, and the amount of
work expended in producing the rotation of the plate, Rossetti has made a
determination of the mechanical equivalent of heat, which gave the number
1,397, agreeing therefore very well with the numbers obtained by other
methods (497).

761(7. Thomson's water-dropping- collector. — This may be given as an
illustration of an arrangement by which a known charge may be almost in-
definitely multiplied. In fig. 691 I is an insulated metal cylinder called the
niductor, and water falls in drops from an uninsulated metal tap the nozzle
of which is in the centre of the cylinder. Directly below the inductor is a
second similar insulated metal cylinder R, with a funnel the nozzle of which
is also in the centre. This second cylinder is called
the receiver. If now a very feeble positive charge be
given to the inductor I, the drops of water .as they
issue will be charged with positive electricity, and will
repel each other as they issue. Falling on the funnel
of the receiver they will give up to this the whole of
their charge, and the water as it issues will be neutral.
The charge thus imparted to R will go on increasing
until the loss equals the production, or until the drops
issuing from the inductor are repelled by the receiver,
so that they do not fall into the funnel.

Suppose two such apparatus I I' and R R' be
arranged near each other, and in such a manner that
the inductor I of the one is in metallic connection with
the receiver R' of the other, and conversely the in-
ductor r in connection with the receiver R of the other.
By this means they will act on each other and recipro-
cally increase their charges. If a feeble charge be
given to one of the inductors, the charges will go on
increasing until sparks pass between. It is not even
necessary to give a charge at the outset, the ordinary electricity of the atmo-
sphere is sufficient.

The energy in this apparatus is derived from that of the falling body, and
would be exactly equivalent to it if there were no loss, and if the drops
reached the funnel without any velocity.

Fig. 631

-762]

Spark.

733

EXPERIMENTS WITH THE ELECTRICAL MACHINE.

762. Spark. — One of the most curious phenomena observed with the
electrical machine is the spark drawn from the conductor when a finger is
presented to it, The positive electricity of the conductor, acting inductively
on the neutral electricity of the body, decomposes it, repelling the positive
and attracting the negative. When the attraction of the opposite electricities
is sufficiently great to overcome the resistance of the air, they recombine
with a smart crack and a spark. The spark is instantaneous, and is accom-
panied by a sharp prickly sensation, more especially with a powerful machine.
Its shape varies. When it strikes at a short distance it is rectilinear, as seen
in fig. 692. Beyond two or three inches in length the spark becomes irre-
gular, and has the form of a sinuous curve with branches (fig. 693). If the
discharge is very powerful, the spark takes a zigzag shape (fig. 694). These
two latter appearances are seen in the discharge of lightning.

Fig. 692

Fig. 693.

Fig. 694.

A spark may be taken from the human body by aid of the insiilati7ig
stool, which is simply a low stool with stout glass legs. The person standing
on this^stooi touches the prime conductor, and, as the human body is a con-
ductor, the electricity is distributed over its surface as over an ordinary
insulated metallic conductor. The hair diverges in consequence of repulsion,
a peculiar sensation is felt on the face, and if another person, standing on
the ground, presents his hand to any part of the body, a smart crack with a
pricking sensation is produced.

734

Friciional Electricity.

[762-

001

Gi^—

A person standing on an insulated stool may be positively electrified by
being struck with a catskin. If the person holding the catskin stands on an
_ insulated stool, the striker becomes

positively and the person struck nega-
tively electrified.

763. Electrical ctalmes. — The
electrical cJiimcs is a piece of apparatus
consisting of three bells suspended to
a horizontal metal rod (fig. 695). Two
of them, A and B, are in metallic con-
nection with the conductor ; the middle
bell hangs by a silk thread, and is thus
insulated from the conductor, but is
connected with the ground by means
of a chain. Between the bells are
small copper balls suspended by silk threads. When the machine is worked,
the bells A and B, being positively electrified, attract the copper balls, and
after contact repel them. Being now positively electrified, they are in turn
attracted by the middle bell, C, which is charged with negative electricity
by induction from A to B. After contact they are again repelled, and this
process is repeated as long as the machine is in action.

Fig. 696 represents an apparatus originally devised by Volta for the
purpose of illustrating what he supposed to be the motion of hail between

Fig. 695

Fig. 696.

Fig. 697.

two clouds oppositely electrified. It consists of a tubulated glass shade,
with a metal base, on which are some pith balls. The tubulure has a metal
cap, through which passes a brass rod, provided with a metal disc or sphere
at the lower end, and at the upper with a ring, which touches the prime
conductor.

When the madiinc is worked, the sphere l)(.'c()ming positively electrified
attracts the light pith l)alls, which arc then immeiliately repelled, and, having

-764]

Electrical Whirl or Vane.

735

lost their charge of positive electricity, are again attracted, again repelled,
and so on, as long as the machine continues to be worked. An amusing
modification of this experiment is frequently made by placing between the
two plates small pith figures, somewhat loaded at the base. When the
machine is worked, the figures execute a regular dance.

764. Electrical wblrl or vane. — The electrical whirl or vatie consists
of 5 or 6 wires, terminating in points, all bent in the same direction, and
fixed in a central cap, which rotates on a pivot (fig. 697). When the appa-
ratus is placed on the conductor, and the machine worked, the whirl begms
to revolve in a direction opposite that of the points. This motion is not
analogous to that of the hydraulic tourniquet (149). It is not caused by a
flow of material fluid, but is owing to a repulsion between the electricity of
the points and that which they impart to the adjacent air by conduction. The
electricity, being accumulated on the points in a high state of density, passes
into the air, and, imparting thus a charge of electricity, repels this electricity,
while it is itself repelled. That this is the case is evident from the fact that
on approaching the hand to the .whirl while in motion, a slight draught is
felt, due to the movement of the electrified air, while in vacuo the apparatus
does not act at all. This draught or wind is known as the electrical aura.

If the experiment be made in water, the fly remains stationary, for water
is a good conductor ; but in olive oil, which is a bad conductor, the whirl
rotates.

When the electricity thus escapes by a point, the electrified air is repelled
so strongly as not only to be perceptible to the hand, but also to engender
a current strong enough to blow out a candle. Fig. 698 shows this experi-
ment. The same efifect is produced by placing a taper on the conductor
and bringing near it a pointed wire held in the hand (fig. 699). The current

Fig. 698.

arises in this case from the flow of air electrified with the contrary electricity
which escapes by the point under the influence of the machine. The loss
of electricity in this way by contact with easily-moving bodies is analogous
to the transmission of heat by convection.

The electrical orrery and the electrical Inclined plane are analogous in
their action to these pieces of apparatus.

The velocity of the electrical aura has been determined by placing a
wire gauze connected with earth at a fixed distance from the point, and an
anemometer at varying distances behind the gauze. The velocity of the

•36

Frictional Electricity

[764-

wind was found to diminish with the distance, but not in direct proportion ;
at a distance of 22 inches it was 5^ feet per second, while at 60 inches its
velocity was 2 feet per second.

The production of the electi'ical aura is accompanied by luminous
phenomena which can be seen in the dark. If positive electricity escapes
from the point a violet aigrette is formed ; while when the electricity is
negative a small brilliant star forms on the point.

It is pretty certain that in these experiments it is not the air itself, but
the particles in it, whether of dust or of moisture, which become electrified.

This may be illustrated by
the following simple ex-
penment. A glass globe
is filled with dense smoke
of turpentine or petro-
leum (fig. 700), and the
bared end of a gutta-
percha-covered wire is
held in it while the other
end is connected with an
electrical machine. On
giving two or three turns
to the machine the smoke
is rapidly deposited, and
the inside becomes quite
clear. Here the smoke
consists of solid particles,
which become polarised by induction and attract each other like the particles
of silk in fig. 676. They thereby become agglomerated, and fall to the
bottom of the globe. Nahrwold proves that if air is freed from dust by
filtration it takes little or no charge from an electrified point.

This phenomenon is employed industrially in the deposition of finely
suspended powders, as in lead works. Two conductors provided with points
arc connected respectively with a positive and negative source of electricity ;
the powder electrified by the one point is repelled and is precipitated on the
other.

-765J

Condensers or Accuniulators.

717

CHAPTER IV.

CONDENSATION OR ACCUMULATION OF ELECTRICITY.

765. Condensers or Accumulators. — A condenser is an apparatus for
condensing a large quantity of electricity on a comparatively small surface.
The form may vary considerably, but in all cases consists essentially of two
insulated conductors, separated by a non-conductor, and the working depends
on the action of induction. When an insulated conductor is near other
conductors, and particularly when these latter are connected with the earth,
the capacity of the conductor is increased ; that is to say, it requires a
greater quantity of electricity to raise it to a given potential than when the
other conductors are away. An arrangement of this kind is called a con-
denser or acciamdator, the latter term, though less usual, being preferable, as
the former tacitly implies some hypothesis of the nature of electricity.

Epinus's condenser consists of two circular brass plates, A and B (fig.
701), with a sheet of glass, C, between them. The plates, each provided

Fig. 701.

with a pith-ball pendulum, are mounted on insulated glass legs, and can be
moved along a support and fixed in any position. When electricity is to be
accumulated, the plates are placed in contact with the glass, and then one of
them, B for instance, is connected with the electrical machine, and the other
placed in connection with the ground, as shown in fig. 702.

73^

Frictional Electricity.

[765-

In explaining the action of the condenser, it will be convenient in each
case to call that side of the metal plate nearest the glass the cwtcrio}' and
the other the posteftor side. And first let A be at such distance from B as
to be out of the sphere of its action. The plate B, which is then connected
with the conductor of the electrical machine, takes its maximum charge,
which is distributed equally on its two faces, and the pendulum diverges

Fig. 702.

widely. If the connection with the machine be interrupted, nothing would
be changed ; but if the plate A be slowly approached, its neutral state being
decomposed by the influence of B, negative electricity is accumulated on its
anterior face, ft (fig. 703), and positive passes into the ground. But as
the negative electricity of the plate A reacts in its turn on the positive of
the plate B, the latter ceases to be equally distributed on both faces, and
is accumulated on its anterior face, m. The posterior ia.ce.,p, having thus
lost a portion of its electricity, its density has diminished, and is no longer
equal to that of the machine, and the pendulum b diverges less widely.
Hence B can receive a fresh quantity from the machine, which, acting as just
described, decomposes by induction a second quantity of neutral electricity
on the plate A. There is then a new accumulation of negative electricity
on the face «, and consequently of posi-
tive electricity on m. But each time that
the machine gives off electricity to the
plate, only a part of this passes to the
face f/i, the other remaining on the face
p ; the density here, therefore, continues
to increase until it equals that of the
machine. From this moment equilibrium
is established, and a limit to the charge
is attained which cannot be exceeded.
The quantity of electricity accumulated
now on the two faces /ii and ;/ is very considerable, and yet the pendulum
diverges just as much as it did when A was absent, and no more ; in fact,
the density at/ is just what it was then — namely, that of the machine.

-766J Shzu Discharge and Instantaneous Discharge. 739

When the condenser is charged— that is, when the opposite electricities
are accumulated on the anterior faces— connection with the ground is broken
by raising the wires. The plate A is charged with negative electricity, but
simply on its anterior face (fig. 703), the other side being neutral. The
plate B, on the contrary, is electrified on both sides, but unequally ; the ac-
cumulation is only on its anterior face, while on the posterior,/, the density
is simply equal to that of the machine at the moment the connections
are interrupted. In fact, the pendulum b diverges, and a remains vertical.
But if the two plates are removed, the two pendulums diverge (fig. 701),
which is owing to the circumstance that, as the plates no longer act on each
other, the positive electricity is equally distributed on the two faces of the plate
B, and the negative on those of the plate A.

766. Slow dlscharg-e and Instantaneous discbargre. — While the plates
A and B are in contact with the glass (fig. 702), and the connections inter-
rupted, the condenser may be discharged — that is, restored to the neutral
state — in two ways ; either by a slow or by an instantaneous discharge. To
discharge it slowly, the plate B— that is, the one containing an excess of elec-
tricity— is touched with the finger ; a spark passes, all the electricity on p
passes into the ground, the pendulum b falls, but a diverges. For B, having
lost part of its electricity, only retains on the face m that held by the inductive
influence of the negative on A. But the quantity thus retained at B is less
than that on A ; this has free electricity, which makes the pendulum a diverge ;
and if it be now touched, a spark passes, the pendulum a sinks while b rises,
and so on by continuing to touch alternately the two plates. The discharge
only takes place slowly ; in very dry air it may require several hours. If the
plate A were touched first, no electricity would be removed, for all it has is
retained by that of the plate B. To remove the total quantity of electricity
by the method of alternate contacts, an infinite number of such contacts would
theoretically be required.

An instantaneous discharge may be effected by means of the discharging
rod (fig. 704). This consists of two bent brass rods, terminating in knobs
and joined by a hinge. When provided with glass
handles, as in fig. 704, it forms a glass discharging
rod. In using this apparatus one of the knobs is
pressed against one plate of the condenser, and the
other knob brought near the other. At a certain dis-
tance a spark strikes from the plate to the knob, caused
by the sudden recomposition of the two opposite elec-
tricities.

When the condenser is discharged by the dis-
charger no sensation is experienced, even though the
latter be held in the hand ; of the two conductors,
the electricity chooses the better, and hence the pig_ ^^^

discharge is effected through the metal, and not

through the body. But if, while one hand is in contact with one plate
the other touches the second, the discharge takes place through the breast
and arms, and a considerable shock is felt ; and the larger the surface of
the condenser, and the greater the electric density, the more violent is the
shock.

3 B 2

740

Frictional Electricity.

[767-

767. Condensing- force. — The cofidensing force is the relation between
the whole charge, which the collecting plate can take while under the in-
fluence of the second plate, and that which it would take if alone ; in other
words, it is the ratio of the capacities under the two conditions.

768. Xlmit of the charge of condensers. — The quantity of electricity
which can be accumulated on each plate is, cceteris paribus., proportional to
the potential of the electricity on the conductor, and to the surface of the
plates ; it decreases as the insulating plate is thicker, and it differs with the
specific inductive capacity of the substance. There is, however, a limit in
the case of each condenser beyond which it cannot be charged. The effect
of dielectric polarisation (747) is to put the medium into a state of strain
from which it is always trying to release itself, and which is the equivalent
of the work done in charging a condenser. This is, indeed, the seat of the
electrical energy. It is as if two surfaces were pulled together by elastic
threads which repelled each other laterally. When the strain exceeds a
certain limit, a discharge takes place through the mass of the dielectric,
generally accompanied by light and sound, and with a temporary or perma-
nent rupture of the dielectric according as it is fluid or solid. This is what
takes place when a substance — glass, for instance— is exposed to a continually
increasing weight ; a point is ultimately reached at which the glass gives
way, and the weight at that point is a measure of the resistance to fracture
of the glass. In like manner, the point at which the electrical discharge takes
place is a measure of the electrical strength of the dielectric. This electrical
strength is greater in glass than in air, and in dense than in rarefied air.

Thus to produce a spark of 0-5 cm. in wire at the pressures 20, 180, and
685 mm. respectively, the only potentials required were 3-23, 12-2, and 36.

We may, following Maxwell, further illustrate this point by the twisting
of a wire : a wire in which a small force produces a permanent twist corre-
sponds to the case
of the conduction
of electricity in a
good conductor ;
one which having
been twisted, re-
\erts to its former
shape when the
twisting force is
removed, is com-
pletely elastic, and
corresponds to a
perfect insulator
with respect to the
charge employed.
If no permanent
twist can be given
to the wire by a
f'S- 705. force which doesnot

break it, the wire is brittle. A dielectric such as air, which does not transmit
electricity except by disruptive discharge, may be said to be electrically brittle.

770]

Lcydcn Jar.

741

769. Fulminating- pane. Franklin's plate. — This is a simple form of
the condenser, and is more suitable for giving strong shocks and sparks. It
consists of a glass plate fixed in a wooden frame (fig. 705) ; on each side of
the glass, pieces of tinfoil are fastened opposite each other, leaving a space
free between the edge and the frame. It is well to cover this part of the
glass with an insulating layer of shellac varnish. One of the sheets of tin-
foil is connected with the ring on the frame by a strip of tinfoil, so that it can
be connected with the ground by means of a chain. To charge the pane the
insulated side is connected with the machine. As the other side communi-
cates with the ground, the two coatings play exactly the part of the condenser.
On both plates there are accumulated large quantities of contrary electricities.

The pane may be discharged by touching one knob of the discharger
against the lower surface, while the other is brought near the upper coating.
A spark ensues, due to the recombination of the two electricities ; but the
operator experiences no sensation, for the discharge takes place through the
wire. But if the connection between the two coatings be made by touching
them with the hands, a violent shock is felt in the hands and breast, for the
combination then takes place through the body.

770. SCieyden jar. — The Ley den jar ^ so named from the town of Leyden,
where it was invented, is essentially a modified condenser, or fulminating
pane rolled up. Fig. 706 represents a Leyden jar of the usual French shape
in the process of being charged. It consists of a glass jar of any conve-
nient size, the interior of which is either coated with tinfoil or filled with thin
leaves of copper, or with gold-leaf. Up to a certain distance from the neck
the outside is coated with tinfoil. The neck is provided with a cork, through
which passes a brass rod,

which terminates at one /^^^ A

end in a knob, and com-
municates with the metal
in the interior. The me-
tallic coatings are called
respectively the inner and
outer coatings or arma-
tures. Like any other con-
denser, the jar is charged
by connecting one of the
coatings with the ground,
and the other with the
source of electricity. When it is held in the hand by the outer coating, and
the knob presented to the positive conductor of the machine, positive elec-
tricity is accumulated on the inner and negative electricity on the outer
coating. The reverse is the case if the jar is held by the knob, and the
outer coating presented to the machine. The positive charge acting
inductively across the dielectric glass, decomposes the electricity of the
outer coating, attracting the negative and repelling the positive, which
escapes by the hand to the ground. Thus it will be seen that the action of
the jar is the same as that of the condenser, and all that has been said of
this applies to the jar, substituting the two coatings for the two plates A and
B of fig. 702.

Fig. 706.

742

F}'ictional Elcctncity.

[770-

Like any other condenser, the Leyden jar may be discharged either
slowly or instantaneously. For the latter purpose it is held in the hand by
the outside coating (fig. 707), and the two coatings are then connected by
means of the simple discharger. Care must be taken to touch first the
external coating with the discharger, otherwise a smart shock will be felt.
To discharge it slowly the jar is placed on an insulated plate, and first the
inner and then the outer coating touched, either with the hand or with a
metallic conductor. A slight spark is seen at each discharge.

Fig. 708 represents a very pretty experiment for illustrating the slow
discharge. The rod terminates in a small bell, d^ and the outside coating-

Fig. 707.

is connected with an upright metal support, on which is a similar bell, e.
Between the two bells a light brass ball is suspended by a silk thread. The
jar is then charged in the usual manner and placed on the support m. The
internal coating contains a quantity of free electricity ; the pendulum is
attracted and immediately repelled, striking against the second bell, to
which it imparts its free electricity. Being now neutralised, it is again

attracted l^y the first bell, and so on for some time, especially if the air be
dry, and the jar somewhat large.

-772 J

Residua/ Charoc.

743

771. Iieyden jar with movable coatings. — This apparatus (fig. 709) is
used i;o demonstrate that in the Leyden jar the opposite electricities are not
accumulated on the coatings merely, but are stored up in the state of strain
into which the glass is put, and this state of strain is the mechanical equiva-
lent of the work done in charging the jar. It consists of a somewhat
conical glass vessel, B, with movable coatings of zinc or tin, C and D. These
separate pieces placed one in the other, as shown in figure A, form a
complete Leyden jar. After having charged the jar, it is placed on an insu-
lating cake ; the inner coating is first removed by the hand, or better by a

glass rod, and then the glass vessel. The coatings are found to contain
little or no electricity, and if they are placed on the table they are restored
to the neutral state. Nevertheless, when the jar is put together again, as
represented in the figure at A, a shock may be taken from it almost as strong
as if the coatings had not been removed. It is therefore concluded that the
coatings principally play the part of conductors, distributing the electricity
over the surface of the glass, which thus becomes polarised, and retains this
state even when placed on the table, owing to its imperfect conductivity.

The experiment may be conveniently made without any special form of
apparatus by forming a Leyden jar, of which the inside and outside coatings
are of mercury, charging it ; then having mixed the two coatings, the apparatus
is put together again, upon which a discharge may be once more taken.

772. Xiicbtenberg-'s fig-ures. — This experiment well illustrates the oppo-
site electrical conditions of the two coatings of a Leyden jar. Holding a

jar charged with positive elec-
tricity by the hand, a series of
lines are drawn with the knob
on a cake of resin or vulcanite ;
then having placed the jar on
an insulator, it is held by the
knob, and another series traced
by means of the outer coating.
If now a mixture of red-lead and
flour of sulphur be projected on
the cake, the sulphur will attach
itself to the positive lines, and
the red lead to the negative
lines ; the reason being that in
mixing the powders the sulphur
has become negatively electri-
fied, and the red lead positively.
The sulphur will arrange itself
in tufts with numerous diverging"
branches, while the red lead will take the form of small circular spots, in-
dicating a difference in the two electricities on the surface of the resin.
These figures form, in short, a very sensitive electroscope for investigating
the distribution of electricity on an insulating surface {"jyj).

Fig. 710 represents the appearance of a plate of resin, which has been
touched by the knob of a Leyden jar charged with positive electricity, and
has then been dusted with lycopodium powder.

744 Frictio7ial Electricity. [773-

'J12,. Residual charg-e. — Not only do the electricities adhere to the two
surfaces of the insulating medium which, separates them, but they penetrate
to a certain extent into the interior, as is shown by the following experi-
ment : — A condenser is formed of a plate of shellac and movable metal plates.
It is then charged, retained in that state for some time, and afterwards com-
pletely discharged. On removing the metal coatings and examining both
surfaces of the insulator, they show no signs of electricity. After some time,
however, each face exhibits the presence of some electricity of the same
kind as that of the plate with which it was in contact while the apparatus was
charged. This is explained, by some, as a kind of elect7'ical absorption.

A phenomenon frequently olaserved in Leyden jars is of the same nature.
When a jar has been completely discharged by bringing the inner and
outer coatings in metallic contact, and allowed to stand a short time, it
exhibits a second charge, which is called the electric residue. The jar may
be again discharged, and a second residue will be left, feebler than the first,
and so on, for three or four times. Indeed, with a delicate electroscope a
long succession of such residues may be demonstrated. The residue is
greater the longer the jar has remained charged. The magnitude of the
residue further depends on the amount of the charge, and also on the
degree in which the metal plates are in contact with the insulator. It
varies with the nature of the substance, but there is no residue with
either liquids or gaseous insulators. Faraday found that with parafifine
the residue was greatest, then with shellac, while with glass and sulphur it
was least of all. Kohlrausch has found that the residue is nearly proportional
to the thickness of the insulator. If successive small charges, alternately
positive and negative, be imparted to the jar, it is found that the residual
charges come out in the reverse order to that in which the original charges go
in. This residue is not to be confounded with that observed when a Leyden
jar is discharged at the greatest striking distance (788), and which residue
Reiss found to be always in a constant proportion, y-\,of the entire charge.

Maxwell proved that a dielectric composed of strata of different materials
may exhibit the phenomena of the residual charge, even though none of the
substances composing it exhibit it when alone.

From what has been said as to the state of mechanical strain in which
the dielectric of a condenser is thrown when charged with electricity, it is
not difficult to account for the phenomenon of the residual charge. An
elastic body, such as a steel plate, which has been
twisted or bent, reverts to its original state when the
force which brought about the deformation ceases to
act, but not at once quite completely. A certain length
of time is required for this alteration to take place, but
I the change is promoted by any gentle mechanical
\ action, such as tapping, which gives the molecules a
^ certain freedom of motion. Dr. Hopkinson has made
an experiment with a Leyden jar which is quite ana-
„. logous to this. A glass vessel (fig. 711) contains sul-

phuric acid, and in it is placed a thinner one, about half
full of the same ]i(|uid. Platinum wires dip in the two liquids, one of which
is in connection wiili the prime conductor of an electrical machine, while the

-775]

Electric Batteries.

745

other is connected with the earth. The arrangement forms, in short, a con-
denser, the coatings of which are sulphuric acid. When, after being thus
charged, the jar is discharged, after some time a residual discharge may be
taken by again connecting the wires ; if, however, the inner jar be gently
struck with a piece of wood, the residue makes its appearance much more
rapidly. The same observer draws a parallel between the phenomena of the
residual charge and those of residual magnetism (715).

774. Electric batteries.— The charge which a Leyden jar can take
depends on the extent of the coated surface, and for small thicknesses is
inversely proportional to the thickness of the insulator. Hence, the larger
and thinner the jar the more powerful the charge. But veiy large jars
are expensive, and liable to break ; and when too thin, the accumulated
electricities discharge themselves through the glass, especially if it is
not quite homogeneous. Leyden jars have usually from ^ to 3 square feet
of coated surface. For more powerful charges electric batteries are used.

An electric battery consists of a series of Leyden jars, whose internal
and external coatings are respectively connected with each other (fig. 712).
They are usually placed in a wooden box lined on the bottom with tinfoil.
This lining is connected with two metal handles in the sides of the box.
The inner coatings are connected with each other by metal rods, and the
battery is charged by placing the inner coatings in connection with the prime
conductor, while the outer coatings are connected with the ground by means
of a chain fixed to the handles. A quadrant electrometer fixed to one jar
indicates the charge
of the battery. Al-
though there is a
large quantity of
electricity accumu-
lated in the appara-
tus, the divergence
is not great, for it
is simply due to
the free electricity
on the inner coat-
ing. The larger
and more numerous
they are, the longer
is the time required
to charge the bat-
tery, but the effects
are so much the
more powerful (784). Fig- 7x2.

When a battery is to be discharged, the coatings are connected by means
of the discharging rod, the outside coating being touched first. Great care is
required, for with large batteries serious and even fatal accidents may occur.

775. The universal discbargrer. — This is an almost indispensable appa-
ratus in experiments with the electric battery. On a wooden stand (fig. 713)
are two glass legs, each provided with universal joints, in which movable
brass rods are fitted. Between these legs is a small ivory table, on which is

746 Frictional Electricity. [775-

placed the object under experiment. The two metal knobs being directed
towards the objects, one of them is connected with the outer coating of the
battery, and the moment communication is made between the outer and the
inner coating by means of the glass discharging rod, a violent shock passes
through the object on the table.

776. Cbarging: by cascade. — A series of Leyden jars are placed each
separately on insulating supports. The knob of the first is in connection
with the prime conductor of the machme, and its outer coating joined to the
knob of the second, the outer coating of the second to the knob of the third,
and so on, the outer coating of the last communicating with the ground.
The inner coating of the first receives a charge of positive electricity from

Fig. 713.

the machine, and the corresponding positive electricity set free by induction
on its outer coating, instead of passing to the ground, gives a positive charge
to the inner coating of the second, which, acting in like manner, develops a
charge in the third jar, and so on to the last, where the positive electricity
ilcvelopcd by induction on the outer coating passes to the ground. The jars
may be discharged either singly by connecting the inner and outer coatings
of each jar, or simultaneously by connecting the inner coating of the first
with the outer of the last. In this way the quantity of electricity necessary
lo charge one jar is available for charging a series of jars.

IT]. Measurement of tbe cbargre of a battery, pane's electro-
meter. \\'hcn the duler and inner coatings of a charged Lcytliu jar arc
gradually Ijrought nearer each other, at a certain ilistance a spontaneous

-778] Harris s Utiit Jar. y^y

discharge ensues. The distance is called the striking or sparkitJg iiisia7ue.
For the same charge it is inversely proportional to the pressure of the air
(768), and, with the same jar, but different charges, directly proportional to the
electric density of that point of the inner coating at which the discharge
takes place. As the density of any point of the inner coating, other things
remaining the same, is proportional to the entire charge, the striking distance
is proportional to the quantity of electricity in a jar. The measurement of
the charge of a battery, however, by means of the striking distance, can only
take place when the charge dis-
appears.

By means of Lane's electro-
meter, which depends on an
application of this principle, the
charge of a jar or batteiy may
be measured. This apparatus,
c (fig. 714), consists of an ordi-
nary Leyden jar, near which
there is a vertical metallic sup-
port. At the upper end is a
brass rod, with a knob at one

Fig. 714.

end, which can be placed in metallic connection with the outside of the jar :
the rod being movable, the knob can be kept at a measured distance from
the knob of the inner coating. Fig. 714 represents the operation of measur-
ing the charge of a jar by means of this apparatus. The jar b^ whose charge
is to be measured, is placed on an insulated stool with its outer coating in
metallic connection with the inner coating of Lane's jar t", the outer coating
of which is in connection with the ground, or still better with a system of gas
or water pipes ; a is the conductor of the machine. When the machine is
worked, positive electricity passes into the jar b ; a proportionate cjuantity of
positive electricity is repelled from its outer coating, passes into the inner
coating of the electrometer, and there produces a charge. When this has
reached a certain limit, it discharges itself between the two knobs, and as
often as such a discharge takes place, the same quantity of positive electricity
will have passed from the machine into the battery ; hence its charge is pro-
portional to the number of discharges of the electrometer.

77S. Harris's unit jar.— Harris's unit jar (fig. 715) is an application
of the same principle, and is often convenient for measuring quantities
of electricity. It consists of a small
Leyden phial, 4 inches in length and
f inch in diameter, coated to about
an inch from the end, so as to expose
about 6 inches of coated surface. It is
fixed horizontally on a long insulator,
and the charging rod connected at P
with the conductor of the machine,
while the outer coating is connected
with the jar or batter)^ by the rod / /.
When the accumulation of electricity in the interior has reached a ceitain
height depending on the distance of the two balls in and ;/, a discharge ensues,

748

Frictional Electricity.

[779-

and marks a certain quantity of electricity received as a charge by the
battery, in terms of the small jar.

779. Volta's condensing- electroscope. — The condensing electroscope
invented by Volta is a modification of the ordinary gold-leaf electroscope
(751). The rod to which the gold-leaves are affixed terminates in a disc
instead of in a knob, and there is another disc of the same size provided with
an insulating glass handle. The discs are covered with a layer of insulating
shellac varnish (fig. 716).

To render very small quantities of electricity perceptible by this apparatus
one of the plates, which thus becomes the collecting plate, is touched with
the body under examination. The other plate, the cofide/isifig plate, is con-
nected with the ground by touching it with the finger. The electricity of

Fig. 716. Fig. 717.

the body, being diffused over the collecting plate, acts inductively through
the varnish on the other plate, attracting the opposite electricity, but
repelling that of like kind. The two electricities thus become accumulated
on the two plates just as in a condenser, but there is no divergence of the
leaves, for the opposite electricities counteract each other. The finger is
now removed, and then the source of electricity, and still there is no diver-
gence ; but if the upper plate be raised (fig. 717) the neutralisation ceases,
and the electricity being free to move diffuses itself over the rod and the
leaves, which then diverge widely. The delicacy of this electroscope is in-
creased by adapting to the foot of the apparatus two metal rods, terminating
in knobs ; for these knobs, being excited by induction from the gold-leaves,
react upon them.

A still further degree of delicacy is attained if the rods be replaced by two

-781] TJiomsons Absolute lilcctronicter. 749

Bohnenbergers dry piles, one of which presents its positive and the other its
negative pole. Instead of two gold-leaves there is only one ; the least trace
of electricity causes it to oscillate cither to one side or to the other, and at
the same time shows the kind of electricity.

780. Thomson's quadrant electrometer. — Sir William Thomson has
devised a new and delicate form of electrometer, by which accurate measure-
ments of the amount of electrical
charge may be made. The prin-
ciple of this instrument may be
understood from the following" de-
scription of a form of it constructed
for lecture purposes by Messrs.
Elliott.

A light flat broad aluminium
needle (fig. 7 1 8) hangs by a very fine
wire from the inner coating of a
charged Leyden jar, the outer coat-
ing being in conducting communi-
cation with the earth. The whole
apparatus is enclosed within a glass
shade, and the air is kept dry by
means of a dish of sulphuric acid ;
there is, therefore, very little loss of
electricity, and the needle remains
at a virtually constant charge.

The needle is suspended over
four quadrantal metal plates, insu-
lated from each other and from the
ground by resting on glass rods.

Fig. 71

The alternate quadrants are in conducting communication with each other
by means of wires. If now all the quadrants are in the same electrical con-
dition, the needle will be at rest when it is directly over one of the diametrical
slits. But if the two pairs of quadrants are charged with opposite kinds of
electricity, as when, for instance, they are connected with the two poles of
an insulated voltaic cell by means of the knobs, then each end of the needle
will be repelled by the pair of quadrants which are electrified like itself, and
will be attracted by the other pair. It will thus be subject to the action of
a couple tending to set it obliquely to the slit.

In order to render the slightest motion of the needle visible, a small silver
concave mirror with a radius of about a metre is fixed above it. The light of
a petroleum lamp, not represented in the figure, strikes against this, and is
reflected as a spot on a horizontal scale. Any deflection of the needle, either
on one side or the other, is indicated by the motion of the spot of light on
the scale (520).

781. Thomson's absolute electrometer. — Another class of electro-
meters, also invented by Sir W. Thomson, have the advantage of furnishing
a direct measure of electrical constants in absolute measure. Fig. 719
represents the essential features of a modified form of the electrometer,
which has been devised by Professor Foster for class experiments.

750

Frictional Electricity.

[781-

Two plane metal discs A and B, about lo cm. in diameter, are kept at a
distance from each other, which is small in proportion to their diameters,
but which can be very accurately measured. Out of the centre of the upper
one is cut a disc c ; this is suspended by insulating threads from one end of
the arm a b oi 7i balance, at the other end of which is a counterpoise, or a
scale pan/. At the end of the arm is a fork, across which is stretched a
fine wire ; when the disc is exactly in the plane of the circular band or ring

which surrounds it, and which
is called the guard ring^ this
fine wire is exactly across the
interval between two marks
in the upright, and the posi-
tion of which can be accu-
rately determined by means
of the lens C. The disc and
the guard ring are kept at
a constant potential, being
connected by a wire with a
constant source of electricity,
while the other can be kept
at any potential.

Suppose now that the
whole system is at the same
potential, and that the disc is exactly balanced so as to be in the plane of the
guard ring. If now A be electrified to a given potential, while the plate B
is connected with the earth, then the body charged with electricity of higher
potential— that is, the disc — will be urged towards the body of lower potential,
the fixed plate ; and in order to retain it exactly in the plane of the guard
ring the force applied at the other end of the lever must be increased. This
may be done by altering the distance of the counterpoise, or by adding weights
to a scale pan, and the additional weight thus applied is a measure of the
attractive force.

Now, it can be shown that the attractive force between any two plates
electrified to different potentials is proportional to the square of the differ-
ence of potentials, provided the distance between them is small in comparison
with their area, and that the portions of the plates opposite each other are
at some distance from the edge. These conditions are fulfilled in the above
case. If S is the area of the disc, ^the distance of the plates, V-A', the
difference of potentials, and F the force required to balance a certain attrac-
tion, then

Fig. 719.

for V

V'S
this is ^ -,.. and \ = d \
and- V

Zndr
/SttF

/ s •

Now as F is expressed Ijy a weight, and S and (/ depend on measures of
length, we have a means of expressing difference of potentials in absolute
measure (709).

It is also clear that the experiments may be modified by making the

-782] Potctitial and Capacity of a Ley den Jar. 751

weight constant, and the distance variable. By means of micromctric
arrangements the distance of the plates maybe varied and measured with
very great accuracy.

782. Potential and capacity of a Xicyden jar — These may be most
conveniently investigated by considering the case of a spherical jar. Let us
suppose A (fig. 720) to represent an insulated metal sphere, and let us con-
sider it placed in conducting communication with a source of, say, positive
electricity, which is supposed to be at a constant potential V. Then its

potential V is ^ , and its charge (^ = VR, R being the radius of the sphere A.

Suppose now it be possible to surround this sphere by an external conduct-
ing shell or envelope B, which is in connection with the ground ; movements of
electricity will take place ; a new equilibrium
will be established, and there will now be two
electrical layers — one on the sphere A, and
the other on the sphere B. These will have
no action on any external point, which is only
possible provided the charges are equal and
contrary. If -t- Q is the charge on the inner,
then-Q is that on the outer sphere (745).

The charge of the original sphere is at
first not altered by this operation, but its
potential is less, its capacity being now
greater ; but, as it is in contact with the
source, which is constant, it receives fresh
charges of electricity until it is again at the
potential of the source V.

Now let us suppose that the insulating layer which separates the inner
from the outer coating is air, and that its thickness is t ; then the potential
y of the whole system is made up of two parts, the first due to the elec-
trical charge of the inner sphere V = -t- ^, and the second due to the charge

Q_Q^Q(R'-R) o = ^^^^^"
R" ' R R' RR' ' ^ R'-R

VR; hence ^ ^R'-R^ But
Q R'
R'-R is the thickness of the dielectric, which, for the sake of simplicity, we

O R'

will suppose is air, and calling this /, we have - ^ = — ; that is, that the

charge is inversely as the thickness of the dielectric.

It is to be observed that the results here obtained apply strictly only to
the supposed case in which the inner conductor is completely surrounded by
the outer one (745), which is not the case with the ordinary form of a Leyden
jar. It may, however, be applied to them if we compare homologous jars ;

in the above formula Q = ^, ,now if R and R' are nearly equal, then

Fig. 72

of the outer sphere = — ^i,; that is, V

Now, the charge of the insulated sphere ^

47r^'

■here 47rR'- = S is the coated

752 Frictional Electricity. [782-

surface of one side and / the thickness of the dielectric. In this formula

is a constant for a Leyden jar of given dimensions, and represents the
47r/
capacity of the jar.

If instead of air there be a solid or liquid dielectric, whose specific induc-
tive capacity is /c, the formula becomes Q = ~^ = !^- If the dielectric be

^Tvt A,T:t

partly air and partly some other material such as glass, then if the thick-

VS
ness of this latter is ^, Q = — - — . The expression 6 is sometimes

47r

('--D

written /', and represents the thickness of the layer of air equivalent to it in

specific inductive capacity. It is also called the reduced thickness.

VRR' RR'

From the expression Q = _ we get the capacity C = ^- — — ; or as

R — R R — R

above = — — , so that the presence of the envelope multiplies the capacity

of the sphere by .

If R' is so great that the value of R in the denominator may be disre-
garded, we get C = R, which is the expression for the capacity of an insulated
sphere (739) ; such a sphere may indeed be regarded as a condenser, in
which the layer of air, between it and the sides of the room, represents the
dielectric. This represents in effect the condensing force (267).

If a series of n identical jars are joined in surface, we have a condenser
whose capacity is equal to the «-fold capacity of a single jar.

If these n jars are joined in cascade, the capacity of the system is that of
a single jar, the dielectric of which is n times as thick.

A cylindrical Leyden jar with the diameter 10 cm. and coated to a height
of 20 cm. will have a total coated surface of 706-5 ; if the glass has the di-
electric constant 5, and its thickness is 3 mm. the capacity of the jar will be
937-5 ; and as the capacity of a sphere is equal to its radius (739), it will be
equal to the capacity of a freely suspended sphere I9'75 metres in diameter
(748).

-783] Effects of the Electric Discharge. 753

THE ELECTRIC DISCHARGE.

7^3- Effects of the electric dlschargre. — The recombination of the two
electricities which constitutes the electrical discharge may be either con-
tinuous or sudden : continuous., or of the nature of a current, as when the
two conductors of a Holtz's machine are joined by a chain or a wire ; and
sudden or disruptive, as when the opposite electricities accumulate on the
surface of two adjacent conductors, till their mutual attraction is strong
enough to overcome the intervening resistances, whatever they may be. But
the difference between a sudden and a continuous discharge is one of degree,
and not of kind, for there is no such thing as an absolute non-conductor, and
the very best conductors, the metals, offer an appreciable resistance to the
passage of electricity. Still the difference at the two extremes of the scale
is sufficiently great to give rise to a wide range of phenomena.

Riess has shown that the discharge of a battery does not consist in a
simple union of the positive with the negative electricity, but that it consists
of a series of successive partial discharges. The direction of the discharge
depends mainly on the length and nature of the circuit.

Feddersen examined the discharge of a Leyden jar in a rapidly rotating
mirror (796), when it was seen as a narrowband of light the length of which
varied with the duration of the discharge. The duration was found to increase
with the striking distance, and with the number of jars.

When the resistance through which the circuit took place was small, it
was found that the discharge was an oscillatory one, consisting of a series of
separate discharges in alternating directions ; the image was traversed by a
number of dark lines.

When the resistance was greater the discharge was a single continuous
one, and its image was that of a continuous band of light. With very great
resistance the discharge was an intermitteiit one, and consisted of sparks
following each other at irregular intervals.

These oscillator)' discharges may be illustrated by means of a simple
hydrostatical experiment. Suppose that in the U-tube (fig. 721) is a valve j-,
by which the two tubes are separated, and that water is
poured in one so that it is at the height -1- L above the
level 00, and in the other in the corresponding distance
— L below the level. When the valve is suddenly opened,
the water passes through and only comes to rest in the
position 00 after several oscillations about this level. Sup-
pose the valve to be suddenly closed during the oscillation, ^
it may easily happen that the water is higher in that limb p-
in which it was previously lower. This would represent
the case observed by Oettingen with the electrical residues, who found them
to be sometimes negative and sometimes positive.

Again, if the valve be only slightly opened, so that great resistance is
offered, the water slowly sinks to its level, the discharge is continuous, and
there are no oscillations.

The oscillator)' nature of the discharge was confirmed by the observations

3 c

754 Frictional Elect ncity. [783-

of Paalzow on the luminous phenomena seen in highly rarefied gases
when it takes place in them, as well as by the manner in which a magnet
affects the phenomena. Helmholtz had already deduced the necessity of
such an oscillating motion from the laws of the conservation of energy,
and Thomson and Kirchhoff had deduced the conditions under which it
occurs.

784. "Work effected by the discharg-e of a Iieyden jar. — The work

required to charge a Leyden jar is W = QV = = ^-^ = V'^ ; that is,

is proportional to the surface and to the square of the potential, and is
inversely as the thickness of the insulator. From the principle of the con-
servation of energy, this stored-up energy reappears when the jar is dis-
charged. This occurs partly in the form of a spark, partly in the heating
effect of the whole system of conductors through which the discharge takes
place. When the armatures are connected by a thick short wire, the spark
is strong and the heating effect small : if, on the contrary, the jar is dis-
charged through a long fine wire, this beconies more heated, but the spark
is weaker.

If a series of identical jars are each separately charged from the same
source, they will each acquire the same potential, which will not be altered
if all the jars are connected by their inner and outer coatings respectively.
The total charge will be the same as if the battery had been charged directly
from the source, and its energy will be W = ^ Vttq = ^VQ : that is, the energy
of a battery of n equal jars is the same as that of a single jar of the same
thickness but of ;z times the surface.

Let us consider two similar Leyden jars having respectively the capaci-
ties c and c', and let one of them be charged to potential V and let the other
remain uncharged. Suppose now that the inner and outer coatings of the
jars are respectively connected with each other. Then the energy of the

charged jar alone is W = i-^, and when it is connected with the other, the

original charge will spread itself over the two, so that the energy of the

charge in the two jars is W = ---^ — r. Hence W : W = c + c' : c ; and there-

2{c + c')
fore, since c + c' \s always greater than c, there must be a loss of energy. In
point of fact, when a charged jar is connected with an uncharged one, a spark
passes which is the equivalent of this loss of energy.

It follows, further, that when two jars at different potentials are united
there is always a loss of energy.

If a series of n similar jars are joined in surface, and a given charge
of electricity is imparted to them, the energy is inversely as the number
of jars; but, when they are charged from a source of constant potential,
the energy is proportional to the number of jars. If, however, the jars
are arranged in cascade, then for a given charge the energy is n times
that of a single jar, while for a given potential it is n times smaller. It is
sometimes convenient to arrange the jars in a combination of the two
systems.

785. Physiological effects. — The shock from the electrical machine
has been already noticed (770). The shock taken from a charged Leyden

-787J Spark and Brush Discharge. 755

jar by grasping the outer coating with one hand and touching the inner
with the other is much more violent, and has a peculiar character. With a
small jar the shock is felt in the elbow ; with a jar of about a quart capacity
it is felt across the chest, and with jars of still larger dimensions in the
stomach.

A shock may be given to a large number of persons simultaneously by
means of the Leyden jar. For this purpose they must form a chain by join-
ing hands. If then the first touches the outside coating of a charged jar,
while the last at the same time touches the knob, all receive a simultaneous
shock, the intensity of which depends on the charge, and on the number of
persons receiving it. Those in the centre of the chain are found to receive
a less violent shock than those near the extremities. The Abbe Nollet dis-
charged a Leyden jar through an entire regiment of 1,500 men, who all
received a violent shock in the arms and shoulders.

With large Leyden jars and batteries the shock is sometimes very dan-
gerous. Priestley killed rats with batteries of 7 square feet coated surface,
and cats with a battery of about 4^ square yards coating.

Experience shows that the physiological effect varies with the electrical
energy ; thus a discharge from an ordinary electrical machine which gives
a spark of nearly a foot may be taken without danger, while one from a
batter}^ of large capacity of a few millimetres could not be borne. The
duration of the discharge has also an influence ; a battery which gives a
violent shock when discharged in ordinary conditions only gives a feeble
one when discharged through a moist cord, which only delays the rapidity
of the discharge.

786. luminous effects. — The recombination of two electricities of high
potential (738) is always accompanied by a disengagement of light, as is seen
when sparks are taken from a machine, or when a Leyden jar is discharged.
The better the conductors on which the electricities are accumulated, the
more brilliant is the spark ; its colour varies not only with the nature of the
bodies, but also with the nature of the surrounding medium and with the
pressure. The spark between two charcoal points is yellow, between two
balls of silvered copper it is green, between knobs of wood or ivory it is
crimson. In atmospheric air at the ordinary pressure the electric spark is
white and brilliant ; in rarefied air it is reddish ; and in vacuo it is violet.
In oxygen, as in air, the spark is white ; in hydrogen it is reddish, and green
in the vapour of mercury ; in carbonic acid it is also green, while in nitrogen
it is blue or purple, and accompanied by a peculiar sound. Generally speak-
ing, the higher the potential the greater is the lustre of the spark.

When these sparks are examined by the spectroscope (576) it is seen that
they show the lines characteristic of the metals between which the spark
passes, and also of the gas in which it takes place. If the knobs are of
different metals the lines of both are seen. Part of the energy is accordingly
consumed in detaching and volatilising the metal particles on the two
electrodes ; when a powerful discharge takes place between a knob of gold
and one of silver, the latter metal is found on the gold ball, while some gold
is found on the silver.

787. Spark and brusb discbargre. — The shapes which luminous electric
phenomena assume may be classed under two heads — the spark and the

3 c 2

756 Frictiotial Electricity. [787-

brush. The brush forms when the electricity leaves the conductor in a
continuous flow ; the spark, when the discharge is discontinuous. The
formation of one or the other of these depends on the nature of the con-
ductor and on the nature of the conductors in its vicinity ; and small altera-
tions in the position of the surrounding conductors transform the one into
the other.

The spark which at short distances appears straight, at longer distances
has a zigzag shape with diverging branches. Its length depends on the
density at the part of the conductor from which it is taken ; and to obtain
the longest sparks the electricity must be of as high a density as possible, but
not so high as to discharge spontaneously. With long sparks the luminosity
is different in different parts of the spark.

The brush derives its name from the radiating divergent arrangement
of the light, and presents the appearance of a luminous cone, whose apex
touches the conductor. Its size and colour differ with the nature and form of
the conductor ; it is accompanied by a peculiar hissing noise, very different
from the sharp crack of the spark. Its luminosity is far less than that of
the spark ; for while the latter can easily be seen by daylight, the former is
only visible in a darkened room. The brush discharge may be obtained by
placing on the conductor a wire filed round at the end, or, with a powerful
machine, by placing a small bullet on the conductor. The brush from a
negative conductor is less than from a positive conductor ; the cause of
this difference has not been satisfactorily made out, but may originate in the
fact, which Faraday has observed, that negative electricity discharges into
the air at a somewhat lower density than positive electricity ; so that a nega-
tively charged knob sooner attains that density at which spontaneous
discharge takes place, than does a positively charged one, and therefore
discharges the electricity at smaller intervals and in less quantities.

When electricity, in virtue of its high density, issues from a conductor, no
other conductor being near, the discharge takes place without noise, and at
the places at which it appears there is a pale blue luminosity called the
electrical glow ^ ox ox\ points, a star-like centre of light. It is seen in the dark
by placing a point on the conductor of the machine. It may be regarded as
a very short brush.

788. striking- distance.- — Sir W. Harris by means of experiments with
his unit jar suitably modified, and Riess by independent researches, found
that for small distances the striking distance is directly proportional to the
quantity of electricity, and inversely proportional to the coated surface ; in
other words, it is proportional to the potential. For his experiments Riess
used the spark micrometer., which consists of two metal knobs on insulating
supports, the distance of which from each other could be varied by a micro-
metric screw.

The striking distance varies slightly with the shape of the electrodes ;
thus for the same distance the difference of potential required is slightly
greater for two spheres than for two plates.

P'or greater distances the difference of potential increases less rapidly
than the distance, and the greater the distance the less is the rate of increase;
this is seen in the following experiments, where the discharge took place
between two knobs 2 '2 cm. in diameter.

-789]

Luminous Tube and Square.

7S7

Distance

Volts

Distance

Volts

cm.

o-i

5,490

5-0

94,800

0-5

26,730

107,700

48,600 .

lo-o

119,100

2-0

64,800

I2-0

124,200

j-o

76,800

I5-0

127,800

The striking distance in air is virtually the same for the spark proper as
for the brush.

The influence of pressure on the electric discharge may be studied by
means of the electric egg. This consists of an ellipsoidal glass vessel (fig.
722), with metal caps at each end. The lower cap is
provided with a stopcock, so that it can be screwed
into an air-pump, and also into a heavy metallic foot.
The upper metal rod moves up and down in a leather
stuffing-box ; the lower one is fixed to the cap. A
vacuum having been made, the stopcock is turned,
and the vessel screwed into its foot ; the upper part
is then connected with a powerful electrical machine,
and the lower one with the ground. On working the
machine, the globe becomes filled with a feeble violet
light continuous from one end to the other, and
resulting from the recomposition of the positive elec-
tricity of the upper cap with the negative of the lower.
If the air be gradually allowed to enter by opening
the stopcock, the light now appears white and
brilliant, and is only seen as an ordinary intermittent
spark.

Some beautiful effects of the electric discharge
are obtained by means of Geissler^s tubes, which will
be noticed under Dynamical Electricity.

789. Iiumlnous tube and square. — The linninous
tube (fig. 723) is a glass tube about a yard long, round
which are arranged in a spiral form a series of lozenge-
shaped pieces of tinfoil, between which are veiy short
intervals. There is a brass cap with hooks at each end, in which the spiral
terminates. If one end be presented to a machine in action, while the other

Fi?. 7=3.
is held in the hand, sparks appear simultaneously at each interval, and pro-
duce a brilliant luminous appearance, especially in the dark.

758 Frictional Electricity. [789-

The luminous pane (fig. 724) is constructed on the same principle, and
consists of a square of ordinary glass, on which is fastened a narrow strip of
tinfoil folded parallel to itself for a great number of times. Spaces are cut
out of this strip so as to represent any figure, a portico for example.
The pane being fixed between two insulating supports, the upper extre-
mity of the strip is connected with

^"""Y^. ^— the electrical machine, and the

'^ ' ^^ ^^ — lower part with the ground. When
the machine is in operation, a spark
appears at each interval, and repro-
duces in liiminous flashes the ob-
ject represented on the glass.

790. Keating' effects. — Besides
being luminous, the electric spark
is a source of great heat. When it
passes through inflammable liquids,
as ether or alcohol, it inflames them.
An arrangement for efl"ecting this is
represented in fig. 725. It is a small
glass cup through the bottom of
which passes a metal rod, termi-
nating in a knob and fixed to a
metal foot. A quantity of liquid
sufficient to cover the knob is
placed in the vessel. The outer
coating of the jar having been
connected with the foot by means of a chain, the spark which passes when
the two knobs are brought near each other inflames the liquid. With ether
the experiment succeeds very well, but alcohol requires to be first warmed.

Coal gas may also be ignited by means of the electric spark. A person
standing on an insulated stool places one hand on the conductor of a

machine which is then worked, while
he presents the other to the jet of gas
issuing from a metallic burner. The
spark which passes ignites the gas.
When a battery is discharged through
an iron or steel wire it becomes
heated, and even made incandescent
or melted if the discharge is very
powerful.

If, in discharging a jar, the dis-
charge does no other work, then the
whole of the energy of the charge
(784) apjiears in the form of heat ; and
if we divide this by Joule's equivalent
(497), we have the total heating due
to any charge.

The laws of this heating effect were investigated independently by
Harris and b)' Ricss by means of the electric tlier/no/zictcr. This consists of

Fig. 724.

-790] Heating Effects of the Electrical Discharge. 759

a glass bulb, fig. 726, closed by a stopper c, and to which is fixed a capillary
tube bent twice, and terminating in an enlargement ; this contains coloured
liquid. The whole apparatus is fixed on a hinged support A, which works
on the base B, so that it can be inclined and fixed at any given angle. The
diameter of the tube being very small compared with that of the enlarge-
ment, a consider-
able displacement
of the liquid may
take place along
the scale without
any material alter-
ation in pressure,
and before making
the experiment the
stopper c is opened
so as to equalise
the pressure. Be-
tween the binding
screws a and b
a fine platinum
wire is stretched.

When a Leyden ~"

jar is discharged ^'=- ^-^■

through the wire this becomes heated, expands the air in the bulb, and the
expansion is indicated by the motion of the liquid along the graduated stem
of the thermometer. In this way it has been found that the increase in
temperature in the wire is proportional to the square of the quantity of
electricity divided by the surface — a result which follows from the formula
already given (784). Riess also found that wilh the satne charge, but with
wires of different dimensions, the rise of temperature is i7iversely as the
fourth power of the diameter. Thus, compared with a given wire as unity,
the rise of te7iiperature in a wire of double or treble the diameter would be
j\ or g\ as small ; but as the masses of these wires are four and nine times
as great, the heat produced would be respectively \ and | as great as in
a wire of unit thickness.

If a jar charged to a given potential be discharged through the electrical
thermometer, the discharge will take place at a certain striking distance,
and a certain depression will be produced which is a measure of the heating
effect in the thermometer. If now a card be interposed in the path of
the discharge, a certain proportion of its energy will be expended in the
mechanical perforation of the card, and the proportion in the thermo-
meter will be less. Thus Riess found that that charge which when passed
through air produced a depression of 15-9, when passed in addition
through one card, two cards, and a plate of mica, produced depressions
of 117, 8-0, and 6-8 respectively ; showing then that the heating effect was
less according as more of the energ^y of the discharge was used for other
purposes.

When an electric discharge is sent through gunpowder placed on the
table of a Henley's discharger, it is not ignited, but is projected in all

760

Frictional Electricity.

[790-

directions. But if a wet string be interposed in the circuit, a spark passes
which ignites the powder. This arises from the retardation which electricity
experiences in traversing a semi-conductor, such as a wet string ; for the
heating effect is proportional to the duration of the discharge.

When a charge is passed through sugar, heavy spar, fluor-spar, and other
substances, they afterwards become phosphorescent in the dark. Eggs,
fruit, &c., may be made luminous in the dark in this way.

When a battery is discharged through a gold leaf pressed between two
glass plates or between two silk ribbons, the gold is volatilised in a violet
powder which is finely divided gold. In this way what are called electric
portraits are obtained.

Siemens has shown that when a jar is charged and discharged sev'eral
times in succession the glass becomes heated. Hence during the discharge
there must be movements of the molecules of the glass, as Faraday sup-
posed (747) ; we have here, probably, something analogous to the heating
produced in iron when it is rapidly magnetised and demagnetised.

791. IVXag-netic eflFects. — By the discharge of a large Leyden jar or
battery, a steel wire may be magnetised if it is laid at right angles to a con-
ducting wire through which the discharge is
effected, either in contact with the wire or at
some distance. And even a steel rod or needle
may be magnetised by placing it inside a spiral
of insulated copper wire A (fig. 727), and passing
one or more discharges through it. The polarity
depends on the direction in which the electricity
enters the coil, and the way in which the wire
is coiled. Thus if the jar is charged in the in-
side with positive electricity, and the direction

"''^' ''^^" in which the wire is coiled is that in which the

hands of a watch move, that end at which the positive electricity enters will
be a south pole.

It is, however, frequently observed that the magnetism is abnormal, and
that for the same charge of the jar the north pole is first at one end and then
at the other. This is to be referred to the residue in the jar, which changes
the sign in an irregular manner (783).

To effect a deflection of the magnetic needle by the electric current pro-
duced by frictional electricity is more difficult. It may be accomplished
by making use of a galvanometer consisting of 400 or 500 turns of fine silk-
covered wire, which is further insulated by being coated with shellac varnish,
and by separating the layers by means of oiled silk. When the prime con-
ductor of a machine in action is connected with one end of the galvanometer
wire, and the other with the ground, a deflection of the needle is produced.

792. iwechanlcal effects. — The mechanical effects are the violent lacera-
tions, fractures, and sudden expansions which ensue when a powerful dis-
charge is passed through a badly conducting substance. Glass is perforated,
wood and stones are fractured, and gases and liquids are violently disturbed.
The mechanical effects of the electric spark may be demonstrated by a
variety of experiments.

Fig. 728 represents an arrangement for perforating a piece of glass or

(miiiimiiiimiiiiiiiiiiii iiTi'iii!

Iimiiiiiiiiiiiir

-792] Mechanical Effects of the Electrical Discharge. 761

card. It consists of two glass columns, with a horizontal cross-piece, in
which is a pointed conductor, B. The piece of glass. A, is placed on an
insulating glass support, in which is placed a second conductor, terminating
also in a point, which is _

connected with the outside
of the battery, while the
knob of the inner coating
is brought near the knob
of B. When the discharge
passes between the two
conductors, the glass is
perforated. The experi-
ment only succeeds with
a single jar when the glass
is very thin ; otherwise a
battery must be used.

When the discharge
takes place through a
piece of cardboard be-
tween two points exactly
opposite each other the
line of perforation is quite
straight ; but if not exactly
opposite a slight hole is
seen near the negative point. This phenomenon, which is known as LulliTis
experiment, is probably connected with the greater facility with which elec-
tricity discharges into air accord-
mg as it is negative or positive
(787).

The perturbation and sudden
expansion which the discharge
produces may be illustrated by
means of what is known as
Kznnersleys thermometer. This
consists of two glass tubes (fig.
729), which fit into metallic caps
and communicate with each
other. At the top of the large
tube is a rod terminating in a
knob, and moving in a stuffing-
box, and at the bottom there is a
similar rod with a knob. The
apparatus contains water up to
the level of the lower knob.
When the electric discharge
passes between the two knobs,
the water is driven out of the
larger tube and rises to a slight extent in the small one. The level is
immediately re-established, and therefore the phenomenon is not due to a
rise of temperature.

y(>2

Frictional Electricity.

[792-

If the upper knob inside a Kinnersley's thermometer be replaced by a
point, and the outside knob is connected with the prime conductor of a
machine at work, the electricity discharges itself in the form of a brush,
and a permanent displacement of the liquid in the stem shows that this
is due to the heating effect of the brush discharge.

For the production of mechanical effects the universal discharger (fig.
713) is of great service. A piece of wood, for instance, placed on the table
between the two conductors, is split when the discharge passes.

When a Leyden jar is charged it undergoes a true
expansion which is not that due to heat. This was
shown by Quincke, one of whose experiments is repre-
sented in fig. 730. It consists of a glass bulb A about
2 inches in diameter at the end of a narrow capillary
tube K, on an enlargement in which a platinum wire k
is fused. The bulb and a portion of the stem contains
a conducting liquid, such as water or sulphuric acid,
and it is placed in a vessel of ice-cold water, K, which
can be connected with the earth by a conducting wire,
G. If now this condenser is charged by connecting
the wire B with an electrical machine, while G is in
connection with the earth, there is a distinct depres-
sion of the liquid in the tube. When the jar is dis-
charged the liquid resumes its original level. Hence
this cannot have been due to heat, apart from the
fact that the temperature was kept constant ; nor is
it due to a contraction of the thickness of the glass.
The same results are obtained if the outer coating is insulated by resting it
on shellac T, which in turn is insulated by resting on a slab of india-rubber,
the inner coating being put to earth. Similar effects are observed with
solid condensers of other materials, and also with liquids.

793. Cbemical effects. — The chemical effects are the decompositions
and recombinations effected by the passage of the electric discharge. When
two gases which act on each other are mixed in the proportions in which
they combine, a single spark is often sufficient to determine their combina-
tion ; but when either of them is in great excess, a succession of sparks is
necessary. Priestley found that when a series of electric sparks was passed
through moist air, its volume diminished, and blue litmus introduced into
the vessel was reddened. This, Cavendish discovered, was due to the for-
mation of nitric acid.

Several compound gases are decomposed by the continued action of the
electric spark. With olefiant gas, sulphuretted hydrogen, and ammonia, the
decomposition is complete ; while carbonic acid is partially decomposed
into oxygen and carbonic oxide. The electric discharge also by suitable
means can feebly decompose water, oxides, and salts ; but, though the same
in kind, the chemical effects of statical electricity are by no means so powerful
and varied as those of dynamical electricity. The chemical action of the
spark is easily demonstrated by means of a solution of iodide of potassium.
A small lozenge-shaped piece of filtering paper, impregnated with iodide of
potassium, is placed on a glass plate, and one corner connected with the

Fig. 730.

-793] Chemical Effects of the Electrical Discharge.

^63

ground. When a few sparks from a conductor charged with positive elec-
tricity are taken at the other corner, brown spots are produced, due to the
separation of iodine.

The electric pistol is a small apparatus which serves to demonstrate the
chemical effects of the spark. It consists of a brass vessel (fig. 731), in
which is introduced a detonating mixture of two volumes of hydrogen and

ITd

-r

Fig. 731. Fig. 732.

one of oxygen, and which is then closed with a cork. In a tubulure in the
side there is a glass tube, in which fits a metal rod, terminated by the
knobs A and B. The vessel is held as represented in fig. 732, and brought
near the machine. The knob A becomes negatively, and B positively, elec-
trified by induction from the machine, and a spark passes between the con-
ductor and A. Another spark passes at
the same time between the knob B and
the side ; this determines the combina-
tion of the gases, which is accompanied
by a great disengagement of heat, and the
vapour of water formed acquires such an
expansive force, that the cork is pro-
jected with a report like that of a pistol.

Among the chemical effects must be
enumerated the formation of ozoiie, which
is recognised by its peculiar odour, and
by certain chemical properties. The
odour is perceiv'ed when electricity issues
from a conductor into the air through
a series of points. It has been estab-
lished that ozone is an allotropic modi-
fication of oxygen.

With these effects may be associated
a certain class of phenomena observed
when gases are made to act as the dielec-
tric in a charged Leyden jar. An appa-
ratus by which this is effected is repre-
sented in fig. 733 ; it is a modification of
one invented by Siemens. It consists
of a glass cylinder E, containing dilute
sulphuric acid ; « is a glass tube closed at the bottom, and also containing
sulphuric acid, in an enlargement of which at the top the inner tube ec fits.

Fig. 733-

764

Frictional Electricity.

[793-

There is a tube /, by which gas enters, and one dt' by which it emerges.
When the acids in E and e are respectively connected with the two combs of
a Holtz machine, or with the two terminals of a Ruhmkorfif's coil, a certain
condition or strain (747) is produced in the dielectric, which is known as the
silent discharge or the electric effluvium. \\'hat that condition is cannot be
definitely stated ; but it gives rise to powerful and characteristic chemical
actions, often differing from those produced by the spark.

By this apparatus large quantities of ozone may be produced.
794. Application of the electrical discharg-e to firing- mines. — By the
labours of Sir F. Abel in this country, and of Baron Von Ebner in Austria, the
electrical discharge has been applied to firing mines for military purposes,
and the methods have acquired a high degree of perfection. The principle on
which the method is based maybe understood from the following statement : —
One end of an insulated wire in which is a small break is placed in con-
tact with the outside of a charged Leyden jar, the other end being placed
near the inner coating. If now this end be brought in contact with the inner
coating the jar is discharged, and a spark strikes across the break ; and
if there be here some explosive compound it is ignited, and this ignition
may of course be communicated to any gunpowder in which it is placed.
If on one side of the break, instead of having an insulated wire direct
back to the outer coating of the Leyden jar, an uncovered wire be led

into the ground, the out-
side of the jar being
also connected with the
ground, the result is un-
changed, the earth acting
as a return wire. More-
over, if there be several
breaks, the explosion will
still ensue at each of them,
provided the charge be
sufficiently powerful.

In the actual applica-
tion it is of course neces-
sary to have an arrange-
ment for generating
frictional electricity which
shall be simple, portable,
powerful, and capable of
working in any weather.
Fig. 734 represents a \iew
of Von Ebner's instrument
as constructed by Messrs.
Elliott, part of the case
being removed to show
the internal construction.
Itconsists of two circu-
lar plates of ebonite, a, mounted on an axis so that they are turned by a
handle b, between rubber, which are so arranged as to be easily removed

F'g- 734-

-794] Application of Electrical Disc Jiargc to Firing Mines 765

for the purposes of amalgamation, &€. Fastened to a knob on the base of
the apparatus and projecting between the plates is a pointed brass rod,
which acts as a collector of the electricity. The condenser or Leyden jar
arrangement is inside the case, part of which has been removed to show the
arrangement. It consists of india-rubber cloth, coated on each side with
tinfoil, and formed into a roll for the purpose of greater compactness.
By means of a metal button the knob is in contact with one tinfoil coating,
which thus receives the electricity of the machine, and corresponds to the
inner coating of the Leyden jar. Another button, connected with the
other tinfoil coating, rests on a brass band at the base of the' apparatus
which is in metallic contact with the cushions, the knob d, and the per-
forated knob in which slides a rod at the front of the
apparatus. These are all in connection with the earth.
The knob e is in metallic connection with a disc _^ pro-
vided with a light arm. By means of a flexible chain this
is so connected with a trigger on the side of the apparatus
not represented in the figure, that when the trigger is
depressed, the arm, and therewith the knob e, is brought
into contact with the inner coating of the condenser.

On depressing the trigger, after a certain number of
turns, a spark passes between the knob e and the sliding
rod, and the striking distance is a measure of the
working condition of the instrument.

The fuse used is known as AbeVs electrical fuse, and
has the following construction : — The ends of two fine
copper wires (fig. 735) are imbedded in a thin soHd
gutta-percha rod, parallel to each other, but at a dis-
tance of about I "5 mm. At one end of the gutta-percha
a small cap of paper c c \s fastened, in which is placed
a small quantity of the priming composition, which con-
sists of an intimate mixture of subsulphide of copper,
subphosphide of copper, and chlorate of potassium.
The paper is fastened down so that the exposed ends of
the wires are in close contact with the powder.

This is the actual fuse ; for service the capped end of the fuse is
placed in a perforation in the rounded head of a wooden cylinder, so as to
project slightly into the cavity g of the cylinder. This «„

cavity is filled with meal powder, which is well rammed
down, so that the fuse is firmly imbedded. It is after-
wards closed by a plug of gutta-percha, and the whole
is finally coated with black varnish.

The free ends of the wire a a are pressed into small
grooves in the head of the cylinder (fig. 736), and each
end is bent into one of the small channels with which the
cylinder is provided, and which are at right angles to
the central perforation. They are wedged in here by
driving in small copper tubes, the ends of which are
then filed flush with the surface of the cylinder. The
bared ends of two insulated conducting wires are then pressed into one of

Fig. 735-

Fig. 736.

766 Frictiojial Electricity. [794-

the small copper tubes or eyes, and fixed there by bending the wire round
on to the wood, as shown at e.

The conducting wire used in firing may be thin, but it must be w-ell
insulated. One end which is bared, having been pressed into the hole d
of the fuse (fig. 735), the other is placed near the exploder. In the other
hole d' of the fuse a wire is placed which serves as earth wire, care being
taken that there is no connection between the two wires. The fuse having
been introduced into the charge, the earth wire is placed in good connection
with the ground. The knob / of the exploder is also connected with the
earth by leading the bare wire into water or moist earth, and the condi-
tion of the machine tested. The end of the insulated wire is then connected
with the knob c and the rod drawn down ; at the proper signal the handle
is turned the requisite number of times, and when the signal is given the
trigger is depressed, and the explosion ensues.

When a number of charges are to be fired they are best placed in a single
circuit, care being taken that the insulation is good.

795. Duration of the electric spark. — Wheatstone measured the dura-
tion of the electric spark by means of the rotating mirror which he invented
for this purpose. At some distance from this instrument, which can be made
to rotate with a measured velocity, a Leyden jar is so arranged that the spark
of its discharge is reflected from the mirror. Now, from the laws of reflec-
tion (520) the image of the luminous point describes an arc of double the
number of degrees which the mirror describes, in the time in which the
mirror passes from the position in which the image is visible to that in which
it ceases to be so. If the duration of the image were absolutely instanta-
neous the arc would be reduced to a mere point. Knowing the number of
turns which the mirror makes in a second, and measuring, by means of a
divided circle, the number of degrees occupied by the image, the duration of
the spark would be determined. In one experiment Wheatstone found that
this arc was 24°. Nov/, in the time in which the mirror traverses 360° the
image traverses 720° ; but in the experiment the mirror made 800 turns in a
second, and therefore the image traversed 576,000° in this time ; and as the
arc was 24°, the image must have lasted the time expressed by^r.!^, or ^j^^-
of a second. Thus the discharge is not instantaneous, but has a certain
duration, which, however, is excessively short.

Feddersen found that when greater resistances were interposed in the
circuit through which the discharge was effected, the duration of the spark
was increased. W'ith a tube of water 9 mm. in length, the spark lasted 0-0014
second ; and with one of 180 mm. its duration was 0-0183 second. The
duration increased also with the striking distance, and with the dimensions
of the battery.

To determine the duration of the electric spark Lucas and Cazin used a
method by which it maybe measured in millionths of a second. The method
is an application of the vernier (10). A disc of mica 15 centimetres in dia-
meter is blackened on one face, and at the edge are traced 180 equal divi-
sions in very fine transparent lines. The disc is mounted on a horizontal
axis, and by means of a gas engine it may be made to turn with a velocity
of 100 to 300 turns in a second. A second disc of silvered glass of the same
radius is mounted on the same axis as the other and very close to it ; at its
upper edge six equidistant transparent lines are traced, forming a vernier

-795]

Duration of the Electric Spark.

767

with the lines on the mica. P'or this, the distance between two consecutive
Hnes on the two discs is such that five divisions of the mica disc DC corre-
spond to six divisions of the glass disc AB, as seen in fig. 72)7- Thus the
vernier gives the sixths of a division of the mica disc (10). In the apparatus
the lines AB are not above the lines CD, but
are at the same distance from the axis, so
that the latter coincide successively with
the former.

The mica disc is contained in a brass
box D (fig. 738), on the hinder face of
which is fixed the vernier. In the front
face is a glass window O, through which the coincidence of the two sets of
lines can be observed by means of a magnifying lens L.

The source of electricity is a battery of 2 to 8 jars, each having a coated
surface of 1,243 square centimetres, and charged continuously by a Holtz
machine. The spark strikes between two metal balls a and b, 1 1 millimetres

Fig- 737-

in diameter. Their distance can be varied, and at the same time measured,
by means of a micrometric screw, r. The two opposite electricities arrive
by wires ;;? and ;/, and the sparks strike at the principal focus of a condensing
lens placed in the collimator C, so that the rays which fall on the \-crnier are
parallel.

y6^ Frictional Electricity. [795-

The motion is transmitted to the toothed wheels and to the mica disc by
means of an endless band, which can be placed on any one of three pulleys
P, so that the velocity may be varied. At the end of the axis of the pulleys
is a bent wire which moves a counter, V, that marks on three dials the
number of turns of the disc.

These details being premised, suppose the velocity of the disc is 400
turns in a second. In each second 400+ 180, or 72,000 lines pass before the
observer's eye in each second ; hence an interval of ~~^ of a second elapses
between two consecutive lines. But as the spark is only seen when
one of the lines of the disc coincides with one of the six hnes of the ver-
nier ; and as this gives sixths of a division of the movable disc, when the
latter has turned through a sixth of a division, a second coincidence is
produced ; so that the interval between two successive coincidences is

7- = 0-0000023 of a second.

72000 X 6 -^

That being the case, let the duration of a spark be something between
23 and 46 ten-millionths of a second ; if it strikes exactly at the moment of
a coincidence, it will last until the next coincidence ; and owing to the per-
sistence of impressions on the retina (625) the observer will see two luminous
lines. But if the spark strikes between two coincidences and has ceased
when the thu'd is produced, only one brilliant line is seen. Thus, if with the
above velocity sometimes i and sometimes 2 bright lines are seen, the dura-
tion of the spark is comprised between 23 and 46 ten-millionths of a second.

By experiments of this kind, with a striking distance of 5 millimetres
between the balls a and <5, and varying the number of the jars, MM. Lucas
and Cazin obtained the following results : —

Duration in millionths
Number of jars of a second.
2 26

4 41

6 45

8 47

It will thus be seen that the duration of the spark increases with the
number of jars. It also increases with the striking distance ; but it is inde-
pendent of the diameter of the balls between which
the spark strikes.

The spark of electrical machines has so short a
duration that it could not be measured with the
/^' \ chrnnoscope.

^.o. /<? • <is |<r"7 796. Velocity Of electricity. — To determine the

' ' \^^J\ — \z^ — velocity of electricity Wheatstone constructed an

apparatus the principle of which will be understood

from fig. 739. Six insulated metal knobs were ar-

— <!r]~L>'~ ranged in a horizontal line on a piece of wood called

Pig ^3g_ a spark board ; of these the knob i was connected

with the outer, while 6 could be connected with the

inner coating of a charged Leyden jar ; the knob i was a tenth of an inch

distant from the knob 2 ; while between 2 and 3 a quarter of a mile of

insulated wire was interposed ; 3 was likewise a tenth of an inch from 4, and

-796] Velocity of lilcctricity. 769

there was a quarter of a mile of wire between 4 and 5 ; lastly, 5 was a tenth
of an inch from 6, from which a wire led directly to the inner coatinj^- of the
Leyden jar. Hence, when the jar was discharged by connecting the wire
from 6 with the inner coating of the jar, sparks would pass between i and 2,
between 3 and 4, and between 5 and 6. . Thus the discharge, supposing it to
proceed from the inner coating, has to pass in its course through a quarter of
a mile of wire between the first and second spark, and through the same
distance between the second and third.

The spark board was arranged at a distance of 10 feet from the rotating
mirror, and at the same height, both being horizontal ; and the observer
looked down on the mirror. Thus the sparks were visible when the mirror
made an angle of 45° with the horizon.

Now, if the mirror were at rest, or had only a small velocity, the images
of the three spots would be seen as three dots \ , but when the mirror had
a certain velocity these dots appeared as lines, which were longer as the
rotation was more rapid. The greatest length observed was 24°, which,
with 800 revolutions in a second, can be shown to correspond to a duration
of jJ^^ of a second. With a slow rotation the lines present the appearance
^== ; they are quite parallel, and the ends in the same line. But with
greater velocity, and when the rotation took place from left to right, they
presented the appearance — , and when it turned from right to left

the appearance == — , because the image of the centre spark was formed

after the lateral ones. Wheatstone found that this displacement amounted
to half a degree before or behind the others ; accordingly this arc corre-
sponds to a duration of about the jy.^|^o °f ^ second ; the space traversed
in this time being a quarter of a mile, gives for the velocity of electricity
288,000 miles in a second, which is greater than that of light. The velocity
obtained from experiments with dynamical electricity is far less ; and, owing
to induction, the transmission of a current through submarine wires is com-
paratively slow.

In the above experiment the images of the two outer sparks appear
simultaneously in the mirror, from which it follows that the electric current
issues simultaneously from the two coatings of the Leyden jar.

From theoretical considerations based upon measurements of constant
electrical currents Kirchhoff concluded that the motion of electricity in a wire
in which it meets with no resistance is like that of a wave in a stretched
string, and has the velocity of 192,924 miles in a second, which is about that
of light in vacuo (507).

According to Walker, the velocity of electricity is 18,400 miles, and
according to Fizeau and Gounclle it is 62,100 miles in iron, and 1 1 1,780 in
copper wire. These measurements, however, were made with telegraph wires,
which induce opposite electricities in the surrounding media ; there is thus
produced a resistance which diminishes the velocity. The velocity is less
in insulated wires in water than in air. The nature of the conductor appears
to have some influence on the velocity ; but not the thickness of the wire
nor the potential of the electricity.

For atmospheric electricity, reference must be made to the chapter on
Meteorology.

770

Dynamical Electricity.

[797-

BOOK X.

DYNAMICAL ELECTRICITY.

CHAPTER I.

VOLTAIC PILE. ITS INIODIFICATIONS.

797. Galvani's experiment and theory. — The fundamental experiment
which led to the discovery of dynamical electricity is due to Galvani, Pro-
fessor of Anatomy in Bologna. Occupied with investigations on the in-
fluence of electricity on the nervous excitability of animals, and especially of

the frog, he observed
that when the lum-
bar nerves of a dead
frog were connected
with the crural mus-
cles by a metallic
circuit, the latter be-
came briskly con-
tracted.

To repeat this
celebrated experi-
ment, the legs of a
recently killed frog
are prepared, and
the lumbar nerves
on each side of the
vertebral column are
exposed in the form
of white threads.
A metal conductor,
composed of zinc
and copper, is then
taken (fig. 740), and one end introduced between the nerves and the vertebral
column, while the other touches one of the muscles of the thighs or legs ;
at each contact a smart contraction of the muscles ensues.

Galvani had some time before observed that the electricity of machines
produced in dead frogs analogous contractions, and he attributed the pheno-
mena first described to an electricity inherent in the animal. He assumed

Fig. 740.

-799] Disengagement of Electricity in Clieniical Actions. yyi

that this electricity, which he called vital fluid, passed from the nerves to
the muscles by the metallic arc, and was thus the cause of contraction.
This theory met with great support, especially among physiologists, but it
was not without opponents. The most considerable of these was Alexander
Volta, Professor of Physics in Pavia.

798. Volta's fundamental experiment. — Galvani's attention had been
exclusively devoted to the nerves and muscles of the frog ; Volta's was
directed upon the connecting metal. Resting on the observation, which
Galvani had also made, that the contraction is more energetic when the con-
necting arc is composed of two metals, than when there is only one, Volta
attributed to the metals the active part in the phenomenon of contraction.
He assumed that the disengagement of electricity was due to their contact,
and that the animal parts only officiated as conductors, and at the same time
as a very sensitive electroscope.

By means of the condensing electroscope, which he had then recently
invented, Volta devised several modes of showing the disengagement of elec-
tricity on the contact of metals, of which the following is the easiest to per-
form : —

The moistened finger being placed on the upper plate of a condensing
electroscope (fig. 716), the lower plate is touched with a plate of copper, c,
soldered to a plate of zinc, 2, which is held in the other hand. On breaking
the connection and lifting the upper plate (fig. 717), the gold leaves diverge,
and, as may be proved, with negative electricity. Hence, when soldered
together, the copper is charged with negative electricity, and the zinc with
positive electricity. The electricity could not be due either to friction or
pressure ; for if the condensing plate, which is of copper, is touched with
the zinc plate 2, the copper plate to which it is soldered being held in the
hand, no trace of electricity is observed.

A memorable controversy arose between Galvani and Volta. The latter
was led to give greater extension to his contact theory, and propounded the
principle that when two heterogeneous substances are placed in contact, one
of them always assumes the positive and the other the ftegative electrical
condition. In this form Volta's theory obtained the assent of the principal
philosophers of his time. Galvani, however, made a number of highly
interesting experiments with animal tissues. In some of these he obtained
indications of contraction, even though the substances in contact were quite
homogeneous.

799. Disengagrement of electricity In chemical actions. — The contact
theory which Volta had propounded, and by which he explained the action of
the pile, soon encountered objectors. Fabroni, a countryman of Volta, having
observed that, in the pile, the discs of zinc became oxidised in contact with
the acidulated water, thought that this oxidation was the principal cause of
the disengagement of electricity. In England Wollaston soon advanced the
same opinion, and Davy supported it by many ingenious experiments.

It is true that in the fundamental experiment of the contact theory (798)
Volta obtained signs of electricity. But De la Rive showed that if the zinc
be held in a wooden clamp, all signs of electricity disappear, and that the
same is the case if the zinc be placed in gases, such as hydrogen or nitrogen,
which exert upon it no chemical action. De la Rive accordingly concluded

3 D 2

772 Dynamical Electricity. [799-

that in Volta's original experiment the disengagement of electricity is due to
the chemical actions which result from the perspiration and from the oxygen
of the atmosphere.

The development of electricity in chemical actions may be demonstrated
in the following manner by means of the condensing electroscope (786) : — A
disc of moistened paper is placed on the upper plate of the condenser, and
on this a zinc capsule, in which some very dilute sulphuric acid is poured. A
platinum wire, communicating with the ground, but insulated from the sides
of the vessel, is immersed in the liquid, and at the same time the lower plate
of the condenser is also connected with the ground by touching it with the
moistened finger. On breaking contact and removing the upper plate, the
gold leaves are found to be positively electrified, proving that the upper plate
has received a charge of negative electricity.

By a variety of analogous experiments it may be shown that various
chemical actions are accompanied by a disturbance of the electrical equili-
brium ; though of all chemical actions those between metals and liquids are
the most productive of electricity. All the various resultant effects are in
accordance with the general rule, that when a liquid acts chemically on a
metal the liquid assumes the positive, and the metal the negative, con-
dition. In the above experiment the sulphuric acid, by its action on
zinc, becomes positively electrified, and its electricity passes off through
the platinum wire into the ground, while the negative electricity excited
on the zinc acts on the condenser just as an excited rod of sealing-wax
would do.

In many cases the electrical indications accompanying chemical actions
are but feeble, and require the use of a veiy delicate electroscope to render
them apparent. Thus, one of the most energetic chemical actions, that of
sulphuric acid upon zinc, gives no more free electricity than water alone does
with zinc.

Opinion — which in this country, at least, had, mainly by the iniluence of
Faraday's experiments, tended in favour of the purely chemical origin of
the electricity produced in voltaic action — has of late inclined more and more
towards the contact theory. The following experiments, due to Sir W.
Thomson, afford perhaps the most conclusive arguments hitherto adduced
in favour of the latter view : —

A very light metal bar is suspended by fine wire, so as to be movable
about an axis perpendicular to the plane of a disc made up of two half discs,
one of zinc, Z, and the other of copper, C (fig.
■^j!^i^^^ 741). The light bar is counterpoised so as to

iDe exactly over one half of the line of separa-
tion of the two discs. When the discs are
placed in contact and the bar is charged posi-
tively by being connected with a Leydcn jar,
the bar moves from the zinc towards the copper ;
'^ ^■''' if the jar, and therefore the bar, is charged

negatively, its motion is in the opposite direction. The same results are ob-
tained when the discs are connected by a wire, thus showing that the contact
of the two metals causes them to assume different electrical conditions, the
zinc taking the positive, and the copper the negative electricity.

-800] Current Electricity. 773

\\'hen, however, the two halves, instead of being in metalHc contact, are
connected by a drop of water, no change is produced in the position of the
bar by altering its electrification, provided it hangs quite symmetrically rela-
tive to the two halves of the ring. This result shows that, under the circum-
stances mentioned, no difference is produced in the electrical condition of
the two metals. Hence the conclusion has been drawn by Sir W. Thomson
and others, that the movement of electricity in the galvanic circuit is entirely
due to the electrical difference produced at the surfaces of contact of the dis-
similar metals. These results have been confirmed by some recent very
careful experiments by Professor Clifton.

There are, however, other facts which are not easily harmonised with this
view ; and indeed the last-mentioned experiment can hardly be regarded as
proving that in all cases two different metals connected by an electrolytic
(8 1 6) liquid assume the same electrical condition. It may, therefore, still be
regarded as possible, or even probable, that the contact between the metals
and the liquids of a cell contributes, at least in some cases, to the production
of the current.

A most complete discussion of the question as to the seat of electromotive
forces in the voltaic cell is published in a series of papers by Prof. Lodge in
the nineteenth volume of the ' Philosophical Magazine.'

Soo. Curreut electricity. — When a plate of zinc and a plate of copper are
partially immersed in dilute sulphuric acid, no electrical or chemical change
is apparent beyond perhaps a slight disengagement of hydrogen from the
surface of the zinc plate. If now the plates are
placed in direct contact, or, more conveniently, ».

are connected by a metal wire, the chemical if

action sets in, a large quantity of hydrogen is
disengaged ; but this hydrogen is no longer dis-
engaged at the surface of the zinc, but at the
surface of the copper plate. Here then we have
to deal with something more than mere chemical

action, for chemical action would be unable to

explain either the increase in the quantity of \ ly-"

hydrogen disengaged when the metals touch, or ~ "^.i-

the fact that this hydrogen is now given off at

the surface of the copper plate. At the same ■"' '

time, if the wire is examined it will be found to possess many remarkable

thermal, magnetic, and other properties which will be afterwards described.

In order to understand what here takes place, let us suppose that we have
two insulated metal spheres, and that one is charged with positive and the
other with negative electricity, and that they are momentarily connected by
means of a wire. Electricity will pass from a place of higher to a place of
lower potential — that is, from the positive along the wire to the negative —
and the potentials become equal. This is, indeed, nothing more than an
electrical discharge taking place through the wire ; and during the infinitely
short time in which this is accomplished, it can be shown that the wire
exhibits certain heating and magnetising effects, of which the increase of
temperature is perhaps the easiest to observe. If now we can imagine some
agency by which the different electrical conditions of the two spheres are

774 Dynamical Electricity. [800-

renevved as fast as they are discharged, which is what very nearly takes
place when the two spheres are respectively connected with the two con-
ductors r and 7\ of a Holtz machine (figs. 687, 688), this equalisation of
potentials, thus taking place, is virtually continuous, and the phenomena
above mentioned are also continuous.

Now this is what takes place when the two metals are in contact in a
liquid which acts upon them unequally. This is independent of hypothesis
as to the cause of the phenomena — whether the electrical difference is only
produced at the moment of contact of the metals, or whether it is due to the
chemical action, or tendency to chemical action, between the metal and the
liquid. The rapidly succeeding series of equalisations of potential, which
takes place in the wire, being continuous, so long as the chemical action
continues, is what is ordinarily spoken of as the electrical cm-rent.

If we represent by +^ the potential of the copper plate, and by —e the
potential of the zinc, then the electrical difference — that is, the difference of
potentials — is +£? — ( — ^) = 2i?. And this is general ; the essential point of any
such combination as the above is, that it maintains, or tends to maintain, a
difference of potentials, which difference is constant. If, for instance, the
zinc plate be connected with the earth which is at zero potential, its potential
also becomes zero ; and since the electrical difference remains constant, we
have for the potential of the copper plate + ■2e. Similarly, if the copper be
connected with the earth the potential of the zinc plate is negative and is — 2e.
The conditions under which a current of electricity is formed in the above
experiment may be further illustrated by reference to the conditions which
determine the flow of water between two reservoirs containing water at dif-
ferent levels. If they are connected by a pipe, water will flow from the
one at a higher level to the one at a lower If vel until the water in the two
is at the same level, when of course the flow ceases. If we imagine the
lower reservoir so large that any water added to it would not affect its level —
if it were the sea, for example — that would represent zero level, and if the
higher reservoir could be kept at a constant level there would be a constant
flow in the pipe.

We must here be careful not to dwell too much on this analogy. It is not
to be supposed that in speaking of current of electricity we mean to assert
that anything actually flows — that there is any actual transfer of matter.
We say ' electricity flows ' or ' a current is produced,' in much the same sense
as that in which we say ' sound or light tra\els.'

801. Voltaic couple. Electromotive series. — The arrangement just
described, consisting of two metals in metallic contact, and a conducting
liquid in which they are placed, constitutes Tvsintple voltaic element or couple.
So long as the metals are not in contact, the couple is said to be open^ and
when connected it is closed.

According to the chemical view, to which wc shall for the present pro-
visionally adhere, it is not necessary for the jnoduction of a current that one
of the metals be unaffected by the liquid, but merely thatthe chemical action
upon the one be greater than upon the other. " For then we may assume
that the current produced would be due to the difference between the differ-
ences of potential which each of the metals separately produces by its con-
tact with the liquid. If the differences of potentials were absolutely equal —

-802] Elect r 01 native Force. 775

a condition, however, impossible of realisation with two distinct metals — we
must assume that when the metals are joined no current would be produced.
The metal which is most attacked is called ihc positive or generating- plate,
and that which is least attacked the negative or collecting plate. The posi-
tive metal determines the direction of the current, which proceeds i?i the
liquid from the positive to the negative plate, and out of the liquid through
the connecting wire from the negative to the positive plate.

In speaking of the direction of the current the direction of the positive
electricity is always understood.

In the fundamental experiment, not only the connecting wire, but also the
liquid and the plates arc traversed by the electrical current — are the scene
of electrical actions.

The mere immersion of two different metals in a liquid Is not alone
sufficient to produce a current ; there must be chemical action. When a
platinum and a gold plate are connected with a delicate galvanometer, and
immersed in pure nitric acid, no current is produced ; but on adding a drop
of hydrochloric acid a strong current is excited, which proceeds in the liquid
from the gold to the platinum, because the gold is attacked by the nitro-
hydrochloric acid, while the platinum is less so, if at all.

As a voltaic current is produced whenever two metals are placed in
metallic contact in a liquid which acts more powerfully upon one than upon
the other, there is a great choice in the mode of producing such currents. '
In reference to their electrical deportment, the metals have.been arranged in
what is called an elcctroniotive series^ in which the most electropositive are
at one end, and the most electro?tegative at the other. Hence when any two of
these are placed in contact in dilute acid, the current in the connecting wire
proceeds from the one lower in the list to the one higher. The principal
metals are as follows : —

1. Zinc 5. Iron 10. Silver

2. Cadmium 6. Nickel 11. Gold

3. Tin 7. Bismuth 12. Platinum

4. Lead 8. Antimony 13. Graphite

9. Copper

It will be seen that the electrical deportment of any metal depends on the
metal with which it is associated. Iron, for example, in dilute sulphuric acid
is electronegative towards zinc, but is electropositive towards copper ; copper
in turn is electronegative towards iron and zinc, but is electropositive towards
silver, platinum, or graphite.

802. Electromotive force. — The force in virtue of which continuous
electrical effects are produced throughout a circuit consisting of two metals
in metallic contact in a liquid which acts unequally upon them, is usually
called the electromotive force. Electromotive force and difference of potentials
are commonly used in the same sense. It is, however, more correct to regard
difference of potentials as a particular case of electromotive force ; for as we
shall afterwards see, there are cases in which electrical currents are pro-
duced without the occurrence of that particular condition which we have called
difference of potentials. The electromotive force is greater in proportion to
the distance of the two metals from one another in the series. I'hat is to

776

Dynamical Electricity.

[802-

say, it is greater the greater the difference between the chemical action upon
the two metals immersed. Thus the electromotive force between zinc and
platinum is greater than that between zinc and iron, or between zinc and
copper. The law extablished by experiment is, that the electromotive force
between any two metals is equal to the sum of the electromotive forces between
all the intervening metals. Thus the electromotive force between zinc and
platinum is equal to the sum of the electromotive forces between zinc and
iron, iron and copper, and copper and platinum.

The electromotive force is influenced by the condition of the metal ;
rolled zinc, for instance, is negative towards cast zinc. It also depends on
the degree of concentration of the liquid ; in dilute nitric acid zinc is positive
towards tin, and mercury positive towards lead ; while in concentrated nitric
acid the reverse is the case, mercury and zinc being respectively electro-
negative towards lead and tin.

The nature of the liquid also influences the direction of the current. If
two plates, one of copper and one of iron, are immersed in dilute sulphuric
acid, a current is set up proceeding through the liquid from the iron to the
copper ; but if the plates, after being washed, are placed in solution of
potassium sulphide, a current is produced in the opposite direction — the
copper is now the positive metal. Other examples may be drawn from the
following table, which shows the electric deportment of the principal metals
with three different liquids. It is arranged like the preceding one ; each
metal being electropositive towards any one lower in the list, and electro-
negative towards any one higher.

Caustic potass

Zinc

Tin

Cadmium

Antimony

Lead

Bismuth

Iron

Copper

Nickel

Silver

Sulphide of
potassium

Zinc

Copper

Cadmium

Tin

Silver

Antimony

Lead

Bismuth

Nickel

Iron

Hydrochloric acid

Zinc

Cadmium

Tin

Lead

Iron

Copper

Bismuth

Nickel

Silver

Antimony .

voltaic current may also be produced by means of two liquids and
_ one metal. This may be shown by the following
experiment : — In a beaker containing strong nitric
acid is placed a small porous pot (fig. 743), con-
taining strong solution of caustic potass. If now
two platinum wires connected with the two ends
of a galvanometer (821) are immersed respectively
in the alkali and in the acid, a voltaic current is
produced, proceeding in the wire from the nitric
acid to the potass, which thus correspond re-
s])ectively to the negative and positive plates in
ordinary couples.
A metal which is acted upon by a liquid can be protected from solution

Fifi.

-804] Voltaic Pile. Voltaic Battery. 777

by placing in contact with it a more electropositive metal, and thus forming
a simple voltaic circuit. This principle is the basis of Davy's proposal to
protect the copper sheathings of ships, which are rapidly acted upon by sea-
water. If zinc or iron be connected with the copper, these metals are dis-
solved and the copper protected. Davy found that a piece of zinc the size
of a nail was sufficient to protect a surface of forty or fifty square inches ;
unfortunately the proposal has not been of practical value, for the copper
must be attacked to a certain extent to prevent the adherence of marine
plants and shellfish.

803. Poles and electrodes.— If the wire connecting the two terminal
plates of a voltaic couple be cut, it is clear, from what has been said about
the origin and direction of the current, that positive electricity will tend to
accumulate at the end of the wire attached to the copper or negative plate,
and negative electricity on the wire attached to the zinc or positive plate.
These terminals have been called the poles of the
battery. For experimental purposes, more especi-
ally in the decomposition of salts, plates of platinum
are attached to the ends of the wires. Instead of the
term poles, the word electrode (t'j^eKTpoi', and 686s, a
way) is now commonly used ; for these are the ways
through which the respective electricities emerge. It
is important not to confound the positive plate with
the positive /^/^ or electrode. The positive electrode
is that connected with the negative plate, while the
negative electrode is connected with the positive plate.

804. Voltaic pile. Voltaic battery. — When a
series of voltaic elements or pairs is arranged so
that the zinc of one element is connected with the
copper of another, the zinc of this with the copper
of another, and so on, the arrangement is called a
voltaic battery ; and by its means the effects pro-
duced by a single element are capable of being very
greatly increased.

The earliest of these arrangements was devised by
Volta himself. It consists (fig. 744) of a series of discs
piled one over the other in the following order : — At
the bottom, on a frame of wood, is a disc of copper,
then a disc of cloth moistened by acidulated water, or
by brine, then a disc of zinc ; on this a disc of copper, ^
and another disc of moistened cloth, to which again
follow as many sets of copper-cloth-zinc, always in the
same order, as may be convenient, the highest disc
being of zinc. The discs are kept in a vertical position by glass rods.

It will be readily seen that we have here a series of simple voltaic couples,
the moisture in the cloth acting as the Iic|uid in the cases already mentioned,
and that the terminal zinc is the negative and the terminal copper the
positive pole. From the mode of its arrangement, and from its discoverer,
the apparatus is known as the voltaic pile, a term applied to all apparatus of
this kind for accumulating the effects of dynamical electricity.

Fig. 744.

yT^

Dynamical Electricity.

[804-

The distribution of electricity in the pile varies according as it is in con-
nection with the earth by one of its extremities, or as it is insulated by being
placed on a non-conducting cake of resin or glass.

Jn the former case, the end in contact with the ground is neutral, and the
rest of the apparatus contains only one kind of electricity ; this is negative
if the copper disc, and positive if the zinc disc, is in contact with the ground.

In the insulated pile the electricity is not uniformly distributed. By
means of a proof-plane and electroscope it may be demonstrated that the
middle part is in a neutral state, and that one-half is charged with positive
and the other with negative electricity, the potential increasing from the
middle to the ends. The half terminated by a zinc disc is charged with nega-
tive electricity, and that by a copper with positive electricity. The pile is
thus similar to a charged Leyden jar ; with this difference, however, that
when the jar has been discharged by connecting its two coatings, the elec-
trical effects cease ; while in the case of the pile, the cause which originally
brought about the distribution of electricity restores this state of charge after
the discharge ; and the continuous succession of charges and discharges
forms the current. The effects of the pile will be discussed in other places.

805. -Wollaston's battery. — The original form of the voltaic pile has a
great many inconveniences, and possesses now only an historical interest.

Fig. 745-

It has received a great many improvements, the principal object of which
has been to facilitate manipulation, and to produce greater electromotive ^
force.

One of the earliest of these modifications was the crown of cups, or
coiironiie des tasscs, invented by Volta himself. An improved form of this is
known as Wollastons battery (fig. 745) ; it is arranged so that when the
current is not wanted, the action of the battery can be stopped.

The plates Z are of thick rolled zinc, and usually about eight inches in
length by six in breadth. The copper plates, C, are of thin sheet, and bent

-806] Enfccblenient of the Current in Batteries. 779

so as to surround the zincs without touching them, contact being prevented
by small pieces of cork. To each copper plate a narrow strip of copper, <?,
is soldered, which is bent twice at right angles and is soldered to the next
zinc plate ; and the first zinc, Z, is surrounded by the first copper C ; these
two constitute a couple, and each couple is immersed in a glass vessel, con-
taining acidulated water. The copper, C, is soldered to the second zinc by
the strip o, and this zinc is in turn surrounded by a second copper, and so on.

Fig. 745 represents a pile of sixteen couples united in two parallel series
of eight each. All these couples are fixed to a cross frame of wood, by which
they can be raised or lowered at pleasure. When the battery is not wanted,
the couples are lifted out of the liquid. The water in these vessels is usually
acidulated with j^^ sulphuric and ^^ nitric acid.

Hare's dcjlagrator. — This is a simple voltaic arrangement, consisting of
two large sheets of copper and zinc rolled together in a spiral, but preserved
from direct contact by bands of leather or horsehair. The whole is immersed
in a vessel containing acidulated water, and the two plates are connected
outside the liquid by a conducting wire.

806. Enfeeblement of the current in batteries. Secondary currents.
The various batteries already described — ^'olta's, Wollaston's, and Hare's,
which consist essentially of two metals and one liciuid— labour under the
objection that the currents produced rapidly diminish in strength.

This is due principally to three causes : the first is the decrease in the
chemical action owing to the neutralisation of the sulphuric acid by its com-
bination with the zinc. This is a necessary action, for upon it depends the
current ; it therefore occurs in all batteries, and is without remedy except by
replacement of acid and zinc. The second is due to what is called local
action ; that is, the production of small closed circuits in the active metal,
owing to the impurities it contains. These local currents rapidly wear away
the active plate, without contributing anything to the continuance of the
general current. They are remedied by amalgamating the zinc with mercury,
by which chemical action is prevented until the circuit is closed, as will be
more fully explained (816). The third arises from the production of an
inverse electromotive force, which tends to produce a current in a contrary
direction to the principal current, and therefore to destroy it either totally
or partially. In the fundamental experiment (fig. 742), when the circuit is
closed, zinc sulphate is formed, which dissolves in the licjuid, and at the
same time a layer of hydrogen gas is gradually formed on the surface of the
copper plate. This diminishes the activity of the combination in more than
one way. In the first place, it interferes with the contact between the metal
and the liquid ; in the second place, in proportion as the copper becomes
coated with hydrogen, we have virtually a plate of hydrogen instead of a
plate of copper opposed to the zinc, and in addition, the hydrogen, by react-
ing on the zinc sulphate, which accumulates in the liquid, gradually causes a
deposition of zinc on the surface of the copper ; hence, instead of having
two different metals unequally attacked, the two metals become gradually
lees different, and, consequently, the total effect and the current become
weaker and weaker.

The polarisation of the plate (as this phenomenon is termed) may be
destroyed by breaking the circuit and exposing the copper plate to the air ;

78o

Dynamical Electricity.

[806-

the deposited hydrogen is thus more or less completely got rid of, and on
again closing the circuit the current has nearly its original strength. The
same result is obtained when the current of another battery is transmitted
through the battery in a direction opposite to that of the first.

_ When platinum electrodes are used

to decompose water, a similar pheno-
menon is produced, called ^cJA^r/^a/ztfiw
of tJte electrodes, which may be illus-
trated by an arrangement represented
in fig. 746, in which B is a constant
element, V a voltameter (846), G a
galvanometer (821), and H a mercury
cup. The wire L being disconnected
from H, a current is produced in the
voltameter, the direction of which is
from P to P' ; if now the wire F be
detached from H, and L be connected therewith, a current is produced
through the galvanometer the direction of which is from P' to P ; that is, the
opposite of that which the element had previously produced. Becquerel and
Faraday have shown that this polarisation of the metals results from the
deposits caused by the passage of the current, and an important application
of this phenomenon will be found described farther on (849).

Fi?. 740.

CONSTANT CURRENTS.

807. Constant currents. — With few exceptions, batteries composed of
elements with a single liquid have almost gone out of use, in consequence
of the rapid enfeeblemcnt of the current produced. They have been replaced
l^y batteries with two liquids, which are called constant batteries because
their action continues without material alteration for a considerable period
of time. The essential point to be attended to in securing a constant current
is to prevent the polarisation of the inactive metal ; in other words, to hinder
any permanent deposition of hydrogen on its surface. This is eflTected by
placing the inactive metal in a liquid upon which the deposited hydrogen
tan act chemically

80S. Baniell's battery. — This was the first form of the constant batteiy,
and was invented by Daniell in the year 1836. As regards the constancy
of its action, it is perhaps still the best of all constant batteries. P'ig. 747
represents a single element. A glass or porcelain vessel, V, contains
a saturated solution of copper sulphate, in which is immersed a copper
cylinder, (i, open at both ends, and perforated by holes. At the upper part
of this cylinder there is an annular shelf, (1, also perforated by small holes,
and below the level of the solution ; this is intended to support crystals of
copper sulphate to replace that decomposed as the electrical action pro-
ceeds. Inside the cylinder is a thin porous vessel, P, of unglazed earthen-
ware. This contains either water, or solution of common salt, or dilute
sulphuric acid, in which is placed the cylinder of amalgamated zinc, Z. Two
thin strips of copper/ and //, fixed by binding screws to the copper and to
the zinc, serve for connecting the elements in series.

-809]

Grove's Battery.

781

Fig. 747.

When a DanielFs element is closed, the hydrogen resulting from the
action of the dilute acid on the zinc is liberated on the surface of the copper
plate, but meets there the copper sulphate, which is reduced, forming sul-
phuric acid and metallic copper, which is deposited on the surface of the
copper plate. In this way copper sulphate in
solution is taken up ; and if it were all con-
sumed, hydrogen would be deposited on the
copper, and the current would lose its con-
stancy. This is prevented by the crystals of
copper sulphate which keep the solution satu-
rated. The sulphuric acid produced by the
decomposition of the sulphate permeates the
porous cylinder, and tends to replace the acid
used by its action on the zinc ; and as the
quantity of sulphuric acid formed in the solu-
tion of copper sulphate is regular, and propor-
tional to the acid used in dissolving the zinc, the
action of this acid on the zinc is regular also, and
thus a constant current is produced.

In order to join together several of these
elements to form a battery, the zinc of one is connected either by a copper
wire or strip with the copper of the next, and so on from one element to
another, as shown in fig. 751, for another kind of battery.

Instead of a porous earthenware vessel, a bag of sailcloth may be used
for the diaphragm separating the two liquids. The effect is at first more
powerful, but the two solutions mix more rapidly, which weakens the current.
The object of the diaphragm is to allow the current to pass, but to prevent
as much as possible the mixture of the two liquids.

The current produced by a Daniell's battery is constant for some hours ;
its action is stronger when it is
placed in hot water. Its electro-
motive force is about i -08 volt.

809. Grove's battery. — In this
battery the copper sulphate solution
is replaced by nitric acid, and the
copper by platinum, by which
greater electromotive force is ob-
tained. Fig. 748 represents one
of the forms of a couple of this
battery. It consists of a glass
vessel. A, partially filled with dilute
sulphuric acid (i : 8) ; of a cyhnder
of zinc, Z, open at both ends ; of a
vessel, \\ made of porous earthen-
ware, and containing ordinary nitric
acid; of a plate of platinum, P (fig. 749),) bent in the form of an S, and fixed
to a cover, c, which rests on the porous vessel. The platinum is con-
nected with a binding screw, (5, and there is a similar binding screw on the
zinc. In this battery the hydrogen, which would be disengaged on the

^VJ

Fig. 748.

782

Dynamical Electricity.

[809-

platinum, meeting,'- the nitric acid, decomposes it, forming hyponitrous acid,
which dissolves, or is disengaged as nitrous fumes. Grove's battery is the
most convenient, and one of the most powerful of the two fluid batteries.
It is, however, expensive, owing to the high price of platinum; besides
v/hich the platinum is liable, after some time, to become brittle and break
very easily. But as the platinum is not consumed, it retains most of its
value, and when the plates which have been used in a battery are heated to
redness they regain their elasticity.

8io. Bunsen's battery .^ — Bunsen's, also known as the sine carbon
battery, was invented in 1843 ; it is in effect a Grove's battery, where
the plate of platinum is replaced by a cylinder of carbon. This is made
either of the graphitoidal carbon deposited in gas retorts, or by calcining
in an iron mould an intimate mixture of coke and bituminous coal, finely
powdered and strongly compressed. Both those modifications of carbon
are good conductors. Each element consists of the following parts : i, a
vessel, F (fig. 750), either of stoneware or of glass, containing dilute sul-
phuric acid ; 2, a hollow cylinder, Z, of amalgamed zinc ; 3, a 'porous
vessel, V, in which is ordinary nitric acid ; 4, a rod of carbon, C, prepared

t'ig- 75

in the above manner. In the vessel F the zinc is first placed, and in it the
carbon C in the porous vessel V as seen in P. To the carbon is fixed a
binding screw, /;/, to which a copper wire is attached, forming the positive
pole. The zinc is provided with a similar binding screw, ;/, and wire, which
is thus a negative pole.

A single cell of the ordinary dimensions, 20 cm. in height and 9 cm. in
diameter, has a resistance of about o"i4 ohm, and taking its E.M.F. at r82
(814), gives a current of 12 to 13 amperes when on short circuit, that is,
when it is closed without measurable external resistance.

The elements are arranged to form a battery (fig. 751) by connecting each'
carbon to the zinc of the following one by means of the clamps w//, and a
strip of copper, c, represented in the top of the figure. The copper is pressed
at one end between the carbon and the clamp, and at the other it is soldered
to the clamp ti, which is fitted on the zinc of the following element, and so
forth. The clamp of the first carbon and that of the last zinc are alone
provided with binding screws, to which are attached the wires.

-811] Since s Battery. 783

The chemical action of Bunsen's battery is the same as that of Grove's,
and being equally powerful, while less costly, is very generally used on the
Continent. But though its first cost is less than that of Grove's battery, it
is more expensive to work, and is not so convenient to manipulate.

Vig. 751.

Callaiis battery is a modified form of Grove's. Instead of zinc and plati-
num, zinc and platinised lead are used ; and instead of pure nitric acid Callan
used a mixture of sulphuric acid, nitric acid, and saturated solution of nitre.
The batter)^ is said to be equal in its action to Grove's, and is much cheaper.

Callan has also constructed a battery in which zinc in dilute sulphuric
acid forms the positive plate, and cast iron in strong nitric acid the negative.
Under these circumstances the iron becomes passive ; it is strongly electro-
negative, and does not dissolve. If, however, the nitric acid becomes too
weak, the iron is dissolved with simultaneous disengagement of nitrous fumes.

After being in use some time, all the batteries in which the polarisation
is prevented by nitric acid disengage nitrous fumes in large quantities, and
this is a serious objection to their use, especially in closed rooms. To pre-
vent this, nitric acid is frequently replaced by chromic acid, or, better, by a
mixture of 4 parts potassium bichromate, 4 parts sulphuric acid, and 18
water. The liberated hydrogen reduces the chromic acid to the state of
oxide of chromium, which remains dissolved in sulphuric acid. With the
same view, sesquichloride of iron is sometimes substituted for nitric acid ;
it becomes reduced to protochloride. But the action of the elements thus
modified is considerably less than when nitric acid is used, owing to the
increased resistance.

811. Smee's battery, — In this battery the polarisation of the negative
plate is prevented by mechanical means. Each element consists of a sheet of
platinum placed between two vertical plates of zinc, as in Grove's battery ;
but as there is only a single liquid, dilute sulphuric acid, the elements have
much the form of those in Wollaston's battery. The adherence of hydrogen
to the negative plate is prevented by covering the platinum with a deposit of
finely divided platinum. In this manner the surface is roughened, which
facilitates the disengagement of hydrogen to a remarkable extent, and con-

784

Dynamical Electricity.

[811-

sequently diminishes the resistance of a couple. Instead of platinum, silver
coveied with a deposit of finely divided platinum is frequently substituted, as
being cheaper.

Walker'' s battery. — This resembles Smee's battery, but the electronegative
plate is either gas graphite or platinised graphite ; it is excited by dilute
sulphuric acid. This battery is used in all the stations of the South-Eastern
Railway ; it has considerable electromotive force^is convenient and economi-
cal in manipulation, and large-sized elements can be constructed at a cheap rate.

812. Kecent batteries. — The mercury sulpJiate battery (fig. 752) de-
vised by Marie Davy, is essentially a zinc-carbon element, but of smaller
dimensions than those elements usually are. In the outer vessel, \\ ordi-
nary water or brine is placed, and in the porous vessel mercury sulphate.
This salt is agitated with about three times its volume of water, in which it is
difficultly soluble, and the liquid poured off from the pasty mass. The carbon
being placed in the porous vessel, the spaces are filled with the residue, and
then the decanted liquor poured into it.

Chemical action takes place when the cell is closed. The zinc then
decomposes the water, liberating hydrogen, which, traversing the porous

rorff^ra

I*'ig. 752- l''K- 7.rv Fig. 754.

vessel, reduces the mercury sulphate, forming metallic mercury, which collects
at the iDOttom of the vessel, while the sulphuric acid formed at the same time
traverses the diaphragm to act on the zinc, and thus increases the action.

The mercury which is deposited may be used to prepare a quantity of
sulphate equal to that which has been consumed. A small quanti ty of the
solution of mercury sulphate may also pass through the diaphragm ; but this
is rather advantageous, as its effect is to amalgamate the zinc.

The electromotive force of this element is about a quarter greater than that
of Danicll's clement, but it has greater resistance ; it is rapidly exhausted
when continuously worked, though it appears well suited for discontinuous
work, as with the telegraph, and with alarums.

Gravity batteries. — The use of porous \essels is open to many objections,
more especially in the case of Daniell's battery, in which they gradually
become encrusted with copper, which destroys them. A kind of battery has
been devised in which the porous vessel is entirely dispensed with, and the
separation of the liquids is effected by the difference of density. Such
batteries are called gravity battel ics. Fig. 753 represents a form dc\ised

-812 j Recent Batteries. 785

by Callaud. V is a glass or earthenware vessel in which is a copper plate
soldered to a wire insulated by gutta-percha. On the plate is a layer of crys-
tals of copper sulphate, C ; the whole is then filled with water, and the zinc
cylinder, Z, is immersed in it. The lower part of the liquid becomes saturated
with copper sulphate ; the action of the battery is that of a Daniell, and the zinc
sulphate which gradually forms, floats on the solution of copper sulphate owing
to its lower density. This battery is easily manipulated, the consumption of
copper sulphate is economical, and when not agitated it works constantly for
some time, provided care be taken to replace the water lost by evaporation.

Meidingcr's element, which is much used in Germany, is essentially a
gravity battery of special construction, with zinc in solution of magnesium
sulphate, and copper in solution of copper sulphate.

Mhwttds battery. — This may be described as a Daniell's element, in
which the porous vessel is replaced by a layer of sawdust or of sand. At
the bottom of an earthenware vessel (fig. 754) is placed a layer of coarsely-
powdered copper sulphate «, and on this a copper plate provided with an
insulated copper wire i. On this there is a layer of sand or of sawdust be,
and then the whole is filled with water, in which rests a zinc cylinder Z.
The action is just that of a Daniell ; the sawdust prevents the mixture of the
liquids, but it also offers great resistance, which increases with its thickness.
From its simplicity and economy, and the facility with which it is constructed,
the battery merits increased attention.

Dc la Rue and Mailer's element consists of a glass tube about 6 inches
long by 075 inch in diameter, closed by a vulcanised india-rubber stopper
through which passes a zinc rod o-i8 inch in diameter and 5 inches long.
A flattened silver wire also passes through the stopper to the bottom of the
tube, in which is placed about half an ounce of silver chloride, the greater
part of the cell being filled with solution of sal-ammoniac. The hydrogen
evolved at the negative plate reduces the chloride to metallic silver, which
is thereby recovered. Since there is only one liquid, and the solid electro-
lyte is not acted upon when the circuit is open, the element is easily worked
and requires little attention. It is very compact, 1,000 elements occupying
a space of less than a cubic yard ; De la Rue and Miiller have used as many
as 14,400 such cells in investigations on the stratification of the electric light.
A battery of 8,040 of these cells gave a spark \ of an inch in length in air
under the ordinary atmospheric pressure ; while under a pressure of a cjuarter
of an atmosphere the striking distance was i^_ inch.

The electromotive force of a silver chloride cell is 1-03 of a volt, and that
of one made with silver bromide is 0-908 ; hence a series of 4 cells, three of
the silver chloride cells with one of bromide, gives an average electromotive
force of I volt (814).

Latimer Clark's element consists of perfectly pure mercury as a negati\e
plate covered with a paste obtained by boiling sulphateof mercury in a satu-
rated solution of zinc sulphate. The positive metal is a plate of zinc resting on
this paste of sulphate. Insulated wire?, leading to the mercury and the zinc
respectively, form the connections. This battery is not well adapted for
continuous work, but it furnishes a standard of electromotive force, which is
constant and can be relied upon. Its electromotive force is i"495 volt at
15°, and it diminishes by 0-00078 for an increase of 1° C.

786

Dynamical Electricity

[812-

Fig. 755

A convenient form of element for many purposes is Xh^ potassium bichro-
mate,or, zs it is frequently teniied, the bichromate of potass ^Xttrntnl (fig. 755).
It consists of a zinc plate Z, attached to a brass
rod, which slides up and down in a brass tube in an
ebonite or porcelain cover, so that it can be wholly
or partially immersed in the liquid. Two graphite
plates, C C, are similarly fitted in the cover, and by
means of strips of brass the carbon and the zinc
plates are respectively in connection with the binding
IJJJHJI jll screws, which thus form the poles. The exciting

|H|i I liquid is a mixture of i part of potassium bichromate,

JIMA "V - of sulphuric acid, and 10 of water.

The electromotive force is about rS or 1-9 that
of a Daniell ; when the element is closed by a wire
of small resistance its E.M.F. increases slightly at
first, then remains constant for some time, after which
it rapidly sinks to half its original amount.

In Niaiidefs eloiietit a zinc cylinder dips in a

solution of common salt and surrounds a porous cell,

in which is a carbon plate surrounded by pieces of

carbon and filled with chloride of lime, which does not act on the zinc even

when the circuit is closed. The electromotive force is i -6 that of a Daniell.

The element of Lalandc a?id Chaperon

^ is zinc in a 30 per cent, solution of caustic

CTn potass and copper in contact with oxide

^ of copper which acts as depolariser. The

E.M.F. is 0-85 volt, and there is no action
unless the circuit is closed. To prevent
the absorption of carbonic acid the solu-
tion is covered with paraffine oil.

813. licclanclie's element. — This
consists (fig. 756) of a rod of carbon,
C, placed in a porous pot, which is then
very tightly packed with a mixture of
pyrolusite (peroxide of manganese) and
gas grajjhite, M. This is covered over
with a layer of pitch. At the top of the
carbon is soldered a mass of lead, L, to
which is affixed a binding screw. The
positive plate is a rod of zinc, Z, in which
is fixed a copper wire. The exciting
liquid consists of a strong solution of sal-
ammoniac, contained in a glass vessel G,
which is not more than one-third full.
The electromotive force of the element
is said to be about one-third greater than that of a Danicll's element ; its in-
ternal resistance varies of course with the size, but is stated to be from ri to
5 times that of an ohm. The battery is not adapted for continuous work
as in heavy telegraphic circuits, or in electro-plating, since it soon becomes

Fig. 756.

-814] Electromotive Force of Different Elements. 787

polarised ; it has, however, the valuable property of quickly regaining its
original strength when left at rest, and is extremely well adapted for dis-
continuous work, such as that of electrical bells.

A rod of carbon 4| x i| x y^^ inches should have a maximum resistance of
I ohm ; but good plates made from the carbon of gas retorts do not average
more than 0-5, and in some cases o-i ohm. If the resistance equals an ohm,
the conducting power of carbon is about 0-003 that of mercury.

A drawback to the use of carbon is that, from its porosity, the exciting
liquid rises, and forms local currents at the junction with the binding
screw, which injure or destroy contact. This may be remedied to a very
great extent by soaking the plates before use in hot melted paraffine, which
penetrates into the pores, expelling the air. On cooling, it solidifies and
prevents the capillaiy action mentioned above. By carefully scraping the
paraffine from the outside, a surface is exposed which is as good a conductor
as if the pores were filled with air. IVIeasurements have shown that the
resistance of a rod thus prepared is not altered.

In a recent modification of his element Leclanche dispensed with the
porous cell, and placed the carbon plate C between two similar flat prisms,
made by compressing a mixture of 55 parts of graphite, 40 parts of pyrolusite,
and 5 parts of shellac in steel moulds at a temperature of 100° under a pressure
of 300 atmospheres.

814. Electromotive force of different elements. — The following num-
bers represent the electromotive force of some of the elements most frequently
used, compared with that of an ordinary Daniell's cell charged as above
described ; they are the means of many careful determinations : —

Daniell's element . . set up with water . . . . i-oo
„ „ . . pure zinc and pure water, with pure

copper and pure saturated solution
of copper sulphate . . .1-02
Leclanche's „ . . zinc in saturated solution of am-
monium chloride . . . .1-32

Latimer Clark's element i -496

Bunsen's „ carbon in nitric acid . . .177

„ „ carbon in chromic acid . . .1-87

Grove's „ platinum in nitric acid . . .182

The greatest electromotive force as yet observed is by Beetz in a couple
consisting of potassium amalgam in caustic potash, combined with pyrolusite
in a solution of potassium permanganate. It is three times as much as that
of a Daniell's element.

The standard of electromotive force on the C. G. S. system is the Volt.
This is equal to 1,000,000,000 or 10' absolute electromagnetic units (709).
The volt is rather less than the electromotive force of a Daniell's cell, the
mean value of which may be taken at ro8 volt. The unit of current, which
is called an Ampere, is the current due to an electromotive force of one volt
working through a resistance of one ohm.

The Coulomb is the practical unit of electrical quantity ; it is that quantity
which, in a second, passes through the section of a conductor traversed by
a current of an ampere.

3 E2

788 Djmamical Electricity. [815-

815. Comparison of the voltaic battery with a frictlonal electrical
machine. — Except in the case of batteries consisting of a very large number
of couples, the difference of potentials between the terminals is far weaker
than in frictional electrical machines, and is insufficient to give any visible
spark. With De la Rue and Miiller's great battery the striking distance
between two terminals was found to increase with the potential, but for high
potentials rather more rapidly than in direct ratio. Thus while the striking
distance was o'oi2 in., with the potential due to 1,200 of their cells, it was
0-049 i"- with 4,800 cells, and 0-133 i"- "^^'ith 11,000 cells.

In the case of a small battery or of a single cell, very delicate tests are
required to detect any signs of free electrification. But by means of a deli-
cate condensing electroscope, and by extremely careful insulation, it can be
shown that one pole possesses a positive and the other a negative charge.
For this purpose one of the plates of the electroscope is connected with
one pole, and the other with the other pole or with the ground. The electro-
scope thus becomes charged, and on breaking the connection electroscopic
indications are observed.

On the other hand, the strength of current which a voltaic element can
produce in a good conductor is much greater than that which can be pro-
duced by a machine. Faraday immersed two wires — one of zinc, and the
other of platinum, each y^ of an inch in diameter — in acidulated water for ~
of a second. The effect thus produced on a magnetic needle in this short
time was greater than that produced by 23 turns of the large electrical
machine of the Royal Institution.

Nystrom has ascertained by quantitative measurements that the potential
of the charge of the cover of an ordinary electrophorus is not less than 50,000
times as great as the potential of a Meidinger's cell (812) ; that is, that not
less than 50,000 of those elements would be required to produce the same
potential as the electrophorus. In practice, a far greater number would be
needed, owing to the difficulty of getting good insulation.

816. Amalgamated zinc. I.ocal currents.— Perfectly pure distilled
zinc is not attacked by dilute sulphuric acid, but becomes so when immersed
in that liquid in contact with a plate of copper or of platinum. Ordinaiy
coinmercial zinc, on the contrary, is rapidly dissolved by dilute acid. This,
doubtless, arises from the impurity of the zinc, which always contains traces
either of iron or lead. Being electronegative towards zinc, they tend to pro-
duce local electrical currc?Jts, which accelerate the chemical action without
increasing the quantity of electricity in the connecting wire.

Zinc, when amalgamated, acquires the properties of perfectly pure zinc,
and is unaltered by dilute acid, so long as it is not in contact with a copper
or platinum plate immersed in the same liquid. To amalgamate a zinc plate,
it is first immersed in dilute sulphuric or hydrochloric acid so as to obtain a
clean surface, and then a drop of mercury is placed on the plate and spread
over it with a brush. The amalgamation takes place immediately, and the
plate has the brilliant aspect of mercury. Zinc as well as other metals are
readily amalgamated by dipping them in an amalgam of one part sodium
and 200 parts of mercury. Zinc plates may also be amalgamated by dipping
them in a solution of mercury prepared by dissohing one pound of mercury

-818] Bohncnberger's Electroscope. 789

in live pounds of aqua regia (one part of nitric to three of hydrochloric acid),
and then adding five parts more of hydrochloric acid.

The amalgamation of the zinc removes from its surface all the impurities,
especially the iron. The mercury effects a solution of pure zinc, which covers
the surface of the plate, as with a liquid layer. The process was first applied
to electrical batteries by Kemp. Amalgamated zinc is not attacked so long
as the circuit is not closed — that is, when there is no current ; when closed
the current is more regular, and at the same time stronger, for the same
quantity of metal dissolved.

817. Dry piles.— In dry piles the liquid is replaced by a solid hygrometric
substance, such as paper or leather. They are of various kinds ; in Zamboni's,
which is most extensively used, the electromotors are tin or silver, and bin-
oxide of manganese. To construct one of these a piece of paper silvered or
tinned on one side is taken ; the other side of the paper is coated with finely-
powdered binoxide of manganese by slightly moistening it, and rubbing the
powder on with a cork. Having placed together seven or eight of these
sheets, they are cut by means of a punch into discs an inch in diameter.
These discs are then arranged in the same order, so that the tin or silver of
each disc is in contact with the manganese of the next. Having piled up 1,200
or 1,800 couples, they are placed in a glass tube, which is provided with a
brass cap at each end. In each cap there is a rod and knob, by which the
leaves can be pressed together, so as to produce better contact. The knob
in contact with the manganese corresponds to the positive pole, while that
at the other end, which is in contact with the silver or tin, is the negative
pole.

Dry piles are remai'kable for the permanence of their action, which may
continue for several years. Their action depends greatly on the temperature
and on the hygrometric state of the air. It is stronger in summer than in
winter, and the action of a strong heat revives it when it appears extinct. A
Zamboni's pile of 2,000 couples gives neither shock nor spark, but can charge
a Leyden jar and other condensers. A certain time is, however, necessary',
for electricity only moves slowly in the interior.

Si 8. Bohnenbergrer's electroscope. — Bohnenberger constructed a dry-
pile electroscope of great delicacy. It is a condensing electroscope (fig. 716),
from the rod of which is suspended a single gold leaf. This is at an equal
distance from the opposite poles of two dry piles placed vertically, inside the
bell jar, on the plate of the apparatus. As soon as the gold leaf possesses
any free electricity it is attracted by one of the poles and repelled by the
other, and its electricity is obviously contrary to that of the pole towards
which it moves.

790 Dynamical Electricity. [819-

CHAPTER II.

DETECTION AND MEASUREMENT OF VOLTAIC CURRENTS.

819. Detection and measurement of voltaic currents. — The remark-
able phenomena of the voltaic battery may be classed under the heads phy-
siological, chemical, mechanical, and physical effects ; and these latter may
be again subdivided into the thermal, luminous, and magnetic effects. For
ascertaining the existence and measuring the strength of voltaic currents,
the magnetic effects are more suitable than any of the others, and, accord-
ingly, the fundamental magnetic phenomena will be described here, and the
description of the rest postponed to a special chapter on electro-magnetism.

820. Oersted's experiment. — Oersted published in 1 8 19 a discovery
which connected magnetism and electricity in a most intimate manner, and
became, in the hands of Ampere and of Faraday, the source of a new branch
of physics. The fact discovered by Oersted is the directive action which a
fixed current exerts at a distance on a magnetic needle.

To make this experiment a copper wire is suspended horizontally in the
direction of the magnetic meridian over
a movable magnetic needle, as repre-
sented in fig. 757. So long as the wire
is not traversed by a current, the needle
remains parallel to it ; but as soon as
the ends of the wire are respectively
connected with the poles of a battery
or of a single element, the needle is de-
flected, and te?tds to take a position
which is the more nearly at right angles
to the magnetic metidian in proportion
Fig- 757- as the current is stronger.

In reference to the direction in which the poles are deflected, there are
several cases which may, however, be referred to a single principle. Re-
membering our assumption as to the direction of the current in the con-
necting wire (803) the preceding experiment presents the following four
cases : —

i. If the current passes above the needle, and goes from south to north,
the north pole of the magnet is deflected towards the west ; this arrangement
is represented in the above figure.

ii. If the current passes below the needle, also from south to north, the
north pole is deflected towards the east.

iii. When the current passes above the needle, but from north to south,
the north pole is deflected towards the east.

-821]

Gahanovietcr or Multiplie

791

iv. Lastly, the deflection is towards the west when the current goes from
north to south below the needle.

Ampere has given the following mcinoria tccJuiica by which all the various
directions of the needle under the influence of a current may be remembered.
If we imagine an observer placed in the connecting wire in such a manner
that the current entering by his feet issues by his head, and that his face is
always turned towards the needle, we shall see that in the above four posi-
tions the north pole is always deflected towards the left of the observer. By
thus personifying the current, the different cases may be comprised in this
general principle : In the directive action of currents on magnets, the north
pole is always deflected towards the left of the current.

821. Galvanometer or multiplier. — The r\a.mQ galvattomcter, or some-
times iiiifltiplicr or rheoinetcr, is given to a very delicate apparatus by which
the existence, direction, and intensity of currents may be determined. It
was invented by Schweigger a short time after Oersted's discovery.

In order to understand its principle, let us suppose a magnetic needle
suspended by a filament of silk (fig. 758), and surrounded in the plane of the

t— -

■ — a

'^_

, — .

'I p

Fig- 758.

1,-'-^

^,,,— ^

^ f

^'' i

^-^■'^"

f^-^^

'I I'

Fig. 759.

magnetic meridian by a copper wire, mnopq, forming a complete circuit
round the needle in the direction of its length. When this wire is traversed
by a current, it follows, from what has been said in the previous paragraph,
that in every part of the circuit an observer lying in the wire in the direction
of the arrows, and looking at the needle ab^ would have his left always turned
towards the same point of the horizon, and consequently, that the action of
the current in every part would tend to turn the north pole in the same
direction ; that is to say, that the actions of the four branches of the circuit
concur to give the north pole the same direction. By coiling the copper
wire in the direction of the needle, as represented in the figure, the action
of the current has been multiplied. If, instead of a single one, there are
several circuits, provided they are insulated, the action becomes still more
multiplied, and the deflection of the needle increases. Nevertheless, the
action of the current cannot be multiplied indefinitely by increasing the
number of windings, for, as we shall presently see, the strength of a current
diminishes as the length of the circuit is increased.

As the directive action of the earth continually tends to keep the needle
in the magnetic meridian, and thus opposes the action of the current, the
effect of the latter is increased by using an astatic system of two needles,

792 Dynamical Electricity. [821-

as shown in fig. 759. The action of the earth on the needle is then very
feeble, and, further, the actions of the current on the two needles become
accumulated. In fact, the action of the circuit, from the direction of the
current indicated by the arrows, tends to deflect the north pole of the lower
needle towards the west. The upper needle a'b\ is subjected to the action
of two contrary currents, no and qp, but as the first is nearer, its action pre-
ponderates. Now this current passing below the needle, evidently tends to
turn the pole a' towards the east, and, consequently, the pole b' towards the
west ; that is to say, in the same direction as the pole a of the other needle.
From these principles it will be easy to understand the action of the
multiplier. The apparatus represented in fig. 760 consists of a thick copper

plate, D, resting on levelling
screws ; on this is a rotating
plate, P, of the same metal,
to which is fixed a copper
frame, the breadth of which
is almost equal to the length
of the needles. On this is
coiled a great number of
turns of wire covered with
silk. The two ends terminate
in binding screws, / and 0.
Above the frame is a gradu-
ated circle, C, with a central
slit parallel to the direction
in which the wire is coiled.
The zero corresponds to the
position of this slit, and there
are two graduations on the
scale, the one on the right
and the other on the left of
zero, but they only extend to
90°. By means of a very fine
filament of silk, an astatic
system is suspended ; it con-
sists of two needles ab and
a'b\ one above the scale,
and the other within the cir-
cuit itself. These needles,
which are joined together by a copper wire, like those in fig. 642 and fig.
759, and cannot move separately, must not have exactly the same magnetic
intensity ; for if they are exactly equal, every current, strong or weak, would
always put them at right angles with itself.

In using this instrument the diameter, to which corresponds the zero of
the graduation, is brought into the magnetic meridian by turning the plate
P until the end of the needle (xb corresponds to zero. The instrument is
fixed in this position by means of the screw-clanip T.

The length and diameter of the wire vary with the purpose for w hicli the
galvanometer is intcMulcd. l'"or one which is to be used in observing the

Fig. 760.

-821] Galvimonietcr or Multiplier. 793

currents due to chemical actions, a wire about \ millimetre in diameter, and
making- about Soo turns, is well adapted. Those for thermo-electric currents,
which have low intensity, require a thicker and shorter wire ; for example,
thirty turns of a wire | millimetre in diameter. For very deHcate experi-
ments, as in physiological investigations, galvanometers with as many as
30,000 turns have been used.

By means of a delicate galvanometer consisting of 2,000 or 3,000 turns
of fine wire, the coils of which are carefully insulated by means of silk and
shellac, currents of high potential, as those of the electrical machine (791)
may be shown. One end of the galvanometer is connected with the con-
ductor, and the other with the ground, and on working the machine the
needle is deflected, affording thus an illustration of the identity of statical
with dynamical electricity.

The deflection of the needle increases with the strength of the current ;
the relation between the two is, however, so complex, that it cannot well
be deduced from theoretical considerations, but requires to be determined
experimentally for each instrument. And in the majority of cases the in-
strument is used as a galvanoscope or rheoscope — that is, to ascertain the
presence and direction of currents — rather than as a galvanometer or rheo-
>neter in the strict sense ; that is, as a measurer of their intensity. The
term galvanometer is, however, commonly used.

The differential galvanometer consists of a needle, as in an ordinary
galvanometer, but round the frame of which are coiled two wires of the same
kind and dimensions, carefully insulated from each other, and provided with
suitable binding screws, so that separate currents can be passed through
each of them. If the currents are of the same strength but in different
directions, no deflection is produced ; where the needle is deflected one
of the currents differs from the other. Hence the apparatus is used to
ascertain a difference in strength of two currents, and to this it owes its
name.

When a current is passed through a galvanometer, the needle does not
usually at once attain its final position of equilibrium, but oscillates about
this position, which in observations causes much loss of time. If such a
needle is surrounded by a mass of a good conductor such as copper, currents
are induced in the mass which, as will afterwards be explained (905), impede,
or damp the motion of the magnetic needle and tend to bring it to rest.
Such an arrangement is called a da7nper., and in practice is frequently used ;
the copper frame on which the wires of the galvanometer are coiled, and
the wires themselves, act in this way. The natural logarithm of the ratio of
the amplitudes of two successive oscillations of the needle, is called the
logarithmic decrement. The logarithmic decrement X is proportional to
the product of the damping power e and the time of an oscillation / ; that
is, A = d. By diminishing the directive power of the earth on the magnet by
making it astatic, the logarithmic decrement becomes infinite, and the
needle attains its position of equilibrium without oscillations. Galvano-
meters in which the needle acquires at once this final deflection are known
as aperiodic, or dead-beat galvanometers.

To this class belong that of Deprez and D'Arsonval represented in fig.
761. Between the branches of a strong horse-shoe magnet is a light iron

794 Dynamical Electricity. [821-

cylinder supported independently, and which becomes magnetised by in-
duction. Between this and the magnet is a light rectangular wire coil,
supported by wires conveying the current which are in connection with
binding screws. When the current passes, the coil is deflected at right angles

to the field, and equilibrium
is established when the electro-
magnetic action is equalled by
the torsion of the wire. The
motion of the coil can be read
off by a spot of light reflected
from a mirror (822) attached to
it, and for small angles the cur-
rent is proportional to tangent
of the angle of deflection (823).
Induction currents due to the
motion of the coil in the field
are produced, and as this is very
powerful the galvanometer is
virtually dead-beat when closed
by a small resistance.

When a current of very small
duration is passed through a
galvanometer, a momentary de-
flection or switig or throw of the
needle will be produced. The

Fig. 761.

product of a constant into the sine of half the angle of the first swing is then
a measure of the strength of the current, so that if momentary currents of
different strengths are passed through one and the same galvanometer they
will be measured by the sines of the corresponding angles of deflection, or
by the angles themselves where these are small. This is known as the ballistic
7iietIiod of measuring currents, and the galvanometers adapted for the pur-
pose are known as ballistic galvatiometers.

822. Sir 'W. Thomson's marine gralvanometer. — In laying submarine
cables the want was felt of a galvanometer sufficiently sensitive to test insula-
tion, which at the same time was not affected by the pitching and rolling of the
ship. For this purpose, Sir W. Thomson invented his marine galvanometer.
B (fig. 762) represents a coil of many thousand turns of the finest copper wire,
carefully insulated throughout, terminating in the binding screws, EE. In
the centre of this coil is a slide, which carries the magnet, the arrangement of
which is represented on a larger scale in D. The magnet itself is made of a
piece of fine watch-spring about \ of an inch in length, and does not weigh
more than a grain ; it is attached to a small and very slightly concave mirror
of very thin silvered glass. A single fibre of silk is stretched across the slide,
and the mirror and magnet are attached to it in such a manner that the
fibre passes exactly through the centre of gravity in every position. As the
mirror and magnet weigh only a few grains, they retain their position rela-
tively to the instrument, however the ship may pitch and roll. The slide fits in
a groove in the coil, and the whole is enclosed within a wrought-iron case
with an aperture in front and a wrought-iron lid on the top. The eflfect of

Sir JJ^. TJiomsoiis Maritie Galvanometer.

795

-822]

this is to act as a viagnetic screen and thereby counteract the influence of
terrestrial magnetism when the ship changes its course.

Underneath the coil is a large bent steel magnet N, which compensates
the earth's directive action upon the magnet D (700) ; and in the side of the
case, and on a level with D, a pair of magnets, C, are placed with opposite
poles together. By a screw, suitably adjusted, the poles of the magnets may
be brought together ; in which case they quite neutralise each other, and thus
e.xert no action on the suspended magnet, or they may be slid apart from
each other in such a manner that the action of either pole on D prepon-
derates to any desired extent. This small magnet is thus capable of very
delicate adjustment. The large magnet N, and the pair of magnets, C, are
analogous to the coarse and fine adjustment of a microscope.

.At a distance of about three feet, there is a scale with the zero in the
centre and the graduation extending on each side. Underneath this zero

Fig. 762.

point is a narrow slit, through which passes the light of a paraffine lamp, and
which, traversing the window, is reflected from the bent mirror against the
graduated scale. By means of the adjusting magnets the image of the slit
is made to fall on the centre of the graduation.

This being the case, if any arrangement for producing a current, however
weak, be connected with the terminal, the spot of light is deflected either to
one side or the other, according to the direction of the current ; the stronger
the current the greater the deflection of the spot ; and if the current remains
of constant strength for any length of time, the spot is stationary in a cor-
responding position.

The movement, on a screen, of a spot of light reflected from a body, is the
most delicate and convenient means of observing motions which of them-
selves are too small for direct measurement or observation. Hence this
principle is frequently applied in experimental investigations and in lecture
illustrations (522). It is used in observing the motion of oscillating bodies,
in measuring the variations of magnetism, in determining the expansion of
solids, &c.

79<5

Dynamical Electricity.

[823-

It will be seen from the article on the Electric Telegraph, how alternate
deflections of the spot of light may be utilised in forming a code of signals.

823. Tang-ent compass, or tangent galvanometer. — When a magnetic
needle is suspended in the centre of a voltaic current in the plane of the
magnetic meridian, it can be proved that the strength of a current is directly

proportional to the tangent of the
angle of deflection, provided the
dimensions of the needle are suffi-
ciently small as compared with the
diameter of the circuit. An instru-
ment based on this principle is
called the tangetit galva7iometer or
tangeitt compass. It consists of a
copper ring, 12 inches in diameter
(fig. 763), and about an inch in
breadth, mounted vertically on a
stand ; the lower half of the ring is
generally fitted in a semicircular
frame of wood to keep it steady. In
the centre of the ring is suspended
a delicate magnetic needle, whose
length must not exceed ~ or i of
the diameter of the circle. Under-
'^' '' ^' neath the needle there is a graduated

circle. The ends of the ring are prolonged in copper wires, fitted with
mercury cups, ab., by which it can be connected with a battery or element.
The circle is placed in the plane of the magnetic meridian, and the deflection
of the needle is directly read off on the circle, and its corresponding value
obtained from a table of tangents.

On account of its small resistance, the tangent galvanometer is well
adapted for currents of low potential, but in which a considerable quantity
of electricity is set in motion.

To prove that the intensities of various currents are proportional to the
tangents of the corresponding angles of deflection, let NS, fig. 764, represent
the wire of the galvanometer and ns the needle, and let (^ be the angle of
deflection produced when a current C is passed. Two forces now act upon
the needle — the force of the earth's magnetism, which we will denote by H,
which tends to place the needle in the magnetic meridian, and the strength
of the current C, which strives to place it at right angles to the magnetic
meridian. Let the magnitudes of these forces be represented by the corre-
sponding lines a7t and bn. Now the whole intensities of these forces do not
act so as to turn the point of the needle round, but only those components
which are at right angles to the needle. Resolving them, we have ng and nf
as the forces acting in opposite directions on the needle ; and since the
needle is at rest these forces must be equal.

The angle nag is equal to the angle (/), and therefore ng=an sin </> ; and
in like manner the angle bfif is equal to (^ and nf^bn cos ^ ; and therefore

since ;//= ng^ bn cos <\i
C = H tan (/).

an sin 0, or bn = an

sm cj)
cos (j>

tan (j) ; that is.

-824] Tangent Galvanometer. 7g7

If any other current be passed through the galvanometer we shall ha\'e
sunilarly C'= H tan (/>' ; and shice the earth's magnetism does not appreci-
ably alter in one and the same place C : C' = tan </> : tan ^'.

In this reasoning it has been assumed that the action of the current on
the needle is the same whatever be the angle by which it is deflected. This
is only the case when the dimensions of the needle are
small compared with the diameter of the ring : it should
not be more than J or {-^ the diameter. In order to mea-
sure with accuracy the deflection a light index is placed
at right angles to the needle.

Wiedoiianns tangent galvanometer consists of a short
thick copper tube, in which is suspended, instead of a
needle, a thin piece of soft iron, silvered on one side so as
to act as a mirror, the position of which can be observed
by a microscope and scale (522). On each side of the
copper tube, and sliding in grooves, are coils of wire which
can be pushed over the tube. By this lateral arrangement
of the current in reference to the magnetic needle, the
error of the tangent galvanometer is diminished ; for
when the needle is deflected, though one end moves away Fig. 764.

from the current, the other approaches it.

In the tangent galvanometer of Helmholtz and of Gaugain the wires are
coiled on the surface of a cone the angle of which is 120°, and the point on
which the needle works is placed in the position of the corresponding apex
of the cone : the law of the tangent holds then even with longer needles, and
especially if the wire is divided between two such cones, one on opposite
sides of the needle.

If the ring of the tangent galvanometer is so constructed that it can turn
about its axis, which is in the magnetic meridian, the action of the current
on the needle is inversely proportional to the cosine of the angle (9, through
which the ring is turned. Hence by increasing (9, the action of any current
on the needle may be made as small as we please.

S24. Sine gralvanometer. — This is another form of galvanometer for
measuring powerful currents. Round the circular frame M (fig. 765), several
turns of stout insulated copper wire are coiled, the two ends of which, z,
terminate on the binding screws at E. On a table in the centre of the ring
there is a magnetic needle, m ; a second light needle, n, fixed to the first",
serves as pointer along the graduated circle N. Two copper wires, a^ b,
from the sources of electricity to be measured, are connected with E. The
circles M and N are supported on a foot O, which can move about a ver-
tical axis passing through the centre of a fixed horizontal circle H.

The circle M being then placed in the magnetic meridian, and therefore
in the same plane as the needle, the current is allowed to pass. The needle
being deflected, the circuit M is turned until it coincides with the vertical
plane passing through the magnetic needle m. The directive action of the
current is now exerted perpendicularly to the direction of the magnetic
needle, and it may be shown that the strength of the current is propor-
tional to the sine of the angle of deflection : this angle is measured on the
circle II by means of a vernier on the piece C. This piece C, fixed to the

798

Dynamical Electricity.

[824-

foot O, turns it by means of a knob A. This angle of deflection, and hence
its sine, being known, the intensity of the current may be thus deduced :
let mm' be the direction of the magnetic meridian, d the angle of deflection,
C the strength of the current, and H the directive action of the earth. If

the direction and intensity of
this latter force be represented
by ak, it may be replaced by
two components, ah and ac (fig.
766). Now, as the first has no
III . -''^^-^^-^■^■^^^^^^^^giJI^ directive action on the needle,

*'' ..*=:*-«®«*6te^^!!*^H\ tl^g component ac must alone

counterpoise the force C ; that
is, C = ac. But in the triangle
ack., ac = ak cos cak^ from which

S^«

Fig. 765

Fig. 766.

ac = H sin </, for the angle cak is the complement of the angle d, and ak is
equal to H ; hence, lastly, C = H sin d, which was to be proved. In like
manner for any other current C, which produces a deflection (/', we shall
have C = H sin d\ whence C : C' = sin ^ : sin d'.

825. Ohm's law. — For a knowledge of the conditions which regulate
the action of the voltaic current, science is indebted to the late G. S. Ohm.
His results were at first deduced from theoretical considerations ; but by
his own researches as well as by those of Fechncr, Pouillet, Daniell, De la
Rive, Wheatstone, and others, they received the fullest confirmation, and
their great theoretical and practical importance has been fully established.

i. The force or cause by which electricity is set in motion in the voltaic
circuit is called the electromotive force. The quantity of electricity which in
any unit of time flows through a section of the circuit is called the intensity^
or, perhaps better, ttie strefigth of the current. Ohm found that this strength
is the same in all parts of one and the same circuit, however heterogeneous
they were ; one and the same magnetic needle is deflected to the same
extent over whatever part of the circuit it is suspended ; and the same
voltameter, wherever interposed in the circuit, indicates the same disengage-
ment of gas ; he also found that the strength is proimrlional to the electro-
motive force.

-825] Ohm's Law. 799

It has further been found that when the current from the same element
is passed respectively through a short and through a long wire of the same
material, its action on the magnetic needle is less in the latter case than in
the former. Ohm accordingly supposed that in the latter case there was a
greater resistance to the passage of the current than in the former ; and he
proved that '■the resistance is inversely proportional to the strength of the
cun-ent.^

On tliese principles Ohm founded the celebrated law which bears his
name, that the strength of the current is equal to the electromotive force
divided by the resistance.

This is expressed by the simple formula

-^-

where C is the strength of the current, E the electromotive force, and R the
resistance.

ii. The resistance of a conductor depends on three elements ; its conduc-
tivity., which is a constant, determined for each conductor ; its section ; and
its length. The resistance is obviously 'nversely proportional to the conduc-
tivity ; that is, the less the conducting power, the greater the resistance. It
has been pro\-ed that the resistance is inversely as the section and directly
as the length of a conductor. If then k is the conductivity, w the section, and \
the length of a conductor, we have

RA , ^ E xtojE

■-= -and C = — = ^- ;

KU) A A

that is, the strength of a current is inversely proportional to the lotgth of the
conductor, and directly proportional to its section and conductivity.

iii. In a voltaic battery composed of different elements, the strength of
the current is equal to the sum of the electromotive forces of all the elements
divided by the sum of the resistances. Usually, however, a batteiy is com-
posed of elements of the same kind, each having, in intention at least, the
same electromotive force and the same resistance.

In an ordinary element there are essentially two resistances to be con-
sidered : I. That offered by the liquid conductor between the two plates,
which is frequently called the internal or essefttial resistance ; and 2. That
offered by the interpolar conductor which connects the two plates outside the
liquid ; this conductor may consist either wholly of metal, or may be partly of
metal and partly of liquids to be decomposed ; it is the external or non-essential
resistafice. Calling the former R and the latter r, Ohm's formula becomes

R + r

iv. If any number, ;/, of similar elements are joined together, there is //
times the electromotive force, but at the same time n times the internal

resistance, and the formula becomes -^ , If the resistance in the inter-

n\\ + r

polar, r, is very small — which is the case, for instance, when it is a short..

8oo Dynamical Electricity. [825-

thick copper wire — it may be neglected in comparison with the internal
resistance, and then we have

C - "^ - ^ ■
~ nR ~ R '

that is, a battery consisting of several elements produces in this case no
greater effect than a single element.

V. If, however, the external resistance is verj' great, as when the current
has to produce the electric light, or to work a long telegraphic circuit, advan-
tage is gained by using a large number of elements, for then we have the
formula

C - ^^
~nRV?'

If r is very great as compared with ;/R, the latter may be neglected, and the
expression becomes

that is, that the strength, within certain limits, is proportional to the number
of elements.

In a thermo-electric pile, which consists of very short metallic conductors,
the internal resistance R is so small that it may be neglected, and the
strength is inversely as the length of the connecting wire.

vi. If the plates of an element be made in times as large, there is no
increase in the electromotive force, for this depends solely on the nature
of the metals and of the liquid (802) ; but the resistance is vi times as small,
for the section is 711 times larger : the expression becomes then

„ _ E _ wE
~ R R-i- w;-'

+ ;-
m

Hence, an increase in the size of the plate — or, what is the same thing, a
decrease in the internal resistance — does not increase the strength to an
indefinite extent ; for ultimately the resistance of the element R vanishes in
comparison with the resistance r, and the strength continually approximates

to the value C = .
?•

vii. Ohm's law enables us to arrange a battery so as to obtain the greatest
effect in any given case. For instance, with a battery of six elements there
are the following four ways of arranging them : — i. In a single series (fig.
767), in which the zinc Z of one element is united with the copper C of the
second, the zinc of this with the copper of the third, and so on. 2. Arranged
in a system of three double elements, each element being formed by joining
two of the former (fig. 768). 3. In a system of two elements, each of which
consists of three of the original elements joined, so as to form one of triple
the surface (fig. 769). Lastly, of one large element, all the zincs and all the
coppers being joined, so as to form a pair of six times the surface (fig. 770).

With a series of twelve elements there maybe six different combinations,
and so on for a larger number.

-825] Ohm's Laiv. 80 r

Now let us suppose that in the particular case of a battery of six elements
the internal resistance R of each element is 3, and the external resistance
r=i2. Then in the first case where there are six elements arranged in
series we have the value

6R + r6x3+i2 30 ' ^ '

If they were united so as to form three elements, each of double the
surface as in the second case (fig. 768), the electromotive force would then

be the electromotive force in each element : there would also be a resistance
R in each element, but this would be only half as great, for the section of
the plate is now double ; hence the strength in this case would be

r'_ 3E^ _ 3E _6E.

-- + r
2

(2)

:th.

accordingly this change would lessen the stren;..

If, with the same elements, the resistance in the connecting wire were
only r = 2, we should have the values in the two cases respectively —
6xE 6E
20'

.3 F

C =

6x3 + 2

8o2 Dynamical Electricity. [825-

, „, 3E 6E 6E

andC =-^ =• = .

,3R^^ 9+12 13
2

The result in the latter case is, therefore, more favourable. If the re-
sistance r were 9, the strength would be the same in both cases. Hence,
then, by altering the size of the plates or their arrangement, favourable
or unfavourable results are obtained according to the relation between R
and r.

826. Arrang-ement of multiple battery for maximuin current. — It can
be shown that in any given co/nbination the viaxinium e^cct is obtainedwhen
the total resistance in the elements is equal to the resistance of the intcrpolar.
For let N be the total number of cells available for a given combination, and
let n be the number of cells arranged tandem., or in series — that is, when.
the zinc of one is connected with the copper of the next, and so on ; then

there will be elements arranged abreast. If e be the electromotive force
n

and r the resistance of one cell, while / is the external resistance, then the

strength of the current will be

C - ^'^ - '^^ - ^
~nr^~rri'r^fnrl
-^^ N-^^ n"^^
n

Therefore C is a maximum when .,7 + - is a minimum. But -7 x -

N n N n

= '' is a constant, therefore the sum ^+ is a minimum when ^^ = ;
N N « N ;/

that is, when'' ^^ = /, or when the total internal resistance is equal to the

external resistance.

For if X and — are any two quantities whose product is A-, then

A- ^ x"- + A- - 2kx + 2A.t-^ (.r- A)- ^ ^^

X X X

This is greater than 2A unless .t--A = o, in which case it is equal to 2A,and
is a minimum. In that case .i- = A, and therefore

It follows thus from the above formula that the best eftect is obtained

wheny;=^/-^_-.

If in a given case we have 8 elements, each oflcring a resistance 15, and
an interpolar with the resistance 40, we get n^^-^. But this is an im-
possil)le arrangement, for it is not a whole number, and the nearest whole
numljcr must be taken. This is 4 ; and it will be found, on making a calcu-
lalinn analogous to that above, that when arranged so as to form 4 elements,,
each of double surface, the greatest eftccl is obtained.

-826] Arrangement of JSIidlipk Battery. 803

The formula for the strength of current from several elements, C= -^-,

may also be applied to the currents produced l^y a magneto-electrical ma-
chine (920). In that case n stands for the number of coils which in a given
time cut the lines offeree of a magnetic field.

The principle that the best eftect is obtained when the total internal is
equal to the total external resistance, holds also for the currents produced by
these machines.

3F2

8o4 Dynamical Electricity. [827-

CH AFTER III.

EFFECTS OF THE CURRENT.

S27. Physlolog-ical actions. — Under this name are included the effects
produced by a battery current on living organisms or tissues.

When the electrodes of a battery of many cells are held in the two hands a
violent shock is felt, especially if the hands are moistened with acidulated
water, which increases the conductivity. The violence of the shock increases
with the number of elements used, and with a large number— as 200 Bunsen's
cells — is even dangerous.

The power of contracting upon the application of a voltaic current seems
to be a very general property oi protoplasiti — the physical basis of both
animal and vegetable life ; if, for example, a current of moderate strength be
passed through such a simple form of protoplasm as an amoeba, it imme-
diately withdraws its processes, ceases its changes of form, and contracts into
a rounded ball — soon, however, resuming its activity upon the cessation of
the current. Essentially similar effects of the current have been observed in
the protoplasm of young vegetable cells.

If a frog's fresh muscle (which will retain its vitality for a considerable
time after removal from the body of the animal) be introduced into a galvanic
circuit, no apparent effect will be observed during the steady passage of the
current, but every opening or closure of the circuit will cause a muscular
contraction, as will also any sudden and considerable alteration in its in-
tensity. By very rapidly interrupting the current, the muscle can be thrown
into a state of uninterrupted contraction, or physiological tetanus^ each new
contraction occurring before the previous one has passed off. Other things
being equal, the amount of shortening exhibited by the muscles increases,
up to a certain limit, with the intensity of the current. These phenomena
entirely disappear with the life of the muscle ; hence the experiments are
somewhat more difficult with warm-blooded animals, the vitality of whose
muscles, after exposure or removal from the body, is maintained with more
difficulty ; but the results of careful experiment are exactly the same here as
in the case of the frog.

The influence of an electric current upon living nerves is very remark-
able ; as a general rule, it may be stated that its effect is to throw the nerve
into a state of activity, whatever its special function may be : thus, if the
nerve be one going to a muscle, the latter will be caused to contract ; if it
be one of common sensation, pain will be produced ; if one of special sense,
the sensation of a flash of light, or of a taste, iSic, will be produced, accord-
ing to the nerve irritated. These effects do not manifest themselves during
the even passage of the current, Ijut only when the circuit is cither opened or

-828] Elect rotomts. 805

closed, or both. Of course the continuity of the nerve with the organ where
its activity manifests itself must be maintained intact. The changes set up
by the current in the different nerve-trunks are probably similar, the various
sensations, &c., produced depending on the difterent terminal organs with
which the nerves are connected.

Professor Burdon Sanderson has ascertained that the movement which
causes the Diomca musciptda (Venus's tly-trap), one of what are called car-
nivorous plants^ to close its hairy leaves ancl thereby entrap insects which
alight upon it, is accompanied by an electrical current in a manner analogous
to that manifested in muscular contraction. The manner in which the irrita-
tion is caused seems immaterial.

828. Slectrotonus. — In a living nerve, as will be stated more fully in
Chapter X., certain parts of the surface are electropositive to certain other
parts, so that if a pair of electrodes connected with a galvanometer be applied
to these two points, a current will be indicated ; if now another part of the
nerve be interposed in a galvanic circuit, it will be found that, if this extra-
neous current be passing in the same direction as the proper nerve-current,
the latter is increased, and vice versa ; and this although it has previously
been demonstrated experimentally that none of the battery current escapes
down the nerve, so as to exert any influence of its own on the galvanometer.
This alteration of its natural electromotive condition, produced through the
whole of a nerve by the passage of a constant current through part of it, is
known as the elcctrotonic state ; it is most intense near the extraneous, or, as
it is called, the exciting cicrrent. It continues as long as the latter is pass-
ing, and is attended with important changes in the excitability of the nerve,
or, m other words, the readiness with which the nerve is thrown into a state
of functional activity by any stimulus applied to it. Pfliiger, who has inves-
tigated these changes, has named the part of the nerve through which the
exciting current is passing the intrapolar region : the condition of the nerve
close to the positive pole is called aiielectrotonus ; that near the negative
pole, kathelcctrotoniis. The excitability of the nerve is diminished in the
anelectrotonic region, so that with a motor nerve, for example, a stronger
stimulus than before would need to be applied at this part in order to obtain
a muscular contraction ; in the kathelectrotonic region, on the contrary, the
excitability of the nerve is heightened. Moreover, with an exciting current
of moderate strength, the power of the nerve to conduct a stimulus is lowered
in the anelectrotonic region, and increased in the kathelectrotonic ; with
strong currents it is said to be diminished in both.

These facts have to be taken into account in the scientific application of
galvanism to medical purposes. If, for instance, it is wished to diminish the
excitability of the sensory nerves of any part of the body, the current should
be passed in such a direction as to throw the nerves of that part into a state
of anelectrotonus — and similarly in other cases.

If a powerful electric current be passed through the body of a recently
killed animal, violent movements are produced, as the muscles ordinarily
retain their vitality for a considerable time after general systematic death :
by this means, also, life has been re-established in animals which were appa-
rently dead — a properly applied current stimulating the respiratory muscles
to contract.

8o6

Dynamical Electricity.

[829-

S29. Heating: effects. — When a voltaic current is passed through a metal
wire the same effects are produced as by the discharge of an electric battery
(790) ; the wire becomes heated, and even incandescent if it is veiy short
and thin. With a powerful battery all metals are melted, even iridium and
platinum, the least fusible of metals. Carbon is the only element which has
not hitherto been fused by it. Despretz, however, with a battery composed
of 600 Bunsen's elements joined in six series (825), raised rods of very pure
carbon to such a temperature that they were softened and could be welded
together, yielding an incipient fusion.

A battery of 30 to 40 Bunsen's elements is sufficient to melt and volatilise
fine wires of lead, tin, zinc, copper, gold, silver, iron, and even platinum, with
differently coloured sparks. Iron and platinum burn with a brilliant white
light ; lead with a purple light ; the light of tin and of gold is bluish-white ;

the light of zinc
is a mixture of
white and gold ;
finally, copper
and silver give
a green light.

The thermal
effects of the
voltaic current
are used for
firing mines for
military pur-
poses and for
blasting opera-
tions. The fol-
lowing arrange-
ment was de-
vised by Colo-
nel Schaw, and
serves to illustrate the principle :— Fig. 771 represents a small wooden box
provided with a lid. Two moderately stout cojiper wires, bb\ insulated by
being covered with gutta-percha, are deprived of this coating at the ends,
which arc then passed through and through the box in the manner repre-
sented in the figure. The distance between them is f of an inch, and a very
fine platinum wire (one weighing 1-92 grain to the yard is the regulation
size) is soldered across. The object of arranging the wires in this manner
is that they shall not be in contact, and that the strain which they exert may
be spent on the box, and not on the jilatinum wire joining them, which,
being extremely thin, would be broken by even a very slight pull. Th.e box
is then filled with fine grained powder, and the lid tied down. The wires of
the fuse are then carefully joined to the long conducting wires which lead to
the battery : these should be of copper, and as thick as is convenient, so as
to offer very little resistance : No. 16 gauge copper wire is a suitable size.
The fuse is then introduced into the charge to be fired : if it is for a sub-
marine explosion the powder is contained in a canister, the neck of which,
after the introduction of the fuse, is carefully fastened by means of cement.

Fig. 771.

-830] Laws of Heating Effects. Galvanothennoinetcr. 807

When contact is made with the battery, which is effected throuj^h the inter-
vention of mercury cups, the current traversing the platinum wire renders it
incandescent, which fires the fuse ; and thus the ignition is communicated
to the charge in which it is placed.

The heating effect depends more on the size than on the number of the
plates of a battery, for the resistance in the connecting wires is small (825).
An iron wire may be melted by a single Wollaston's element, the zinc of
which is 8 inches by 6. Hare's battery (805) received its name deflagrator
on account of its greater heating effect, produced by the great surface of its
plates.

When any circuit is closed, a definite amount of heat, H, is produced
throughout the entire circuit ; and the amount of heat, h, produced in any
particular part of the circuit bears to the total heat, H, the same ratio which
the resistance, r, of this part bears to R, that of the entire circuit. Hence,
in firing mines, the wire to be hea'.ed should be of as small section and of as
small conductivity as practicable. These conditions are well satisfied by
platinum, which has over iron the advantage of being less brittle and of not
being liable to rust. Platinum too has a low specific heat, and is thus raised
to a higher temperature, by the same amount of heat, than a wire of greater
specific heat. On the other hand, the conducting wires should present as
small a resistance as possible, a condition satisfied by a stout copper wire ;
and again, as the heating effect of any circuit is proportional to the square
of the electromotive force, and inversely as the resistance, a battery with a
high electromotive force and small resistance, such as Grove's or Bunsen's,
should be selected.

Another application of the heating effect is to what are called safety catches.
These are lengths of lead wire or strips interposed in the circuit of the
powerful currents used for electrical lighting and the like. Their dimensions
are so calculated that when the current attains a certain strength, the heat
generated is sufficient to melt them and thus break the continuity of the
circuit. As this can be arranged with great accuracy, it is possible so to
regulate the circuit that it shall not exceed a certain limit.

By means of a heated platinum wire, parts of the body may be safely
cauterised which could not be got at by a red-hot iron ; the removal ot
tumours and the like may be effected by drawing a loop of cold platinum
wire round their base, which is then made hot by pressing the button of a
contact arrangement, and gradually pulled together. It has been observed
that when the temperature of the wire is about 600° C, the combustion of the
tissues is so complete that there is no haemorrhage; while at 1500° the action
of the wire is like that of a sharp knife. For other purposes of this galvajiic
cauterisaiioiiy platinum wire coiled in grooves cut in a porcelain rod is used.

830. Xiaws of heatlng^ effects. Calvanothermometer. — Although the
thermal effects are most obvious in the case of thin wires, they are by no
means limited to them. The laws of the heating effect were investigated by
Lenz, by means of an apparatus called the Galvanothcrmojiieter (fig. 772).
A wide-mouthed stoppered bottle was fixed upside down, with its stopper, b^
in a wooden box ; the stopper was perforated so as to give passage to two
thick platinum wires, connected at one end with binding screws, ss, while
their free ends were provided with platinum cones by which the wires under

8o8

Dynamical Electricity

[830-

investigation could be readily affixed ; the vessel contained alcohol, the tem-
perature of which was indicated by a thermometer fitted in a cork inserted
in a hole made in the bottom of the vessel. The current is passed through
the platinum wires, and its strength measured by means of a tangent
compass interposed in the circuit. By observing the increase of tempera-
ture in the thermometer in a given time, and
knowing the weight of the alcohol, the mass
of the wire, the specific heat, and the calori-
metric values (453) of the vessel, and of the
thermometer, compared with alcohol, the heat-
ing effect which is produced by the current in
a given time can be calculated.

By apparatus of this kind the truth of the
following law may be established.

Tlic heat disengaged in a given time, t, is
directly proportional to the square of the
stre?tgth of the current, and to the resistance.
This is known as Joule's law (831), and

is expressed in the formula H = C-R/ = -— -

= EC/. If the values E, C, R are expressed in
ergs, we get the value H in water-gramme de-
grees if we divide by the mechanical equivalent of a water-gramme degree,
that is by 4-16 x 10". If the values are expressed in practical units — volt,
ohm, ampere (964) — we get the value in the same unit by dividing by 10^. .

If the current passes through a chain of platinum and silver wire of equal
sizes, the platinum becomes more heated than the silver from its greater re-
sistance ; and with a suitable current the platinum may become incandescent
while the silver remains dark. This experiment was devised by Children.

If a long thin platinum wire be raised to dull redness by passing a voltaic
current through it, and if part of it be cooled down by ice, the resistance of
the cooled part is diminished, the strength of the current increases, and the
rest of the wire becomes brighter than before. If, on the contrary, a part
of the feebly incandescent wire be heated by a spirit-lamp, the resistance of
the heated part increases ; the effect is the same as that of introducing
fresh resistance, the strength of the current diminishes, and the wire ceases
to be incandescent in the non-heated part.

The cooling by the surrounding medium exercises an important influence
on the phenomenon of ignition. A round wire is more heated by the same
current than the same wire which has been beaten out flat : for the latter
with the same section pffers a greater surface to the cooling medium than the
other. For the same reason, when a wire is stretched in a glass tube on
which two brass caps are fitted airtight, and the wire is raised to dull in-
candescence by the passage of a current, the incandescence is more vivid
w hen the air has been pumped out of the tube, because it now simply loses
heat by radiation, and not by communication to the surrounding medium.

Similarly, a current which will melt a wire in air will only raise it to dull
redness in ether, and in oil or in water will not heat it to redness at all, for
the liquids conduct heat away more readily than air does.

-831J Relation of Heating Effect to IVor/c of a Battery. 809

From the above laws it follows that the heating effect is the same in awn-e
whatever be its length, provided the current is constant ; but it must be remem-
bered that by increasing the length of the wire we increase the resistance,
and consequently diminish the current ; further, in a long wire there is a
greater surface, and hence more heat is lost by radiation and by conduction.

It must be added that Joule's law only holds provided the current does
no external work, such as acting on adjacent conductors, or magnets — that,
in short, the thermal is the only action of the current.

831. Graphical representation of the heating: effects in a circuit. —
The law representing the production of heat in a circuit in the unit of time
is very well seen by the following geometrical construction, due to Professor
Foster.

The heat H produced in a circuit in the unit of time is proportional to
the square of the strength of the current C, and to the resistance R (830),

that is H = C-R ; but since C = ^ (825), we have H = "I'.
R -R

Draw a straight line DAB (fig. ITZ)-, and from any point A in it draw a
line AC, at right angles to DAB, and of a length proportional to the electro-
motive force of
the cell. Lay
off a length AB
proportional to
K "^..^^ the resistance

^"^-^..^^^ of the circuit.

^\ Join CB, and at

^""^ C draw a line

^"""--..^^^ at right angles

^ -^ ~ -^^ to BC, and let

Fig. 773. ^ I) l^e the point

where this line

cuts the line DAB. Then the length AD is proportional to the heat produced

in the whole circuit in unit time. For the triangles ADC and ACB are similar,

and therefore AD : AC = AC : AB ; that is, AD = ^^ ■ that is, H = ^\

AB R _

By drawing figures similar to the above it will be found that for a given
electromotive force the heat is inversely proportional to the resistance, and for
a given resistance directly proportional to the square of the electromotive
force. That is, if the resistance is doubled, the heat is reduced to one-half ; if
the electromotive force is doubled the heat is quadrupled.

S32. Relation of heating^ effect to work of a battery. — In every
closed circuit chemical action is continuously going on ; in ordinary cir-
cuits, the most common action is the solution of zinc in sulphuric acid, which
may be regarded as an oxidation of the zinc to form oxide of zinc, and
a combination of this oxide of zinc with sulphuric acid to form water and
zinc sulphate. It is a true combustion of zinc, and this combustion serves to
maintain all the actions which the circuit can produce, just as all the work
which a steam-engine can effect has its origin in the combustion of fuel (473).

By independent experiments it has been found that, when a given weight
of zinc is dissolved in sulphuric acid, a certain definite measurable quantity

8io Dynamical Electricity. [832-

of heat is produced, which, as in all cases of chemical action, is the same,
whatever be the rapidity with which this solution is effected. If this solution
takes place while the zinc is associated with another metal so as to form a
voltaic couple, the rapidity of the solution will be altered and the whole cir-
cuit will become heated — the liquid, the plates, the containing vessel as well
as the connecting wire. But although the distribution of the heat is thus
altered, its quantity is not. If the values of all the several heating effects in
the various parts of the circuit be determined, it will still be found that,
however the resistance of the connecting wire be varied, this sum is exactly
equivalent to that produced by the solution of a certain weight of zinc.

If the couple be made to do external mechanical work the case is dif-
ferent. Joule made the following remarkable experiment : — A small zinc
and copper couple was arranged in a calorimeter, and the amount of heat
determined while the couple was closed for a certain length of time by a
short thick wire. The couple still contained in the calorimeter was next
connected with a minute electromagnetic engine (899), by which a weight was
raised. It was thus found that the heat produced in the calorimeter in a
given time — while, therefore, a certain amount of zinc was dissolved — was
less while the couple was doing work than when it was not ; and the
amount of this diminution was the exact thermal equivalent of the work
performed in raising the weight (497).

That the whole of the chemical work and disengagement of heat in the
circuit of an ordinary cell has its origin in the solution of zinc in acid is con-
firmed by the following experiment, due to Favre : —

In the muffle of his calorimeter (456), five small zinc platinum elements
were introduced ; the other muffle contained a voltameter. Now when the
element was closed until one equivalent of zinc was dissolved in the whole of
the cells, \ of an equivalent of water should be decomposed in the voltameter
(846), which was found to be the case. In one case the current of the
battery was closed without inserting the voltameter, and the heat disengaged
during the solution of one equivalent of zinc was found to be 18,796 thermal
units ; when, however, the voltameter was introduced, the quantity disengaged
was only 1 1,769 thermal units. Now the diftcrence, 7,027, is represented by
the chemical work of decomposing \ of an equivalent of water : this agrees

very well with the number, 6,892 --^ 34>4_r.^ which represents the heat disen-
gaged during the formation of \ of an equivalent of water.

However complicated may be a voltaic combination the total heat pro-
duced in it is the sum of the quantities of heat which are produced and absorbed
in the various chemical processes which take place in it.

We may illustrate this important principle by reference to the element
of l)e la Rue and Muller (812), the chemical actions in which are perhaps
the simplest of all constant elements. The normal action is that, when the
clement is closed, zinc decomposes ammonium chloride with the formation
of zinc chloride, while the liberated ammonium unites with the chlorine of
the silver chloride, re-forming ammonium chloride and dcjxisiting silver.
The heat of decomposition and of re-formation of the ammonium chloride
compensate one another, and the net result is the formation of zinc chloride,
and the decomposition of silver chloride. Now the heat produced in the

-833] Ljcminoiis Effects. 8 1 1

formation of a molecule ot zinc chloride (ZnCl.,) is 112,840 gramme units,
and that of the equivalent silver chloride (2Ag CI) is 58,760. The difference
is 54,800, which is less than 58,360, the heat required to decompose a mole-
cule of water. Hence it is that one such element will not effect a continuous
decomposition of water, but at least two are required for the purpose. In
like manner the heat disposable in one Daniell's cell is represented by 47,300,
and accordingly at least two of these elements are also required.

In some cases, however, the current of a single cell does produce a feeble
but continuous decomposition of water. This arises from the fact that the
water of the voltameter contains air in solution, and the hydrogen as it is
liberated unites with the dissolved oxygen. This process is known as
electrolytic convection.

833. Xinmlnous effects. — Luminous effects are obtained when the battery
is sufficiently powerful, by bringing the two electrodes very nearly in contact ;
a succession of bright sparks springs sometimes across the interval, which
follow each other with such rapidity as to produce continuous light. Although
the quantity of electricity put in motion by the voltaic current is very great,
the distance across which the spark passes is very small. Jacobi found that
with a battery of 12 Grove's elements the electrodes could be approached
v.'ithin 0-0013 nim. before the spark passed.

When one terminal of a battery of a few elements is connected with a
pile, and an iron wire connected with the other is moved over the pile, a
stream of brilliant luminous sparks is obtained, which obviously arises from
a combustion.

The most beautiful effect of the electric light is obtained when two pencils
of charcoal are connected with the terminals of the battery in the manner
represented in fig. 774.
The charcoal b is fixed,
while the charcoal a can
be raised and lowered by
means of a rack and pinion
motion, c. The two char-
coals being placed in con-
tact, the current passes,
and their ends soon be-
come incandescent. If
they are then removed to
a distance of about the
tenth of an inch, accord-
ing to the strength of the
current, a luininous arc
extends between the two
points, which has an ex-
ceedingly brilliant lustre,
and is called the voltaic
arc. _ _

The length of this arc ^

varies with the force of '° ''"*"

the current. In air it may exceed 2;^inches, with a batteiy of 600 elements,

8i2 Dynamical Electricity. [833-

arranged in six series of loo each, provided the positive pole is uppermost,
as represented in the figure ; if it is undermost, the arc is about one-third
shorter. In a partial vacuum the distance of the charcoals may be greater
than in air ; in fact, as the electricity meets with no resistance, it springs
between the two charcoals, even before they are in contact. The voltaic arc
can also be produced in liquids, but it is then much shorter, and its brilliancy
is greatly diminished.

The voltaic arc has the property that it is attracted when a magnet is pre-
sented to it — a case of the action on magnets on currents (865).

The voltaic arc may be considered as formed of a very rapid succession
of bright sparks. Its colour and shape depend on the nature of the conduc-
tors between which it is formed, and it is probably due to the incandescent
particles of the conductor, which are volatilised and transported in the direc-
tion of the current ; that is, from the positive to the negative pole. The
more easily the electrodes are disintegrated by the current, the greater is
the distance at which the electrodes can be placed. Charcoal, which is a
very friable substance, is one of the bodies which give the largest luminous
arc.

Davy first made the experiment of the electric light, in 1801, by means of
a battery of 2,000 plates, each four inches square. He used charcoal points
made of light wood charcoal which had been heated to redness, and im-
mersed in a mercury bath ; the mercury penetrating into the pores of the
charcoal increased its conductivity. When any substance was introduced
into the voltaic arc produced by this battery, it became incandescent ; pla-
tinum melted like wax in the flame of a candle ; sapphire, magnesia, lime,
and most refractory substances were fused. Fragments of diamond, of
charcoal, and of graphite rapidly disappeared without undergoing any
previous fusion.

As charcoal rapidly burns in air, it was necessary to operate in vacuo,
and hence the experiment was for a long time made by fitting the two points
in an electric egg, like that represented in fig. 722. At present the electrodes
are made of gas graphite, a modification of charcoal deposited in gas retorts ;
this is hard and compact, and only burns slowly in air ; hence it is unneces-
sary to operate in vacuo. When the experiment is made in vacuo, there is
no combustion, but the charcoal wears away at the positive pole, while it is
somewhat increased on the negative pole, indicating that there is a transport
of solid matter from the positive to the negative pole.

It appears from the researches of Edlund that the disintegration of the
electrodes which takes place when the voltaic arc is formed gives rise to a
counter-electromotive force which is analogous to the polarisation which takes
place in the decomposition of water (806), and the existence of which can be
demonstrated by similar experiments. The magnitude of this force varies
with the nature of the electrodes ; it is greatest with carbon, amounting to
35 volts ; with iron it is 25 ; copper, 24 ; zinc, 19 ; and cadmium 10 volts.

The resistance of the arc itself, due to the medium, increases like other
resistances with the distance of the terminals ; it diminishes as the strength
of the current increases, for then the temperature increases. Working
with carbon electrodes, it was found to amount lo \T) ohm for each mm. of
distance.

-835] Regulator of the Electric Light. 813

This counter-electromotive force explains how it is that a continuous arc
can only be obtained with a current of considerable electromotive force.

834. Foucault's experiment. — This consists in projecting on a screen
the image of the charcoal points produced in the camera obscura at the
moment at which the electric light is formed (fig. 775). By means of this

Fig- 775.

experiment, which is made by the photo-electric microscope already de-
scribed (fig. 573), the two charcoals can be readily distinguished, and the
positive charcoal is seen to become somewhat hollow and diminished, while
the other increases. The globules represented on the two charcoals arise
from the fusion of a small quantity of silica contained in the charcoal. When
the current begins to pass, the negative charcoal first becomes luminous,
but the light of the positive charcoal is the brightest ; as it also wears away
about twice as rapidly as the negative electrode it ought to be rather the
larger.

835. Regrulator of the electric light. — When the electric light is to be
used for illumination, it must be as continuous as other modes of lighting.
For this purpose, not only must the current be constant, but the distance of
the charcoals must not alter, which necessitates the use of some arrange-
ment for bringing them nearer together in proportion as they wear away.
One of the best modes of effecting this is by an apparatus invented by
Duboscq.

In this regulator the two charcoals are movable, but with unequal veloci-
ties, which are virtually proportional to their waste. The motion is trans-
mitted by a drum placed on the axis xy (fig. 776). This turns, in the direc-
tion of the arrows, two wheels, a and b., the diameters of which are as i : 2,
and which respectively transmit their motion to two rackworks, C and C.
C lowers the positive charcoal, /, by means of a rod sliding in the tube
H, while the other C raises the negative charcoal, ;/, half as rapidly. By
means of the milled head y the drum can be wound up, and at the same
time the positive charcoal moved by the hand ; the milled head x moves the

8i4

Dynamical Electricity,

[835-

negative charcoal also by the hand, and independently^ of the first. For this
purpose the axis, xy^ consists of two parts pressing against each other with
some force, so that, holding the milled head x between the fingers, the other,
_y, may be moved, and by holding the latter the former can be moved. But
the friction is sufficient when the drum works to move the two wheels a and
h and the two rackworks.

The two charcoals being placed in contact, the current of a powerful
battery of 40 to 50 elements reaches the apparatus by means of the wires E
and E'. The current rising in H descends by the positive charcoal, then by
the negative charcoal, and reaches the apparatus • but without passing into
the rackwork C, or into the part on the right of the plate N ; these pieces

being insulated by ivory
discs placed at their lower
part. The current ultimately
reaches the bobbin B, which
forms the foot of the regu-
lator, and passes into the
wire E'. Inside the bobbin
is a bar of soft iron, which
is magnetised as long as the
current passes in the bobbin,
and demagnetised when it
does not pass, and this tem-
porary magnet is the regu-
lator. For this purpose it
acts attractively on an arma-
ture of soft iron. A, open in
the centre so as to allow the
rackwork C to pass, and
fixed at the end of a lever,
which works on two points,
;//;//, and transmits a slight
oscillation to a rod, d^ which,
by means of a catch, /, seizes
the wheel z, as is seen on a
larger scale in fig. il"]. By
an endless screw, and a series
of toothed wheels, the stop is
transmitted to the drum, and
the rackwork being fixed, the
same is the case with the
carbons. This is what takes
place so long as the mag-
netisation in the bobbin is
strong enough to keep down
the armature A ; but in pro-
])ortion as the carbons wear away, the current becomes feebler, though the
voltaic arc continues, so that ultimately the attraction of the magnet no
longer counterbalances a spring r, which continually tcinis to raise the arma-

FlR 776

-836]

Brozvnincc's Rcsrulator.

815

ture. It then ascends, the piece d disengages the stop z, the drum works,

and the carbons come nearer ; they do not, however, touch, because the

strength of the current gains the upper

hand, the armature A is attracted, and

the carbons remain fixed. As their

distance only varies within very narrow

Hmits, a regular and continuous light

is obtained with this apparatus until

the carbons are quite used.

By means of a regulator, Duboscq
illuminates the photogenic apparatus
represented in fig. 573, by which all
the optical experiments may be per-
formed for which sunlight was formerly
necessary.

836. Browning's reg'ulator. — -A
much simpler apparatus, represented
in fig. 778, has been devised by Brown-
ing, which is less costly than the other
lamps, and also requires a smaller
number of elements to work it. The
current enters the lamp by a wire at-
tached to a binding screw on the base
of the instrument, passing up the pillar _-__

by the small electro-magnet to the :i"lr^
centre pillar along the top of the hori- "— ==§
zontal bar, down the left-hand bar ~~

through the two carbons, and away by
a wire attached to a binding screw on

the left hand. A tube holding the upper carbon slides freely
up and down a tube at the end of the cross-piece, and would by
its own weight rest on the lower carbon, but the electromagnet
is provided with a keeper, to which is attached a rest that en-
circles the carbon tube and grasps it. When the electro-magnet
works and attracts the keeper, the rest tightens, and thereby
prevents the descent of the carbon. When the keeper is not
attracted the rest loosens, and the carbon-holder descends.

When the two carbons are at rest, on making contact with
a battery the current traverses both carbons and no light is
produced. But if the upper carbon be raised ever so little, a
brilliant light is emitted. When the lamp is thus once set to
work, the rod attached to the upper carbon may be let go, and
the magnet will afterwards keep the lamp at work. For when
some of the carbon is consumed, and the interval between the
two is too great for the current to pass, the magnet loses some
of its power, the keeper loosens its hold on the carbon, and this
descends by its own weight. When they are sufficiently near,
but before they are in contact, the current is re-established ;
the magnet again draws on the keeper, and the keeper again checks the

Fig. 77S.

i---i^-

Fig. 779.

8i6 Dynamical Electricity. [836-

descent of the carbon, and so forth. Thus the points are retained at the
right distances apart, and the hght is continuous and brilhant.

Stohrer has devised a regulator for the electrical light which is very
simple in principle, and which also only requires a few elements. Its essen-
tial features are represented in fig. 779, in which ^ is a cylinder containmg
vaseline and surrounded by the wire of the circuit _/I In this is a hollow
cylindrical floater a., nearly as wide as the vessel ; at its top is a copper
tube r, in which the carbon point d can be fixed. A stout copper wire fixed
to the bottom of the float dips in an iron tube filled with mercury, with
which is connected one pole of the battery ; the other pole is connected with
the carbon d\ which is supported in a suitable manner. The size of the float
is such that it moves slowly upwards, so that the carbon d presses with but
very slight force against d'. This can be regulated by placing small weights
in the collar on c. An insulated wire forming part of the circuit is coiled in
a spiral k round the cylinder, and aids the regulation.

837. Properties and intensity of the electric Ilgrht. — The electric
light has similar chemical properties to solar light ; it effects the combina-
tion of chlorine and hydrogen, acts chemically on chloride of silver, and
can be applied in photography, though not for taking portraits, as it fatigues
the sight too greatly.

Passed through a prism, the electric light, like that of the sun, is decom-
posed and gives a spectrum. WoUaston, and more especially Fraunhofer,
found that the spectrum of the electric light differs from that of other lights,
and of sunlight, by the presence of several very bright lines, as has been
already stated (578). Wheatstone was the first to observe that by using
•electrodes of different metals, the spectrum and the lines are modified.

Masson, who experimented upon the light of the electric machine, that of
voltaic arc, and that of Ruhmkorff's coil, found the same colours in the
•electric spectrum as in the solar spectrum, but traversed by very brilliant
luminous bands of the same shades as that of the colour in which they occur.
The number and position of these bands do not depend on the intensity of
the light, but, as we have seen (833), upon the substances between which
the voltaic arc is formed.

With carbon the lines are remarkable for their number and brilliancy ;
with zinc the spectrum is characterised by a very marked apple-green tint,
silver produces a very intense green ; with lead a violet tint predominates,
and so on with other metals.

Bunsen.in experimenting with 48 couples, and removing the charcoals to
a distance of a quarter of an inch, found that the intensity of the electric
light is equal to that of 572 candles.

Fizcau and Foucault compared the chemical effects of the solar and the
electric lights by investigating their action on iodised silver plates. Re-
jiresenting the intensity of the sun's light at midday at 1,000, these physicists
found that the light from a battery of 46 Bunsen's elements was 235, while
that from one of 80 elements was only 238. It follows that the intensity does
not increase to any material extent with the numl)er of the couples ; but ex-
])criment shows that it increases considerably with their surface. For with
a battery of 46 elements, each consisting of three elements, with their zinc
and copper respectively united so as to form one element of triple surface

-838J

Electric LigJiti7ig.

817

(82 5), the intensity was 385, the battery working for an hour ; that is to say,
more than a third of the intensity of the solar light.

Too great precautions cannot be taken against the effects of the electric
light when they attain a certain intensity. The light of 100 couples may
produce very painful affections of the eyes. With 600, a single moment's
exposure to the light is sufficient to produce very violent headaches and
pains in the eye, and the whole frame is affected as by a powerful sunstroke.

838. Electric llgrbtingr. — Great progress has of late been made in the
application of the electric light to purposes of ordinary illumination. This
progress has been mainly due to the improvements which have been made
in the means of generating electricity, for which some form of magneto or

Fig. 780.

Fig. 781.

dynamo-electrical machine (916), driven by steam or water power or by gas
engines (476), is used. So long as the electricity from the voltaic battery
was alone available for the production of the electric light, no great exten-
sion was possible, for the cost and inconvenience were far too great to
permit it to be used for anything more than lecture purposes and occasional
scenic illumination.

Veiy considerable improvements have also been made in the lamps, which
are ordinarily divided '\n\.o arc lamps, in which the light is produced between
carbon points automatically kept at a constant distance by the action of the
current itself, and incandescent lamps, in which the light is produced by the

3 O

8i8 Dynamical Electricity. [838-

incandescence of a thin continuous solid conductor. To this may be added
the electrical candles, of which the best known is \\\& JablochkoJ^ candle. It
consists (fig. 780) of two rods of gas carbon, a and b, from 2 to 4 mm. in
diameter, separated by a layer of kaolin or Chinese clay about 2 mm. thick,
fixed respectively in the supports, to which the positive and negative
electrodes A B are respectively attached. The rods are insulated from each
other by the whole being bound by some insulating material.

The current is started by a small piece of carbon, n, placed across the
top. As the arc passes, the kaolin melts away, and the arrangement may
therefore fitly be called a candle. The positive electrode wears away twice
as fast as the negative, which would soon destroy the arc, but by using alter-
nalin^ currents the unecjual waste of the carbons is prevented.

Fig. 775, which represents one of the forms of an arc lamp, may be taken
as an example of the manner in which the regulation of the arc is effected.

Regmc7^s electric lamp, fig. 781, consists of a rectangular copper rod, B,
moving in a copper tube A, guided by four pulleys, «, of which only two are
shown ; to B is fixed a cross-piece holding a thin carbon pencil, «, the lower
part of which passes through a silver guide, and its end presses, but not
quite over the centre, against a carbon disc, w, which moves about a hori-
zontal axis. The piece supporting this is insulated from A, but is connected
with the negative pole by a wire, b. The positive current, entering by A,
passes by C to a small block of carbon, o, which presses against the pencil.
Thus the current only passes through a very small portion of this pencil,
and it is this small portion which becomes incandescent and forms the arc.
The rod, as it burns away and sinks by its own weight, rotates the disc in
slowly, and prevents its being irregularly worn away.

When either of the carbon electrodes which produce the electric light is
increased in size its increase of temperature is lessened, while that of the
other is greater. When the negative electrode is large the light of the
positive electrode is very bright. This is seen in Werder mannas electric
lamp, which consists essentially of a carbon disc about 2 inches in diameter
and an inch in thickness, which is connected with the negative pole of the
battery ; the positive pole is a rod of carbon about 3 cm. in diameter, of any
suitable length ; it slides vertically in a copper tube, which serves both as a
guide and as a contact for it ; this is pressed upwards against the centre by
a weight passing over a pulley. The current can be passed abreast through
as many as ten of such lamps, though it seems that the total illuminating
power of this arrangement is not so great as when only two parallel lights
are employed.

The electrical arc has had a very useful application to the tcclding or
autogenous soldering of metals, that is to say, joining them without the use of
a solder ; a method which is of great service in the case of iron. The two
plates to be joined are placed in contact, and having been connected with
the negative pole, the positive carbon fixed in a suitable holder is held at
such distance that the arc passes, which then melts one plate on the other.
In other cases the two pieces of metal are pressed against each other, and
the current passed through the line of contact.

For these operations accumulators (849) are used charged by dynamos,
whi( li )ield very powerful currents ; by means of a commutator the electro-

-838]

Electric Lii'iitinc.

819

in \ciy wide

Fig. 782.

motive force and the strength of the current can be varied w i
limits at the will of the operator.

\'on Hefner's differential lamp is represented in fig. 782 ; the current
arriving by A divides at / (961) ; one portion passing through a fine wire
coil, R, offering a large resistance, and the other through a short thick coil r,
whence it passes to a lever which
turns about d ; to this is connected
at one end, w, a soft iron core which
plays in the two coils, and at the
other end is the positive carbon C,.

When the carbons are apart a
great resistance is presented, and
the current passes chiefly through
R, so that the core is drawn within
R, and the lever, and with it the
carbon C^ falls ; the fastening in the
holder is such that at a certain
angle the carbon C, slips in the
holder a, and, touching the lower
one, the current now passes by
rdQ^ C, B ; the iron core is then drawn down, but the holder a moves up,
grips the carbon, which it moves with it, and the arc is reproduced ; when
its normal length is attained its resistance increases to an amount such that
the currents passing through the two coils now balance themselves, and
their attraction on the iron being equal the core is stationary. Several such
lamps may be arranged in a circuit, and if one of them is extinguished it
does not affect the others.

Schwendler has devised a new unit of luminous intensity, which he
calls the platinum light standard, specially for use with the electric light.
It is the incandescence produced by a current of known strength passing-
through a U-shaped strip of platinum-foil 36-28 mm. in length, 2 mm. in
breadth, and 0-017 mm. in thickness. The circuit contains a rheostat and a
galvanometer, by which the constancy of the current can be ensured and
observed. When the strength of the current is constant the intensity of the
light, radiated by the platinum, is constant also, and fulfils all the conditions
of a standard measure of light, as it can always be reproduced in exactly the
same form from pure platinum.

The standard of light adopted by the International Congress of Electri-
cians in 1884 is the light emitted by a square centimetre of melted platinum
when on the point of solidifying.

According to Rosetti the temperature of the positive carbon is between
2400° and 3900° C. ; it is higher the smaller is the radiating surface. The
temperature of the negative electrode lies between 2138° and 2530°.

The resistance of the heated air in the arc is from i to 12 ohms (834).

Incandescent lamps, though not so economical as arc lights, lend them-
selves best to the distribution of the electric light. We have seen that when
a strong current of electricity is passed through a wire of small conductivity
(829), its temperature is raised to incandescence ; if the strength of the
current is increased, the brightness of the light increases, but in a greater

3 G 2

820

Dynavi ical Electricity

[838-

ratio than the strength of the current. Unfortunately, at such high tempera-
tures, wires even of the most difficultly fusible metals fuse or are disinte-
grated ; and the only material which does not fuse at the highest temperature
is carbon. The first lamps in which this was applied were constructed inde-
pendently by Edison in America and Swan in this country. Fig. 783 is a
representation oi Siuaiis lamp. Inside the globular glass \essel with a neck,
and fused to it, is a glass rod, through which pass two platinum wires, bent

outside in loops. These loops
can be easily fitted in the two
bent wires in the holder (fig.
784), which are in contact with
the binding screws, and thus
allow a current to be transmitted.
The spring wire exerts an up-
ward pressure, so as to always
ensure good contact. To the
other ends of the platinum are
fixed the characteristic part, the
carbon filament ; this is about
0-25 mm. in diameter, and is
bent in the form of a double loop.
It is prepared by immersing
crochet cotton in sulphuric acid
of a certain strength, by which
it is converted into what is

Fig. 783-

Fig. 784.

known as vegetable parchment. This is then carbonised by heating it to a
high temperature in closed vessels. Before sealing the bulb it is exhausted
of air by means of a Sprengel pump, and the vacuum is so perfect that elec-
tricity does not pass in it. The carbon of such a lamp, which is a thread
about 127 cm. in length, and 0-013 cm. in diameter, has a resistance of 143
ohms in its normal incandescence.

In Edison's lamp the carbon filament is made of a special kind of
bamboo carbonised at high temperatures in closed nickel moulds. In
the Maxim lamp, and in that of Lane Fox, the carbon filaments, after
being carbonised and mounted, are heated by the current itself in an atmo-
sphere of coal gas or the vapour of a hydrocarbon ; in this way carbon is
deposited on the filament, by which it is rendered more uniform and durable.

If we surround an electric light in one case by an opaque calorimeter,
which therefore absorbs the entire radiation, and then by a transparent one,
which allows the light to pass, it will be found that the luminous radiation
is about 10 per. cent, in the case of arc lamps and 5 in incandescent lamps.

The lighting power varies in different lamps according to the strength
of the currents. Edison's lamp, giving i6-candle power, requires a current of
0-6 amperes ; taking its resistance when hot at 170 ohms, the potential dif-
ference at the connections would be from Ohm's law (S25) o-6 x 170= 102
volts. For the same standard of light. Swan's lamp requires a current of
1-28 amperes, its resistance is 40, and hence the potential difference is 52
volts.

The electric effect \'A, dividctl by the liL;lu expressed in candles, gives

-839] Mechanical Effect of the Battery. 82 1

the electric effect required for one candle, and the number 746, divided by
the number thus obtained, gives the number of candles which can be obtained
from one electrical horse power. In the above cases these are 198 and 180
respectively. Lamps are usually classed according to the number of volts
they require. Whatever care may be exerted in their manufacture, the
carbons at last give way ; their life, however, ought to be from 1,000 to 2,000
hours.

839. Mechanical effects of the battery. — Under this head may be in-
cluded the motion of solids and liquids effected by the current. An example
of the former is found in the voltaic arc, in which there is a passage of the
molecules of carbon from the positive to the negative pole (834).

The mechanical action of the current may be shown by means of the
following experiment (fig. 785). A glass tube, AB, bent at the two ends, about
50 cm. in length and i cm. in diameter, is almost filled with dilute sulphuric
acid, and a globule of mercury, ;;/, is introduced. The whole is fixed in a
support, and the level of the tube can be adjusted by the screw n, the drop
of mercury itself serving as index.

When the two poles of a batteiy of 4 or 5 cells are introduced into the two
ends, the globule of mercuiy elongates and moves towards the negative pole
with a velocity which increases with the number of elements. With 24, a
long column of mercury can be moved through a tube a metre in length ;
with 50, the velocity is greater and the mercury divides into globules, all
moving in the same direc-
tion. If the direction of the
current is reversed, the mer-
cury first remains stationary,
and then moves in the oppo-
site direction.

If the tube is gently in-
clined towards the positive
pole, the mercury is still
moved with the current ; and
a moment is at length reached
at which there is equilibrium
between the force of the
current and the weight of the
mercury. The component of
this weight parallel to the plane may then be taken as representing the
mechanical action of the current which traverses the globule of mercury.

A similar phenomenon, known as electrical endosniose, is observed in the
following experiment, due to Porrett. Having divided a glass vessel into two
compartments by a porous diaphragm, he poured water into the two com-
partments to the same height, and immersed two platinum electrodes in
connection with a battery of 80 elements. As the water became decomposed,
part of the liquid was carried in the direction of the current through the
diaphragm, from the positive to the negative compartment, where the level
rose above that in the other compartment. A solution of copper sulphate is
best for these experiments, because then the disturbing influence of the dis-
engagement of gas at the negative electrode is avoided.

822 Dynmnical Electricity. [839-

A porous vessel is necessary, for otherwise the transport by the Hquid
would be at once hydrostatically equalised.

According to Zollner earth currents (894) are analogous to diaphragm
currents ; there are currents in the liquid mass in the interior of the earth, and
these currents coming in contact with the solidified masses produce electrical
currents.

The converse of these phenomena is observed when a liquid is forced
through a diaphragm by mechanical means. Such currents, which were dis-
covered by Quincke, are called diaphragm currents. A porous diaphragm,
p, is fixed in a glass tube (fig. 786), in which are also fused two platinum
wires terminating in platinum electrodes, a and b ; on forcing a liquid
through the diaphragm the existence of a current is evidenced by a galvano-
meter with which the wires are connected, the direction of which is that of
the flow of the liquid. The difference of potential due to this flow is pro-
portional to the pressure.

According to Zollner, all circulatory motions in liquids, especially when
they take place in partial contact with solids, are accompanied by electrical

currents, which have generally
the same direction as that in
which the current flows.

Wertheim found that the
elasticity of metal wires is di-
minished by the current, and
not by the heat alone, but by the electricity ; he has also found that the
cohesion is diminished by the passage of a current.

To the mechanical effects of the current may be assigned the sounds
produced in soft iron when submitted to the magnetising action of a discon-
tinuous current — a phenomenon which will be subsequently described.

840. Electrocapillary phenomena. — If a drop of mercury be placed in
dilute sulphuric acid containing a trace of chromic acid, and the end of a
bright iron wire be so fixed that it dips in the acid and just touches the edge
of the mercury, the latter begins a series of regular vibrations which may
last for hours. The explanation of this phenomenon, which was first ob-
served by Kiihne, is as follows : — When the iron first touches the mercury,
an iron-mercury couple is formed, in consequence of which the surface of the
mercury is polarised by the deposition of an invisible layer of hydrogen ;
this polarisation (806) increases the surface-tension of the mercury (138), it
becomes rounder, and contact with the iron is broken ; the chromic acid
present depolarises the mercury, its original shape is restored, the couple is
again formed, and the process repeats itself continuously.

Lippmann was led by the observation of this phenomenon to a series
of interesting experimental results, which have demonstrated a relation
between capillary and electrical phenomena. Of these results the most
important is the construction of a capillary electrometer.

A glass tube, A (fig. 787), is drawn out to a fine point, and is filled with

mercury : its lower end dips in a glass vessel, B, containing mercury at the

bottom and dilute sulphuric acid at the top. Platinum wires are fused in the

tubes A and B, and terminate in the binding screws a and b respectively.

Now at the beginning of the experiment, the i)osition of the mercury in the

-841]

Chemical Effects.

823

drawn-out tube is such that the capillary action due to the surface-tension
at the plane of separation of the mercury in the tube and the liquid is suffi-
cient to counterbalance the pressure of the column A. This position is
observed by means of a
microscope, the focus of
which is at the fiducial
mark on the glass at which
the mercurj' stops. If
now a difference of po-
tential be established, by
connecting the poles of
a cell with the wires a
and b, the surface-tension
is increased, the mercury
ascends in the capillary
tube, and in order to
bring the meniscus back
to its foriiier position the
pressure on A must be
increased. This is most
simply effected by means
of a thick caoutchouc
tube, T, connected with
the top of A, and with a
manometer, H ; and which
can be more or less com-
pressed by means of a
screw, E. The difference

Fig. 7S7.

in level of the two legs of the manometer is thus a measure of the increase
of the surface-tension, and therewith of the difference of potential. Lipp-
mann found, by special experiments, that this increase is almost directly
proportional to the electromotive force, up to about 0-9 of a Daniell's ele-
ment. Each electrometer requires a special table of graduation, but when
once this is constructed it can be directly used for determining electromotive
forces. It should not be used for greater electromotive forces than o-6 of a
Daniell ; but it can estimate the one-thousandth part of this quantity, and,
as its electrical capacity is very small, it can show rapid changes of potential,
which ordinary electrometers cannot do. For very small electromotive
forces, the pressure is kept constant, and the displacement of the meniscus
is measured by the microscope. Its use is especially convenient with zero
methods.

841. Cbemlcal eflfecta.^The first decomposition effected by electricity
was that of water, in 1800, by Carlisle and Nicholson, by means of a voltaic
pile. Water is rapidly decomposed by 4 or 5 Bunsen's cells ; the apparatus
(fig. 788) is convenient for the purpose. It consists of a glass vessel fixed on
a wooden base. In the bottom of the vessel two platinum electrodes,/ and
71, are fitted, communicating by means of copper wires with the binding
screws. The activity of these electrodes is increased by covering them with
a deposit of pulverulent platinum by electrolysis. The vessel is filled with

824

Dynamical Electricity.

[841-

water to which some sulphuric acid has been added to increase its conduc-
tivity, for pure water is a very imperfect conductor ; two glass tubes filled
with water are inverted over the electrodes, and on interposing the apparatus
in the circuit of a battery, decomposition is rapidly set up, and gas bubbles

rise from the surface of each pole.
The volume of gas liberated at the
negative pole is about double that
at the positive, and on examination
the former gas is found to be hy-
drogen and the latter gas oxygen.
This experiment accordingly gives
at once the qualitative and quanti-
tative analysis of water. The oxy-
gen thus obtained has the peculiar
and penetrating odour observed
when an electrical machine is
worked (793), and which is due to
ozone. The water contains at the
same time peroxide of hydrogen, in producing which some oxygen is con-
sumed. Moreover, oxygen is somewhat more soluble in water than hydrogen.
Owing to these causes the volume of oxygen is less than that required by the
composition of water, which is two volumes of hydrogen to one of oxygen.
Hence voltametric measurements are most exact when the hydrogen alone
is determined, and when this is liberated at the surface of a small electrode.
842. electrolysis. — The term electrolyte was applied to those substances
which, like water, are resolved into their elements by the voltaic current, by
Faraday, to whom the principal discoveries in this subject and the nomen-

clature are due. Electrolysis is the decomposition by the voltaic battery ;
the positive electrode, or that by which posili\c electricity enters, was by
Faraday called the a/iode, and the negative electrode the katliodc. The
|)roducts of decomposition are ions ; kation, that which appears at the
kathode ; and a/iio;i, that which appears at the anode.

By means of the battery, the compound nature of several substances
which had previously been considered as elements has been determined. By
means of a battery of 250 couples, Davy, shortly after the discovery of the
decomposition of water, succeeded in decomposing the alkalies potass and
soda, and proved that they were the oxides of the hitherto unknown metals

842]

Electrolysis.

825

potassium and sodium. The decomposition of potass may be demonstrated,
with the aid of a battery of 4 to 6 elements, in the following manner : a
small cavity is made in a piece of solid caustic potass, which is moistened,
and a drop of mercuiy placed in it (fig. 789). The potass is placed on a
piece of platinum connected with the positive pole of the battery. The
mercury is then touched with the negative pole. When the current passes,
the potass is decomposed, oxygen is liberated at the positive pole, while the
potassium liberated at the negative pole amalgamates with the mercury. On
distilling this amalgam out of contact with air, the mercury passes off,
leaving the potassium.

A very convenient arrangement for the preparation of metallic magnesium
and some of the rarer metals consists of an ordinary clay tobacco pipe (fig. 790),
in the stem of which an iron wire is inserted just extending to the bowl, which
is nearly filled with a mixture of the chlorides of potassium and magnesium.
This is melted by a Bunsen's burner, and a piece of graphite connected by a
wire with the positive pole of a battery is dipped in it, the wire in the stem
forming the negative pole. When the current passes, chlorine gas is libe-
rated at the positive pole, while metallic magnesium collects about the end
of the iron wire in the bowl.

The decomposition of binary compounds — that is, bodies containing two
elements — is quite analogous to that of water and of potass ; one of the
elements goes to the positive and the other to the negative pole. The bodies
separated at the positive pole are called electronegative elements, because at
the moment of separation they are considered to be charged with negative
electricity, while those separated at the negative pole are called electro-
positive elements. One and the same body may be
electronegative or electropositive, according to the
body with which it is associated. For instance,
sulphur is electronegative towards hydrogen, but
is electropositive towards oxygen. The various
elements may be arranged in such a series that any
one in combination is electronegative to any fol-
lowing, but electropositive towards all preceding
ones. This is called the electrochemical series, and
begins with oxygen as the most electronegative
element, terminating with potassium as the most
electropositive.

The decomposition of hydrochloric acid into its
constituents, chlorine and hydrogen, may be shown
by means of the apparatus represented in fig. 791.
Carbon electrodes must, however, be substituted for those of platinum,
which is attacked by the liberated chlorine : a quantity of common salt also
must be added to the hydrochloric acid, in order to diminish the solubility
of the liberated chlorine. The decomposition of potassium iodide may be
demonstrated by means of a single element. For this purpose a piece of
bibulous paper is soaked with a solution of starch, to which potassium
iodide has been added. On touching this paper with the electrodes, a blue
spot is produced at the positive pole, due to the action of the liberated iodine
on the starch.

826 Dynamical Electricity. [842-

One of the best methods of determining whether a body is, or is not, an
electrolyte, is to place it between the two platinum electrodes of a battery,
and then, disengaging the electrodes from the battery, connect it with a
galvanometer, and observe whether a reverse current, due to polarisation of
the electrodes (806), passes through the galvanometer. Such a current, being
due to the accumulation of different substances on the two electrodes, is a
proof that the substance has been electrolytically decomposed by the original
current from the battery. This method can often be applied when it is dif-
ficult, by direct chemical methods, to detect the presence of products of
decomposition at the electrodes.

843. Decomposition of salts. — Ternary salts in solution are decomposed
by the battery, and then present effects varying with the chemical affinities
and the intensity of the current. In all cases the acid, or the body which is
chemically equivalent to it, is electronegative in its action towards the other
constituent. The decomposition of salts may be readily shown by means of
the bent tube represented in fig. 791. This is nearly filled with a saturated
solution of a salt, say sodium sulphate, coloured with syrup of violets.
The platinum electrodes of a battery of four Bunsen's elements are then
placed in the two legs of the tube. After a few minutes the liquid in the
positive leg. A, becomes of a red, and that in the negative leg, B, of a green
colour, showing that the salt has been resolved into acid which has passed
to the positive, and into a base which has gone to the negative pole, for these
are the effects which a free acid and a free base respectively produce on
syrup of violets.

In a solution of copper sulphate, free acid and oxygen gas appear at the
positive electrode, and metallic copper is deposited at the negative electrode.
In like manner, with silver nitrate, metallic silver is deposited on the nega-
tive, while free acid and oxygen appear at the positive electrode.

This decomposition of salts was formerly explained by saying that the
acid was liberated at the positive electrode and the base at the negative. Thus
potassium sulphate, K,OS03, was considered to be resolved into sulphuric
acid, SO.,, and potash, K.,0. This view regarded salts composed of three
elements as different in their constitution from binary or haloid salts. Their
electrolytic deportment has led to a mode of regarding the constitution of
salts which brings all classes of them under one category. In potassium
sulphate, for instance, the electropositive element is potassium, while the
electronegative element is a complex of sulphur and oxygen, which is regarded
as a single group, SO,, and to which the name cjij-j'/^^/wi?/'/ may be assigned.
The formula of potassium sulphate would thus be K,,SO„ and its decom-
position would be quite analogous to that of potassium chloride, KCl,
lead chloride, PbCl^, potassium iodide, KI. The electronegati\c group
SO, corresponds to a molecule or two atoms of chlorine or iodine. In the
decomposition of potassium sulphate, the potassium liberated at the negative
pole decomposes water, forming potash and liberating hydrogen. In like
manner the electronegative constituent SO,, which cannot exist in the free
state, decomposes into oxygen g'as, which is liberated, and into anhydrous
sulphuric acid, SO3, which immediately combines with water to form ordi-
nary sulphuric acid, H.,S04. ^" ^'^^^^ where the action of the battery is
strong, these gases are liberated at the corresponding poles ; in other cases

-845] Grothilss's Hypothesis. 827

they combine in the Hquid itself, reproducing water. The constitution of
copper sulphate, CuSO^, and of silver nitrate, AgNOg, and their decom-
position, will be readily understood from these examples.

844. Transmissions efiTected by the current. — In chemical decompo-
sitions effected by the battery there is not merely a separation of the elements,
but a passage of the one to the positive and of the other to the negative
electrode. This phenomenon
was demonstrated by Davy by
means of several experiments,
of which the two following are
examples : —

i. He placed solution of so-
dium sulphate in two capsules
connected by a thread of as-
bestos moistened with the same
solution, and immersed the

positiv'-e electrode in one of the capsules, and the negative electrode in the
other. The salt was decomposed, and at the expiration of some time all the
sulphuric acid was found in the first capsule, and the soda in the second.

ii. Having taken three glasses. A, B, and C (fig 792), he poured into the
first solution of sodium sulphate, into the second dilute syrup of violets,
and into the third pure water, and connected them by moistened threads
of asbestos. The current was then passed in the direction from C to A.
The sulphate in the vessel A was decomposed, and in the course of time
there was nothing but soda in this glass, which formed the negative end,
while all the acid had been transported to the glass C, which was positive,
B containing only pure water. If, on the contrary, the current passed from
A to C, the soda w^as found in C, while all the acid remained in A ; but in
both cases the remarkable phenomenon was seen that the syrup of violets in
B neither became red nor green by the passage of the acid or base through
its mass, a phenomenon the explanation of which is based on the hypothesis
enunciated in the following paragraph.

845. Grottaiiss's liypotbesis. — Grothiiss has given the following expla-
nation of the chemical decompositions effected by the battery. Adopting the
hypothesis that in every binary compound, or body which acts as such, one
of the elements is electropositive, and the other electronegative, he assumes
that, under the influence of the contrary electricities of the electrodes, there
is effected, in the liquid in which they are immersed, a series of successive
decompositions and recompositions from one pole to the other, Hence it is
only the elements of the terminal molecules which do not recombine, but,
remaining free, appear at the electrodes. Water, for instance, is formed of
one atom of oxygen and two atoms of hydrogen ; the first gas being electro-
negative, the second electropositive. Hence when the liquid is traversed by
a sufficiently powerful current, the molecule a in contact with the positive
pole arranges itself as shown in fig. 793 — that is, the oxygen is attracted and
the hydrogen repelled. The oxygen of this molecule is then given off at the
positive electrode, the liberated hydrogen immediately unites with the oxygen
of the molecule b, the hydrogen of this with the oxygen of the molecule c,
and so on, to the negative electrode, where the last atoms of hydrogen

Fig. 793-

828 Dynamical Electricity. [845-

become free and appear on the poles. The same theory appHes to the
metallic oxides, to the acids and salts, and explains why in the experiment

mentioned in the preceding para-
graph the syrup of violets in the
vessel B becomes neither red nor
green. The reason why, in the
fundamental experiment, the hy-
' drogen is gi\en off at the negative
pole when the circuit is closed will
be readily understood from a consideration of this hypothesis.

Clausius objected that, according to this theory, a very great force must
be required for overcoming the affinity for each other of the oppositely
electrolysed particles of the compound ; and that below a certain minimum
strength of current no decomposition could occur. Now Buff has shown that
the action of even the feeblest currents continued for a long time can pro-
duce decomposition. Again, when the necessary strength of the current is
obtained, it should be sudden and complete ; whereas we know it to be pro-
portional to the strength of the current.

To overcome this difficulty Clausius applies the theory now generally
admitted of the constitution of liquids (292). The particles of a compound
liquid have not the rigid unalterable condition of a solid body ; they are in a
perpetual state of separation and reunion, so that we must suppose compound
bodies and their elementary constituents to coexist with each other in a liquid.
Water, for instance, contains particles of water, together with particles of
oxygen and of hydrogen ; the former are being continually decomposed and
the latter continually reunited. When the voltaic current passes, it acts on
the motion of the molecules in such a manner that the negatively electrical
particles of oxygen pass to the positive electrode, and the positive electrical
particles of hydrogen to the negative electrode, and so prevents their re-
combination. Hence the current does not bring about the decomposition,
but utilises it, to give definite direction to the particles which arc already,
separated.

These considerations explain why the conductivity of a liquid increases
with the temperature (95S) ; for the velocity of the molecules (294) and the
number of the partial molecules are thereby increased. It also shows that the
conductivity should increase with the concentration of the liquid, seeing that
a great number of decomposable molecules must be favoural^le to the move-
ment of electricity. On the other hand, an increase in the number must
be owing to the increased number of collisions ; hence it is that, though
the conductivity increases with the concentration, it does so more slowly
than in direct ratio, and it is not diftlcult to understand that for some liquids
a maximum concentration corresponds to a maximum conductivity.

This also explains why solid chemical compounds, such as water and pure
acids, which within the ordinary range of temperatures are not subject to
dissociation (389), are not electrolysed, and therefore not decomposed, while
mixtures of acids and water, and solutions of salts, which may be regarded
as chemical compounds in a slate of dissociation, are easily electrolysed
and conduct well.

In dealing with iiiolccular maj^nitudcs, theoretical investigations make it

-846J Laivs of Electrolysis. 829

probable that the electrolytic resistance, which the molecules experience in
their being moved by the current, is of the same order of magnitude as the
capillary resistance which results from their friction in the liquid (147).
Nothing is opposed to the idea that electrolysis is a purely mechanical pro-
cess. Decomposition occurs in the first place by dissociation ; the differ-
ence of potential is the force in virtue of which the previously united mole-
cules are urged in contrary directions. The moving molecules are the
carriers of the motion of electricity and produce the current ; the resistance
which they thereby experience is the electrical resistance of the liquid. This,
therefore, is the cause of the development of heat in the circuit.

846. Xiaws of electrolysis. — The laws of electrolysis were discovered
by Faraday ; the most important of them are as follows : —

I. Elecfrolysis cantiot take place unless the electrolyte is a co7iductor.
Hence ice is not decomposed by the battery, because it is a bad conductor.
Other bodies, such as lead oxide, silver chloride, &c., are only electrolysed
in a fused state — that is, when they can conduct the current. The converse
of this is true ; if a liquid transmits a current it must be an electrolyte. From
the fact that he was able to obtain a current in liquids which deflected a
galvanometer without producing any visible decomposition, Faraday inferred
that liquids had a slight conductivity like that of metals independently of
their electrolytic conductivity. This apparent conductivity is however to be
assigned to electrical convectioji (832).

II. The energy of the electrolytic action of the current is the same in all
its parts.

For if a number of voltameters V, V, V" {vide st/p.), are arranged in
series so that they are all traversed by the same current (fig. 794), it is found
that the weight of hy-
drogen in each of them
in the same time is the
same, whatever may be
the nature and distance
of the electrodes, the
proportion and nature of
the acid.

If the current from the battery divides at A into two branches (fig. 795),
in which are two equal voltameters Vj and ¥„, then the quantities of gas
liberated in V and V"
will still be equal to each
other ; and the quantities
in Vj and Vn will be equal
to each other, but each
will only have half the
quantity which passes in
either of the voltameters V and V".

III. The same quantity of electricity — that is, the same electric current —
decomposes chemically equivalent quantities of all the bodies which it tra-
verses ; from which it follows, that the weights of elements separated in these
electrolytes are to each other as their cJiemical equivale7its.

In a circuit containing a voltameter, V, Faraday introduced a tube, AB,

830

D vnaiii ical Electric it j '.

[846

containing tin chloride kept in a state of fusion by the Jieat of a spirit
lamp (fig. 796). In the bottom of this the negative pole was fused, while the
positive electrode consisted of a rod of a graphite ; when the current passed
chlorine was liberated at the positive, while tin collected at the negative
pole ; in like manner lead oxide was electrolysed and yielded lead at the
negative and oxygen at the positive pole. Comparing the quantities of
substances liberated, they are found to be in a certain definite relation.

Fig. 796.

Thus for every 18 parts of water decomposed in the voltameter there will
be liberated 2 parts of hydrogen, 207 parts of lead, and 117 of tin at the
respective negative electrodes, and 16 parts of oxygen and 71 (or 2 x 35-5)
parts of chlorine at the corresponding positive electrodes. Now these num-
bers are exactly as the equivalents (not as the atomic weights) of the bodies.

It will further be found that in each of
the cells of the battery 65 parts by weight
of zinc have been dissolved for every two
parts by weight of hydrogen liberated ;
that is, that for every equivalent of a sub-
stance decomposed in the circuit one equi-
valent of zinc is dissolved. This is the
case whatever be the number of cells. An
increase in the number only has the effect
of overcoming the great resistance which
many electrolytes offer, and of accelerating
the decomposition. It does not increase
the quantity of electrolyte decomposed. If
in any of the cells more than 65 parts of
zinc arc dissolved for every two parts of
hydrogen liberated, this arises from a dis-
advantageous local action ; and the more
perfect the battery, the more nearly does
it approach this ratio.
Kiy. 7yj,_ Chemistry takes account of the valency

of an element, and divides them into
vi07iads^ dyads, triads, and tetrads — a classification based on their equiva-
lence to and their power of replacing other elements ; thus one atom of the

-846]

Silver Voltameter.

831

monad hydrogen (H = i), the basis of this classification, or one atom of
silver (Ag= 108), would combine with one atom of chlorine (€1 = 35-5) oi' one
atom of iodine (I = 127). One atom of oxygen (O = 16) unites with two atoms
of hydrogen to form water, or with two atoms of silver to form silver oxide ;
one atom of the dyad zinc (Zn = 65) unites with one atom of the dyad oxygen or
of the dyad sulphur (S = 32). Again, gold is a triad, and one atom (Au = 196)
can combine with three atoms of chlorine, and, accordingly, one monad is
equivalent to one-third of the atom of the triad. Now electrolysis proceeds
according to the equivalence ; that is, the same quality of electricity which
liberates one atom of a monad liberates half a one of a dyad, and a third of
a triad. This remark applies to the compound groups such as NO3, which
is a monad, and SO.,, which is a dyad.

IV. It follows from the above law, that the quantity of a body decomposea
in a given time is proportional to tJie strength of the ciin'ent. On this is
founded the use of Faraday's voltameter^ in which the intensity of a current
is ascertained from the quantity of water which it decomposes in a given time.

A convenient form of this instrument is that represented in fig. 797. The
vessel a is that in which the water is decomposed, and contains two platinum
plates, and is in connection with the flask b, which contains water. In this
is a lateral dehvery tube, c, which is inclined until the level of the liquid in
it is the same as in the funnel tube n. The air is then under the same pres-
sure as the atmosphere. When the battery is connected with the decom-
posing cell a, the gases disengaged expel a corresponding volume of water
through the delivery tube c ; at the conclusion of the experiment, this tube
is inclined until the liquid is at the same level as in the tube n and in the
flask. The weight of the liquid expelled
is then a direct measure of the volume of
the disengaged gases.

The use of this voltameter appears
simple and convenient ; and hence some
physicists have proposed as unit of the
strength of current, that current which
in one viitiute yields a cubic centimetre of
mixed gas reduced to the temperature 0°
and the pressure 760 mm. This isfacobPs
unit. It is equal to 0-09567 ampere. Yet,
for reasons mentioned before (841), the
measurements should be based on the
volume of hydrogen liberated.

Poggendorft's silver voltai/ieter, fig.
798, is an instrument for measuring the
strength of the current. A solution of
silver nitrate of known strength is placed
in a platinum dish which rests on a brass -^
plate that can be connected with the
negati\e pole of the battery by means of
the binding screw b. In this solution ^'^' ^'^^'

dips the positive pole, which consists of a rod of silver wrapped round with
muslin, and suspended to an adjustable support. When the current passes.

832 Dynavtical Electricity. [846-

silver separates at the negative pole, and is washed, dried, and weighed ;
and the weii^dit thus produced in a given time is a very accurate measure
of the strength of the current. Some silver particles which are apt to
become detached from the positive pole are retained in the muslin.

It has been found by experiment that, when water is decomposed, a
current of i ampere liberates 0-000010386 gramme or o-ii68 cc. of hydrogen
in a second; this, then, is the electrochemical equivalent of hydrogefi^ and
from this we can deduce the weight of any element liberated in the same
time by unit current, if we multiply it by the equivalent weight of the element
referred to hydrogen. The equivalent of silver is usually taken at 108 ;
hence, if any of its salts are decomposed, the weight of silver liberated by
an ampere in a second is 0-0011217 gramme ; this is the electrochemical
equivalent of silver, and similarly that of copper is 0-0003281.

The quantity of electricity which passes through a conductor with a
current of one ampere is called a coulomb {!]Z'S)i ^.nd thus we may say that a
coulomb of electricity, in traversing an electrolyte, carries with it a weight
of a metal which is represented by its electrochemical equivalent.

The current from the electrical machine, which is of very high potential,
is capable of traversing any electrolyte, but the quantity which it can decom-
pose is extremely small as compared with even the smallest voltaic apparatus,
and the quantity of electricity developed by the frictional machine is very
small as compared with that developed by chemical action. It has been
calculated by Weber that if the quantity of positive electricity required to
decompose a grain of water were accumulated on a cloud at a distance of
3,000 feet from the earth's surface, it would exert an attractive force upon
the earth of upwards of 1,500 tons.

846^;. IWigration of the Ions. — From what has been said, it would seem
that when a solution of copper sulphate is electrolysed between copper elec-
trodes, for every equivalent of copper deposited at the negative electrode
an equivalent weight should be dissolved at the positive, and, the transfer
taking place as described, the concentration of the solution should remain
unchanged. This, however, is not the case ; when the operation takes
place without any agitation of the solution, the liquid about the negative
pole becomes lighter in colour, indicating that the solution there is weaker.

This phenomenon, which was investigated by Hittorf, is ascribed by him
to the fact that in electrolysis both electricities, together with their ions or
products of electrolytical decomposition, travel in the liquid towards their
respective electrodes, but with unequal velocities, and this transference is
called the migration of the ions. Each ion has a special velocity in the liquid
independently of the compound of which it forms part ; thus in the same
time S04 travels twice as fast as Cu.

The number which expresses this rate of travel is called «, and has this
meaning : let us conceive a vertical layer in the liquid the concentration of
which remains unchanged by what takes place on each side ; then, if after
electrolysis we determine the quantity of the constituents on each side, there
is an increase of the positive on one side and of the negative on the other.
These increases correspond to the iiuantitics of the two constituents which
have been driven through.

The number // expresses the ratio of the luunber of molecules of the

-847]

Tangent Galvanometer and Voltameter.

anion which passes through the imaginary layer in a given time to that of
the electrolyte decomposed.

If X- is the velocity of the kation, and a that of the anion, then
a . k \ -n k

k + a

Hittorfif has shown that n is a constant independent of the strength of the
current, but which varies with the concentration of the licjuid.

S47. Comparison between tbe tangent gralvanometer and the volta-
xneter. — There are several objections to the use of the voltameter. In the
first place, it does not indicate the strength at any given moment, for in order
to obtain measurable quantities of gas the current must be continued for some
time. Again, the voltameter gives no indications of the changes which take
place in this time, but only the mean intensity. It offers also great resistance,
and can thus only be used in the case of strong currents ; for weak currents
either do not decompose water, or only yield quantities too small for accurate
measurement. In addition to this, the indications of the voltameter depend
not only on the strength of the current, but on the acidity of the water, and
on the distance and size of the electrodes. But although it does not measure
the strength of the current at any one time, it does, apart from accidental
influences, give a measure of the total quantity of electricity that has passed
within the period of observation.

The magnetic measurements are preferable to the chemical ones. Not
only are they more delicate and offer less resistance, but they give the
strength at any moment. On the other hand, indications furnished by the
tangent galvanometer hold only for one special instrument. They vary
with the diameter of the ring and the number of turns ; moreover, one
and the same instrument will give different indications on different places,
seeing that the force of the earth's magnetism varies from one place to
another (701).

The indications of the two instruments may, however, be readily com-
pared with one another. For this purpose the voltameter and the tangent
galvanometer are simultaneously inserted in the circuit of a battery, and the
deflection of the needle and the amount of gas liberated in a given time are
noted. In one set of experiments the following results were obtained : —

Number of elements

Deflection

Gas liberated in three minutes

28-5°

125 cc.

24-8

106

22-0

1375

6-9

If we divide the tangents of the angles into the corresponding volumes of
gas liberated in one minute, we should obtain a constant magnitude which
represents how much gas is developed in a minute by a current which could
produce on the tangent galvanometer the deflection 45°, for tang. 45° = i.
Making this calculation with the above obsei-vations, we obtain a set of
closely agreeing numbers the mean of which is 76-5. The gas was measured

834 Dy}iamical Electricity. [847-

under a pressure of "jy] mm. and at a temperature of 15°, and therefore
under normal conditions (332) its volume would be 70 cubic centimetres.
That is to say, this is the volume of gas which corresponds to a deflection
of 45°. Hence in chemical measure the strength C of a current which pro-
duces in this particular tangent galvanometer a deflectron of ^° is

C = 70 tang. 0.

For instance, supposing a current produced in this tangent galvanometer
a deflection of 54°, this current, if it passed through a voltameter, would
liberate in a minute 70 x tang. 54° = 7ox 1*376 = 96*32 cubic centimetres of
^as.

If once the reduction factor for a tangent galvanometer has been deter-
mined, the strength of any current may be readily calculated in chemical
measure by a simple reading of the angle of deflection. This reduction factor
of course only holds for one special instrument, and for experiments in the
same place, seeing that the force of the earth's magnetism varies in different
places.

The indications of the sine-compass may be compared with those of the
galvanometer in a similar manner.

848. Polarisation. — When the platinum electrodes, which have been
used in decomposing water, are disconnected from the battery, and connected
with a galvanometer, the existence of a current is indicated which has the
opposite direction to that which had previously passed. This phenomenon
is explained by the fact that oxygen has been condensed on the surface of the
positive plate, and hydrogen on the surface of the negative plate, analogous
to what has been already seen in the case of the nonconstant batteries (806).
The effect of this is to produce two different electromotors, which produce a
current opposed in direction to the original one, and which, therefore, must
weaken it. As the two electrodes thus become the poles of a new current,
they are said to \>q. polarised.,7\x\^ the current is called 2l polarisation current.
The polarisation is not instantaneous, but may increase continuously from
zero to a certain maximum limit which may be considerable ; it increases
with the strength of the current, attaining the force of 2*6 volts with platinum
plates in dilute sulphuric acid. It constitutes a negative electromotive force,
and must be allowed for in* Ohm's formula.

The quantity of electricity required to produce a given state of polarisa-
tion depends on the condition and dimensions of the plate, and is often
called the capacity oj polar isatioti relative to the gi\-en system.

849. Secondary batteries. Accumulators. — Ritter was the first to show
that on this principle batteries might l)e constructed of pieces of metal of
the same kind — for instance, platinum — which otherwise give no current.
A piece of moistened cloth is interposed between each pair, and each end of
this system is connected with the poles of a battery. After some time the
apparatus has received a charge, and if separated from the battery can itself
produce all the effects of a voltaic battery. Such batteries are called second-
ary batteries or, also, accumulators. Their action depends on an alteration
of the surface of the metal produced by the electric current, the constituents
of the liquid with which the cloth is moistened having become accumulated
on the opposite plates of the circuit.

-849]

Secondary Batteries.

835

Fig. 799.

Plante first showed the practical importance of these batteries. His ele-
ment (fig. 799) is constructed as follows : A broad strip of sheet lead with a
tongue is laid upon a second
similar sheet, contact being
prevented by narrow strips
of felt ; and two similar
strips having been laid on
the upper piece, the sheets
are rolled together so as to
form a compact cylinder.
This is placed in a vessel
containing dilute sulphuric
acid, and, being connected
by wires attached to the
tongues with a battery of two Grove's cells, a current is passed through it.
The effect of this is that water is decomposed, oxygen being liberated at
the anode, or plate, which serves as positive pole, and there unites with
the lead, forming peroxide of lead, while hydrogen is accumulated at the
other plate. If now the plates are detached from the charging battery and
are connected with each other, a powerful polarisation current is produced
in the opposite direction to the primary ; the oxygen of the peroxide at the
anode decomposes the dilute acid, combining with its hydrogen, and so
travels through to the other plate, where it combines with the lead. When
these operations are repeated several times the activity of the element in-
creases, owing in great measure to the alteration in the surfaces which is
thereby produced. The element does, in fact, require some time and energy
to charge or form it. Faure has made a great improvement in this direction.
It consists in coating the lead plates with a thick paste of red lead, Pb^O,,
so as to have about one gramme to the square centi-
metre. This is kept in its place by a sheet of parch-
ment paper and slips of felt, and is then coiled up as
in Plante's (fig. 799). When the current is passed,
the ultimate effect is that the red lead at the one elec-
trode is oxidised to Pb.jOj, and that at the other into
metallic lead in the form of a sponge, which therefore
exposes a greater surface.

In accumulators it is important to increase the
surface while diminishing the weight, as well as to
make the oxide adhere more firmly ; this is promoted
by constructing the plates of gratings, or by making
the surface ribbed.

The inverse electromotive force of such a couple
is about 2i times that of a Daniell's cell, so that three
DanielFs or two Grove's cells are required to charge
it. In charging, a considerable number of elements
are joined together by their similar poles, and connected with the respective
electrodes of the charging battery ; the effect is the same as that of using a
single element of a surface equal to the sum of the surfaces of all the
elements. By means of a specially contrived commutator they may be

3H 2

S^6 Dytiamical Electricity. [849-

arranged tandem, and then discharged, and in this way very high potentials
can be obtained. So long as such batteries could be charged only from a
voltaic battery they could never be economical ; but the fact that after having
been once charged they retain the charge for a considerable time, has led
to their use in what is called ' storing electricity,' produced by mechanical
power through the agency of dynamo- and magneto-electrical machines.
What they do is to store the products of chemical decomposition, and that
in a form in which they are immediately available for electrical effects.

An accumulator of great capacity is obtained by placing a plate of zinc
plate in a solution of zincate of potass or soda, and a porous plate of copper
obtained by compression. During the charge the zinc in the solution is pre-
cipitated on the zinc plate, and the copper absorbs an equivalent quantity, of
oxygen. During the discharge the copper is reduced and the zinc redissolves.
This accumulator, however, does not retain its charge, and is only suitable
for cases in which the discharge rapidly succeeds the charge.

During the charge the E.M.F. of a secondary battery at first rises rapidly
until it is about 2-3 volts, and then remains constant until the charge is
complete, which is known by the disengagement of gas. In discharging
the potential sinks rapidly the first few minutes, and then remains constant
at about 2 volts until towards the end of the charge, when it again sinks.

An accumulator gradually loses its charge by leakage ; the excellence of
an accumulator depends on its power of retaining its charge, on its capacity,
and on its efficiency. By this latter is meant the ratio of the electrical work
which is accumulated in order to charge it, to that which it gives out in
sinking to its initial condition.

The following experiments, which are the earliest of their kind, will give
a fair idea of the results produced by their means. A battery of thirty-five
cells, each weighing nearly 437 kilog., was connected with a Siemens dynamo
machine (918), in working which one horse-power was employed during
thirty-five hours. When this was discharged through eleven Maxim's lamps,
these were kept lighted for 10 hours 40 minutes. The measured work
transmitted to the dynamo machine in that time was 9,570,000 kilogram-
metres (61). This accumulated in the battery an amount of electric energy
of 6,382,000 kgm., or 66 per cent. While the battery was being discharged
it yielded 3,809,000, or 60 per cent, of the work stored in the form of elec-
tricity, which is therefore equivalent to 40 per cent, of the work transmitted
to the dynamo machine.

It thus appears that each kilogramme weight of battery — that is, the
weight of the lead and coating, together with the acid — requires a work of
6,257 kilogrammetres to charge it, and yields 2,500 kgm. in the form of
electricity. Each of the above lamps gave a light equal to i'4 Carrel lamps
— a standard lamp much used in France and equal to 7*4 standard candles
(509). This, therefore, is ecjual to 1,215 candles for one hour; hence this
represents 3,135 kgm. per hour per candle, which is equal to o-oii6 of a
horse-power, or, if an amount of energy equal to one horse-power were
stored in the accumulator, it would produce 86 candles ; but as only 40 per
cent, of the power transmitted to the dynamo appears as light, one horse-
power in the engine is equivalent to the production of 2,2) candles wheil
worked through a battery of this kind.

-850]

Grove's Gas Battery.

S37

The capacity of an accumulator is the quantity of electricity which can
be stored for unit weight ; this quantity may be expressed in ampere hours,
that is to say, a current of one ampere maintained for one hour or 3,600
coulombs. The whole charge which can be imparted to an accumulator
cannot be utilised, for it is found to injure the accumulator if this is done,
and in practice the charge is only allowed to run down until the potential is
10 per cent, less than at the outset. A good accumulator, such as those of
the Electric Power Storage Company, will take a utilisable charge which
may be represented at 4,250 kilogrammetres for one kilo, of battery ; suffi-
cient therefore to raise the battery through a height of 4,250 metres, and of
this 85 to 90 per cent, can be utilised as electricity ; this being its efficiency.

In accumulators which are to be used as motors in such cases as
tramcars, electrical boats, the capacity is of first importance, while with
the use of stationary accumulators, as in electric lighting, the efficiency is
the chief point.

jNIany instructive comparisons may be made between a secondary bat-
tery and a charged Leyden jar. Thus, for instance, when the poles of a
secondary battery have been connected until no current passes, and are
then disconnected for a while, a current in the same direction as the first is
obtained on again connecting them ; this is the residual discharge. The
capacity of a secondary battery depends on the area of the electrodes, on
their nature, and on that of the interposed liquid, but not on the distance
between them. The energy of the Leyden jar is stored in that state of strain
which is called polarisation of the dielectric ; in the secondary battery the
energy consists in the products which are stored up on the surface of the
electrodes in a state ranging from chemical combination to mechanical
adherence or simple juxtaposition.

A dry pile which has become inactive may be used as a secondary
battery. When a current is passed through it, in a direction contrary to
that which the active battery yields, it then regains its activity.

850. Grove's gras battery. — On the property, which metals have, of con-
densing gases
on their sur-
faces, Grove
constructed his
gas battery, fig.
Soi. A single
cell consists of
two glass tubes.
B and A, in
each of whicli
is fused a plati-
num electrode,
provided on
the outside
with binding
screws. These
electrodes are
made more efficient by being covered with finely divided platinum. One of

g. 801

838 Dynamical Electricity. [850-

the tubes is partially filled with hydrogen, and the other partially with
oxygen, and they are inverted over dilute sulphuric acid, so that half the
platinum is in the liquid and half in gas. On connecting the electrodes
with a galvanometer, the existence of a current is indicated whose direction
in the connecting wire is from the platinum in oxygen to that in hydrogen •
so that the latter is negative towards the former, As the current passes
through water this is decomposed : oxygen is separated at the positive plate
and hydrogen at the other. These gases unite with the gases condensed on
their surface, so that the volume of gas in the tubes gradually diminishes,
but in the ratio of one volume of oxygen to two volumes of hydrogen. These
elements can be formed into a battery (fig. 767) by joining the dissimilar
plates with one another just as they are joined in an ordinary battery. One
element of such a battery is sufficient to decompose potassium iodide, and
four will decompose water.

851. Passive state of iron. — With polarisation is probably connected a
very remarkable chemical phenomenon, which many metals exhibit, but more
especially iron. When this is immersed in concentrated nitric acid it is
unattacked. This condition of iron is called the passive state, and upon it
depends the possibility of the zinc-iron battery (810). It is probable that in
this experiment a thin superficial layer of protosesquioxide of iron is formed ;
on the one hand this protects the iron from further attack, and on the other it
acts as an electromotor, like the layer of peroxide of lead in Plante's element
(849). The position of passive iron in the electromotive series is near that
of platinum.

852. iTobili's ring's. — When a drop of acetate of copper is placed on a
silver plate, and the silver is touched in the middle of a drop with a piece
of zinc, there are formed around the point of contact a series of copper rings
alternately dark and light. These are N'obilfs coloured rings. They may
be obtained in beautiful iridescent colours by the following process : A solu-
tion of lead oxide in potash is obtained by boiling finely powdered litharge
in a solution of potash. In this solution is immersed a polished plate of
silver or of German silver, which is connected with the positive electrode of
a battery of eight Bunsen's elements. With the negative pole is connected
a fine platinum wire fused in glass, so that only its point projects ; and this
is placed in the liquid at a small distance from the plate. Around this point
binoxide of lead is separated on the plate in very thin concentric layers, the
thickness of which decreases from the middle. They show the same series
of colours as Newton's coloured rings in transmitted light (650). The bin-
oxide of lead owes its origin to a secondary decomposition ; by the passage
of the current some lead oxide is decomposed into metallic lead, which is
deposited at the negative pole, and o.xygen which is liberated at the positive ;
and this oxygen combines with some oxide of lead to form bioxide, which
is deposited on the positive pole as the decomposition proceeds. This
process is used for the metallic coloration of objects of domestic use and
ornamentation.

The effects are also well seen if a solution of copper sulphate is placed
on a silver plate, which is touched with a zinc rod, the point of which is
in the solution ; for then a current is formed liy these metals and the
liquid.

-853] Arbor Satiirni, or Lead Tree. Arbor Diamv. 839

853. Arbor Saturni, or lead tree. Arbor Bianse. — When in a solu-
tion of a salt is immersed a metal which is more oxidisable than the metal
of the salt, the latter is precipitated by the former, while the immersed metal
is substituted, equivalent for equivalent, for the metal of the salt. This pre-
cipitation of one metal by another is partly attributable to the difference
in their affinities, and partly to the action of a current which is set up as
soon as a portion of the less oxidisable metal has been deposited. The
action is promoted by the presence of a slight excess of acid in the solu-
tion.

A remarkable instance of the precipitation of one metal by another is
the Arbor Sahirni. This name is given to a series of brilliant ramified
crystallisations obtained by zinc in solutions of lead acetate. A glass flask
is filled with a clear solution of this salt, and the vessel closed with a cork,
to which is fixed a piece of zinc in contact with some copper wire. The
flask, being closed, is left to itself The copper wire at once begins to be
covered with a moss-like growth of metallic lead, out of which brilliant
crystallised lamina? of the same metal continue to form ; the whole pheno-
menon has great resemblance to the growth of vegetation, from which indeed
the old alchemical name is derived. For the same reason the name arbor
Diancv has been given to the metallic deposit produced in a similar manner
by mercury in a solution of silver nitrate.

If a rod of zinc be dipped in an acid solution of stannous chloride
crystallised tin is formed upon it ; the experiment is more beautiful by
dipping the platinum electrodes of a battery in the solution ; if the poles
are reversed the crystallised lamiucE disappear at one pole to reappear at
the other.

840 Dynamical Electricity. [854-

ELECTROMETALLURGY,

854. Electrometallurgy. — The decomposition of salts by the battery-
has received a most important application in electrometallurgy, or galvano-
plnsttcs, or the art of precipitating certain metals from their solutions by the
slow action of a galvanic current, by which means the salts of certain metals
are decomposed, the metal being deposited on the negative pole, while the
acid is liberated at the positive. The art was discovered independently by
Spencer in England and by Jacobi in St. Petersburg.

In order to obtain a galvanoplastic reproduction of a medal or any other
object, a mould must first be made, on which the layer of metal is deposited
by the electric current.

For this purpose several substances are in use, and one or the other
is preferred according to circumstances. For medals and similar objects
which can be submitted to pressure, gutta-percha may be used with advan-
tage. The gutta-percha is softened in hot water, pressed against the object
to be copied, and allowed to cool, when it can be detached without difficulty.
For the reproduction of engraved woodblocks or type, wax moulds are now
commonly used. They are prepared by pouring into a narrow flat pan a
suitable mixture of wax, tallow, and Venice turpentine, which is allowed to
set, and is then carefully brushed over. with very finely powdered graphite.
While this composition is still somewhat soft, the woodblock or type is
pressed upon it either by a screw press, or, still better, by hydraulic pressure.
If plaster of Paris moulds are to be made use of, it is essential that they be
first thoroughly saturated with wax or tallow so as to become impervious to
water.

In all cases, whether the moulds be of gutta-percha or wax, or any non-
conducting substance, it is of the highest importance that the surface be
brushed over very carefully with graphite, and so made a good conductor.
The conducting- surface thus prepared must also be in metallic contact with
a wire or a strip of copper by which it is connected with the negative elec-
trode. Sometimes the moulds are made of a fusible alloy (340), which may
consist of 5 parts of lead, 8 of busmuth, and 3 of tin. Some of the melted
alloy is poured into a shallow box, and just as it begins to solidify, the medal
is placed horizontally on it in a fixed position. When the alloy has become
cool, a slight shock is sufficient to detach the medal. A copper wire is then
bound round the edge of the mould, by which it can be connected with
the negative electrode of the battery, and then the edge and the back are
covered with a thin non-conducting layer of wax, so that the deposit is only
formed on the mould itself

The most suitable arrangement for producing an electro-deposit of copper
consists of a trough of glass, slate, or of wood, lined with india-rubber or
coated with marine glue (fig. 802). This contains an acid solution of copper
sulphate, and across it are stretched copper rods, B and D, connected re-
spectively with the negative and positive poles of a battery. By their copper
conductors the moulds, ;//, are suspended in the liquid from the negative
rod B, whilst a sheet of copper, C, presenting a surface about ci|ual to that

-854]

Elcttrovietallu rgy.

841

Fig.

of the moulds to be covered, is suspended from the positive rod D, at the
distance of about 2 inches, directly opposite to them.

The battery employed for the electric deposition of metals ought to be
one of great constancy, and Daniell's and Smee's are mostly in use. The cur-
rents of electricity furnished by magneto-electrical machines of a special
construction are
also used in
large establish-
ments (913) ;
they furnish a
current which
has small ;E.
]\I.F., but great
quantity.

The density
of a current is
the strength di-
vided by the
surface of the
electrodes, or the number of amperes per square decimetre.

The copper plate suspended from the positive pole acts not only as elec-
tricity, but it keeps the solution in a state of concentration, for the acid
liberated at the positive pole dissolves the copper, and reproduces a quantity
of copper sulphate equal to that decomposed by the current.

Another, and veiy simple, process for producing the electric deposit of
copper consists in making use of what is in effect a Daniell's cell. A porous
pot, or a glass cylinder covered at the bottom with bladder or with vegetable
parchment, is immersed in a vessel of larger capacity containing a concen-
trated solution of copper sulphate. The porous vessel contains acidulated
water, and in it is suspended a piece of amalgamated zinc of suitable form,
and having a surface about equal to that of the mould. The latter is attached
to an insulated wire connected with the zinc, and is immersed in the solution
of copper sulphate in such a position that it is directly opposite to the
diaphragm. The action commences by the mould becoming covered with
copper, commencing at the point of contact with the conductor, and gradually
increasing in thickness in proportion to the action of the Daniell's element
thus formed. It is, of course, essential in the process to keep the solution of
copper sulphate at a uniform strength, which is done by suspending in it
muslin bags filled with crystals of this salt. How great is the delicacy which
such electric deposits can attain appears from the fact that galvanoplastic
copies can be made of daguerreotypes, which are of the greatest accuracy.

An important industrial application is made of electrolysis in \\\& refining
of copper. The metal is extracted by the ordinary chemical processes so as
to obtain plates with 95 per cent, of pure copper. These plates are used as
positive electrodes in a bath of copper sulphate, and the metal is deposited
in a state of perfect purity on thin sheets which form the negative electrode,
while the impurities fall to the bottom. As the electrodes are practically
identical, there is no polarisation (848), and the work of the current is solely
emi)loyed in overcoming the resistance of the baths.

842 Dynamical Electricity. [855-

855. Blectrogilding. — The old method of gilding was by means of
mercury. It was effected by an amalgam of gold and mercury, which was
applied on the metal to be gilt. The objects thus covered were heated in a
furnace, the mercury volatilised, and the gold remained in a very thin layer
on the objects. The same process was used for silvering ; but they were
expensive and unhealthy methods, and have now been entirely replaced by
electrogilding and electrosilvering. Electrogilding only differs from the
process described in the previous paragraph in that the layer is thinner and
adheres more firmly. Brugnatelli, a pupil of Volta, appears to have been
the first, in 1803, to observe that a body could be gilded by means of the
battery and an alkaline solution of gold ; but De la Rive was the first who
really used the battery in gilding. The methods both of gilding and silver-
ing owe their present high state of perfection principally to the improve-
ments of Elkington, Ruolz, and others.

The pieces to be gilt have to undergo three processes before gilding.

The first consists in heating them so as to remove the fatty matter which
has adhered to them in previous processes.

As the objects to be gilt are usually of what is called gilding iiietal or red
brass, which is a special kind of brass rich in copper, and their surface
during the operation of heating becomes covered with a layer of cupric or
cuprous oxide, this Is removed by the second operation. For this purpose
the objects, while still hot, are immersed in very dilute nitric acid, where
they remain until the oxide is removed. They are then rubbed with a hard
brush, washed iji distilled water, and dried in gently heated sawdust.

To remove all spots they must undergo the third process, which consists
in rapidly immersing them in ordinary nitric acid, and then in a mixture of
nitric acid, bay-salt, and soot.

When thus prepared the objects are attached to the negative pole of a
battery, consisting of three or four Bunsen's or Daniell's elements. They are
then immersed in a bath of gold, as previously described. They remain in
the bath for a time which depends on the thickness of the desired deposit.
There is a great difference in the composition of the baths. That most in
use consists of i part of gold chloride and 10 parts of potassium cyanide,
dissolved in 200 parts of water. In order to keep the bath in a state of con-
centration, a piece of gold is suspended from the positive electrode, which
dissolves in proportion as the gold dissolved in the bath is deposited on the
objects attached to the negative pole.

The method which has just been described can also be used for silver,
bronze, German silver, &c. But other metals, such as iron, steel, zinc, tin,
and lead, are very difficult to gild well. To obtain a good coating, they must
first be covered with a layer of copper, by means of the battery and a bath
of copper sulphate ; the copper with which they are coated is then gilded,
as in the previous case.

The tint of the deposit is modified by adding solutions of copper or of
silver to the gold bath ; the former gives a reddish and the latter a greenish
tint.

856. Electrosllverlngr. — What has been said about gilding applies exactlj^
to the process of electrosilvering. The difference is in the composition of
the bath, which consists of 2 parts of silver cyanide and 2 parts of potas-

-857J Electric Deposition of Iron and Nickel. 843

sium cyanide, dissohed in 250 parts of water. To the positive electrode is
suspended a plate of siher, which prevents the bath from becoming poorer ;
the pieces to be silvered, which must be well cleaned, are attached to the
negative pole. It may here be observed that these processes succeed best
with hot solutions, and when the baths are old.

Knowing the weight of any given metal which is transported by unit of
electricity (846), it is easy to calculate the weight deposited in a given time
Ij)- a current of known strength. A deposit of one ounce of silver on a square
foot of surface gives a good coating ; its thickness, g|j inch or 0'03 mm., is
about that of thin writing paper.

857. Electric deposition of Iron and nickel. — One of the most valuable
applications of the electric deposition of metals is to what is called the
steeling {acierage) of engra\ed copper plates. The bath required for this
purpose is obtained by suspending a large sheet of iron, connected with the
positive pole of a battery, in a trough filled with a saturated solution of sal-
ammoniac ; whilst a thin strip of iron, also immersed, is connected with the
negative pole. By this means iron from the large plate is dissolved in the
sal-ammoniac, while hydrogen is given off on the surface of the small one.
When the bath has thus taken up a sufficient quantity of iron, an engraved
copper plate is substituted for the small negative strip. A bright deposit of
iron begins to form on it at once, and the plate assumes the colour of a
polished steel plate. The deposit thus obtained in the course of half an hour
is exceedingly thin, and an impression of the plate thus covered does not
seem different from an uncovered plate ; it possesses, however, an extraordi-
nary degree of hardness, so that a very large number of impressions can be
taken from such a plate before the thin coating of iron is worn off. When,
however, this is the case, the film of iron is dissolved off by dilute nitric acid,
and the plate is again covered with the deposit of iron.

An indefinite number of perfect impressions may, by this means, be
obtained from one copper plate, without altering the original sharp condition
of the engraving.

The covering of metals by a deposit of nickel has of late come into use.
The process is essentially the same as that just described. The bath used
for the purpose can, however, be made more directly by mixing, in suitable
proportions, salts of nickel with those of ammonia. The positive pole con-
sists of a plate of pure nickel. A special difficulty is met with in the electric
deposition of nickel, owing to the tendency of this metal to deposit in an un-
even manner, and then to become detached. This is got over by frequently
removing the articles from the bath, and submitting them to a polishing
process.

Objects coated with nickel show a highly polished surface of the charac-
teristic bright colour of this metal ; this is moreover very hard and durable,
and is not affected either by the atmosphere or even by sulphuretted hydro-
gen. A deposit of 2 grammes of nickel on the square decimetre represents a
coating 0-023 n^iri. in thickness.

844

Dynamical Electricity.

[858-

CHAPTER IV.

ELECTRODYNAMICS. ATTRACTION AND REPULSION OF CURRENTS BY
CURRENTS.

858. Electrodynamics. — By the term electrodynamics is understood the
laws of electricity in a state of motion, or the action of electric currents upon
each other and upon magnets, while electrostatics deals with the laws of elec-
tricity in a state of rest.

The action of one electrical current upon another was first investigated
by Ampere, shortly after the discovery of Oersted's celebrated fundamental

Fig. 803.

experiment (820). All the phenomena, even the most complicated, folloVv
from two simple laws, which are —

I. Tiuo currents which arc parallel, and in the same direction, attract one
another.

II. Two currents parallel, hut in contrary directions, repel one another.
In order to demonstrate these laws, the circuit which the current traverses

must consist of two parts, one fixed and the other movable. This is effected

-859]

Kogefs Vibrating Spiral.

845

Fig.

by the apparatus (fig. 803), which is a modified and improved form of one
©riginally devised by Ampere,

It consists of two brass columns, A and D, between which is a shorter
one. The column D is provided with a multiplier (821) of 20 turns, MN (fig
805), which greatly increases the sensitiveness of the instrument. This can
be adjusted at any height, and in any position, by means of a universal screw
clamp (see figs. 805-807).

The short column is hollow, and in its interior slides a brass tube termi-
nating in a mercury cup, c, which can be raised or lowered*. On the column
A is another mercury cup represented in section at
fig. 804 in its natural size. In the bottom is a
capillary aperture through which passes the point
of a sewing-needle fixed to a small copper ball.
This point extends as far as the mercury, and turns
freely in the hole. The movable part of the circuit
consists of a copper wire proceeding from a small
ball, and turning in the direction of the arrows
from the cup a to the cup c. The two lower branches are fixed to a thin
strip of wood, and the whole system is balanced by two copper balls,
suspended to the ends.

These details being known, the current of a Bunsen's battery of 4 or 5 cells
ascending by the column
A (fig. 805) to the cup a,
traverses the circuit BC,
reaches the cup c^ descends
the central column, and
thence passes by a wire,
P, to the multiplier MN,
whence it returns to the bat-
teiy by the wire Q. Now if,
before the current passes,
the movable circuit has
been arranged in the plane
of the multiplier, with the
sides B and M opposite
each other, when the cur-
rent passes, the side B is re-
pelled, which demonstrates
the second law ; for in the branches B and M the currents, as indicated
by the arrows, are proceeding in opposite directions.

To demonstrate the first law the experiment is arranged as in fig. 807
— that is, the multiplier is reversed ; the current is then in the same direc-
tion both in the multiplier and in the movable part ; and when the latter is
removed out of the plane of the multiplier, so long as the current passes
it tends to return to it, proving that there is attraction between the two
parts.

859. Kogret's vibrating- spiral. — The attraction of parallel currents may
also be shown by an experiment known as that of Rogcfs vibrating sptj-al.
A copper wire about 07 mm. in diameter is coiled in a spiral of about 30

Fig. 80s.

846

Dynamical lilcciricity.

[859-

coils of 25 mm. in diameter. At one end it is hung vertically from a binding-
screw, while the other just dips in a mercury cup. On passing the current
of a battery of 3 to 5 (drove's cells through the spiral by means of the mer-
cury cup and the binding screw, its coils are traversed by parallel currents ;
they therefore attract one another, and rise, and thus the contact with the
mercury is broken. The current having thus ceased, the coils no longer
attract each other, they fall by their own weight, contact with the mercury
is re-established, and the series of phenomena are indefinitely produced.
The experiment is still more striking if a magnetised rod the thickness of a
pencil is introduced into the interior. This will be intelligible if we consider
the action between the parallel Amp^rian currents of the magnet and of the
helix.

860. Xiaws of angrular currents. — I. Two rectilinear crcrrents^ the direc-
tions of which form an angle with each other, attract one another when both
approach or recede from the apex of the angle.

II. They repel one another, if one approaches and the other recedes from
the apex of the angle.

These two laws may be demonstrated by means of the apparatus above

described, replac-
ing the movable
circuit by the cir-
cuit BC. If then
the multiplier is
placed horizontally,
so that its current
is in the same direc-
tion as in the mov-
able current, on re-
moving the latter it
quickly approaches
the multiplier,

which verifies the
first law.

To prove the

second law, the multiplier is turned so that the currents are in opposite direc-
tions, and then repulsion ensues (fig. 805).

/;/ a rectilinear current each clement of the current repels the succeeding
one, and is itself repelled.

This is an im])ortant consequence of Ampere's law, and may be experi-
mentally demonstrated by the following arrangement, which was devised
by Faraday. A U-shaped jiiece of copper wire, whose ends dip in two
separate deep mercury cups, is suspended from one end of a delicate balance
and suitably equipoised. When the mercury cups are connected with the
two poles of a Ijattery, the wire rises very appreciably, and sinks again
to its original position when the current ceases to pass. The current passes
into the mercury and into the wire ; but from the construction of the appa-
ratus the former is fixed, while the latter is movable, and is accordingly^
repelled.

Kig. 806.

862]

Action of an Infinite Current.

847

861. Xiaws of sinuous currents. — The action of a sinuous current
is equal to tliat oj a rectilinear current of the same length in projection.
This principle is demon-
strated by arranging the
multiplier vertically and
placing near it a movable
circuit of insulated wire
half sinuous and half
rectilinear (fig. 807). It
will be seen that there
is neither attraction nor
repulsion, showing that
the action of the sinuous
portion ?ii?i is equalled
by that of the rectilinear
portion.

An application of this
principle will presently be
met with in the appara-
tus called solenoids (874),
which are formed of the combination of a sinuous with a rectilinear current.

862. Action of an infinite current on a current perpendicular to its
direction. — From the action exerted between two angular currents (860) the
action of a fixed and infinite rectilinear current, PQ (fig. 808), on a movable
current, KH, perpendicular to its direction can be determined. Let OK be
the perpendicular common to KH and PQ, which is null if the two lines PQ

Fig. 807.

/A-

.--r

Fig. 808.

ig. 809.

and KH meet. The current PQ flowing from Q to P in the direction of the
arrows, let us first consider the case in which the current KH approaches the
current QP. From the first law of angular currents (860) the portion OQ of
the current PQ attracts the current KH, because they both flow towards the
summit of the angle formed by their directions. The portion PO, on the con-
trar)?^, will repel the current KH, for here the two currents are in opposite
directions at the summit of the angle. If then mq and mp stand for the two
forces, one attractive and the other repulsive, which act on the current KH,
and which are necessarily of the same intensity, since they are symmetrically
arranged in reference to the two sides of the point O, these two forces may
be resolved into a single force, w//, which tends to move the current KH
parallel to the current QP, but in a contrary direction.

848

Dj ni a in zeal Electricity.

[862-

A little consideration will show that when the current KH is below the
current PQ, its action will be the opposite of what it is when above.

On considering the case in which the current KH moves away from PQ
(fig. 809), it will be readily seen from similar considerations that it moves
parallel to this current, but in the same direction.

Hence follows this general principle. A finite movable current which
approaches a fixed infiiiite current is acted on so as to move in a directio7t
parallel and opposite to that oj the fixed current ; if the movable current
tends from the fixed current, it is acted on so as to move pa7-allel to the
curreiit and in the same direction.

It follows from this, that if a vertical current is movable about an axis,
XY, parallel to its direction (figs. 810 and 811), any horizontal current PQ

Fig. 810. Fig. 811.

will have the eftect of turning the movable current about its axis, until the
plane of the axis and of the current have become parallel to PQ ; the vertical
current stopping, in reference to its axis, on the side frojn which the current
PQ comes (fig. 810), or 07i the side towards which it is directed (fig. 811),
according as the vertical cu7'rent desce7ids or asce7ids — that is, according" as it
approaches or moves from the horizontal axis.

It also follows from this principle that a system of two vertical currents

rotating about a
Xi vertical axis

(figs. 812 and
813) is directed
by a horizontal
current, PQ, in
a plane parallel
to this current
when one of
the vertical cur-
rents is ascend-

Fig. S12.

Fig. S13.

ing and the other descending (fig. 812) ; but that if they are both ascending
or both descending (fig. 813), they arc not directed.

863. Action of an Infinite rectilinear current on a rectangrular or
circular current. — It is easy to see that a horizontal infinite current exer-
cises the same directive action on a rectangular current movable about a
vertical axis (fig. 814) as what has been above stated. For from the direction of
the currents indicated by the arrows, the part QY acts by attraction not
only on the horizontal portion YD (law of a/igula/- curre7its), but also on the
vertical portion AD {/aw of pc7pcndicular ci/iTC/its). The same action

-864] Rotation of a Finite Horico?ital Current. 849

evidently takes place between the part PY and the parts CY and BC.
Hence, the fixed current VQ tends to direct the movable rectangular current
A BCD into a position parallel to PQ, and such
that itt the wires CD and PQ the direction of the
two currents is the sa7ne.

This principle is readily demonstrated by
placing the circuit ABCD on the apparatus with
two supports (fig. 814), so that at first it makes
an angle with the plane of the supports. On
passing a somewhat powerful current below the
circuit in the same plane as the supports, the
movable part passes into that plane. It is best
to use the circuit in fig. 822, which is astatic, while
that of fig. 814 is not.

What has been said about the rectangular ' '*' ""*■

current in fig. 814 applies also to circular currents, and is demonstrated by
the same experiments.

864. Rotation of a finite horizontal current by an infinite horizontal
rectilinear current. — The attractions and repulsions which rectangular
currents exert on one another
may readily be transformed
into a continuous circular mo-
tion. Let OA (fig. 815) be a
current movable about the
point O in a horizontal plane,
and let PQ be a fixed infinite
current also horizontal. As !L
these two currents flow in the
direction of the arrows, it fol-

Fig.

lows that in the position OA the movable current is attracted by the current
PQ, for they are in the same direction. Having reached the position OA',
the movable current is attracted by the part NQ of the fixed current, and
repelled by the part PN. Similarly in the position OA", it is attracted by
MQ and repelled by PM, and so on ; from which follows a continuous rota-
tory motion in the direction AA'A"A"'. If the movable current, instead of
being directed from O towards A, were directed from A towards O, it is
easy to see that the rotation would take place in the contrar}^ direction.
Hence, by the action of a fixed infinite current, PQ, the movable current
OA tends to a continuous motion in a direction opposite to that of the fixed
currefit.

If, both currents being horizontal, the fixed current were circular instead
of being rectilinear, its effect would still be to produce a continuous circular
motion. For, let ABC (fig. 816) be a fixed circular current, and w;; a rec-
tilinear current movable about the axis ;/, both currents being horizontal.
These currents, flowing in the direction of the arrows, would attract one
another in the angle «AC, for they both flow towards the summit (860). In
the angle 7zAB, on the contrary, they repel one another, for one goes towards
the summit and the other moves from it. Both effects coincide in moving
the wire jnn in the same direction .\CR.

b^O

Dynamical Electricity.

865-

'fffl'Tr'r^""''* igBffiSiif

865. Rotation of a vertical current by a horizontal circular current.

A horizontal circular current, acting on a rectilinear vertical, also imparts to
it a continuous rotatory motion. In order to show this, the apparatus repre-
sented in fig. 817 is used.

It consists of a brass vessel, round which are rolled several coils of in-
sulated copper wire, through which a current passes. In the centre of the
vessel is a brass support, a, terminated by a small cup containing mercury.
In this dips a pivot supporting a copper wire, bb^ bent at its ends in two ver-
tical branches, which are soldered to a very light copper ring immersed in
acidulated water contained in the vessel. A current entering through the
wire wz, reaches the wire A, and having made several circuits, terminates
at B, which is connected by a wire underneath with the lower part of
the column a. Ascending in this column, it passes by the wires bb into

the copper ring,
into the acidu-
lated water, and
into the sides
of the vessel,
whence it re-
turns to the
battery by the
strip D. The
current being
thus closed, the
circuit bh and

the iiUj, tend to turn m a dnection contiary to th it of the fixed current, a
motion due to the action of the circular current on the current in the vertical
branches bb ; for, as follows from the two laws of angular currents, the
branch b on the right is attracted by the portion A of the fixed current, and
the branch b on the left is attracted in the contrary direction by the opposite
part, and these two motions coincide in giving the ring a continuous rotatory
motion in the same direction. The action of the circular current on the
horizontal part of the circuit bb would tend to turn it in the same direction ;
but from its distance it may evidently be neglected.

866. Rotation of mag-nets by currents. — Faraday proved that currents
impart the same rotatory motions to magnets which they do to currents. This
may be shown by means of the apparatus represented in fig. 818. It consists
of a large glass vessel, almost filled with mercury. In the centre of this is
immersed a magnet, A, about eight inches in length, which projects a little
al)ove the surface of the mercury, and is loaded at the bottom with a pla-
tinum cylinder. At the top of the magnet is a small cavity containing
mercury ; the current ascending the column ;// passes into this cavity
hy the rod C. Yxom. the magnet it passes by the mercury to a copper
ring, G, whence it emerges by the column //. When this takes place the
magnet begins to rotate round its own axis with a velocity depending on its
magnetic power and on the intensity of the current.

Instead of making the magnet rotate on its a.xis, it may be caused to^
rotate round a line parallel to its axis byarrani;ing the experiment as shown
in fijj-. 822.

866]

Rotation of Magnets by Currents.

851

Fig. 819.

This rotatory motion is readily intelligible on Ampere's theory~of mag-
netism (879), according to which, magnets are traversed on their surface
by an infinity of circular currents in the same direction, in planes perpendi-
cular to the axis of the magnet. At the moment at which the current
passes from the
magnet into the
mercury, it di-
vides on the
surface of the
mercury into an
infinity of rec-
tilinear currents
proceeding from
the axis of the
magnet to the
circumference of
the glass. Figs.
820 and 8:
which corre-
spond respec-
tively to figs.
818 and 819,

give on a larger scale, and on a horizontal plane passing through the surface
of the mercury, the direction of the currents to which the rotation is due. In
fig. 820 the north pole being at the top, the Amperian currents pass round
the magnet in the reverse direction to that of the hands of a watch, as indi-
cated by the arrow i
(879), while the cur-
rents which radiate
from the rod C
towards the metal
ring GG', have
the directiom CD,
CE. Thus (860)
any given element
c of the magnetic
current of the bar
A is attracted by
the current CE
and repelled by the current CD ; hence results a rotation of the bar about
its axis in the same direction as the hands of a watch.

In fig. 821 the currents CD, CF being in the opposite direction to those
of the bar would repel the latter, which would be attracted by the currents
CE, CH. Hence the bar rotates in a circular direction, shown by the arrow
J-, about the vertical axis which passes through the rod C.

If the north pole is below, or if the direction of the current be altered, the
rotation of the magnet is in the opposite direction.

Fig. 820.

Fig. 821.

3 12

852

Dynamical Electricity.

[867-

ACTION OF THE EARTH AND OF MAGNETS ON CURRENTS.

867. Directive action of mag-nets on currents. — Not only do currents
act upon magnets, but magnets also act upon currents. In Oersted's funda-
mental experiment (fig. 757), the magnet being movable while the current is
fixed, the former is directed and sets at right angles with the current. If,
on the contrary, the magnet is fixed and the current movable, the latter is
directed and sets across the direction of the magnet. This may be illus-
trated by the apparatus represented in fig. 822. This is the original form
of Ampere's stand, and is frequently used in experimental demonstration.
It needs no explanation. The circuit which the current traverses is movable,
and below its lower branch a powerful bar magnet is placed ; the circuit
immediately begins to turn, and stops after some oscillations in a plane
perpendicular to the axis of the magnet.

Fig. S23.

For demonstratmg the action of magnets upon currents, De la Rive's
floating battery (fig. 823) is well adapted. It consists of plates of zinc and
copper which^are immersed in dilute sulphuric acid contained in a gl.iss
iKilb slightly loaded with mercury to keep it upright, and which can float
freely on water. With the plates can be connected either circular or rect-
angular wires, coils, or solenoids ; they are then traversed by a current, and
can be subjected to the action either of magnets or of currents.

868. Rotation of currents by mapnets.— Not merely can currents
be directed by magnets, but they may also be made to rotate, as is seen
from the following experiment, devised by Faraday (fig. 824). On a base
with levelling screws, and resting on an ivory support, is a copper rod, BD.
It is surrounded in part of its length by a bundle of magnetised wires, AB;
;uk1 at the top is a mercury cup. A copper circuit, EF, balanced on a steel

-869] Electrodynamic and Electromagnetic Rotation of Liquids. 853

point, rests in the cup, and the other ends of the circuit, which terminate
in steel points, dip in an annular trough full of mercury.

The apparatus being thus arranged, the current from 4 or 5 Bunsen's
elements enters at the binding screw b ; it
thence rises in the rod D, descends by the
two branches, reaches the mercury by the
steel points, whence it passes by the frame-
work, which is of copper, to the battery by
the binding screw a. If now the magnetised
bundle be raised, the circuit EF rotates,
either in one direction or the other, according
to the pole by which it is influenced. This
rotation is due to currents assumed to circu-
late round magnets ; currents which act on
the vertical branches EF in the same way as
the circular current on the branches bb in
fig. 817.

In this experiment the magnetised bundle
may be replaced by a solenoid (874) or by
an electromagnet, in which case the two
binding screws in the base of the apparatus
on the left give entrance to the current
which is to traverse the solenoid or electro-
magnet.

S69. Electrodynamic and electromagr-
netic rotation of liquids. — The condition
of a linear current assumed in the previous
experiments is not necessary. Fig. 825
represents an apparatus devised by Bertin
to show the electrodynamic and electromag- Fig. 824.

netic rotation of liquids. This apparatus

consists of an annular earthen vessel, VV ; that is to say, it is open in the
centre so as to be traversed by a coil, H. It rests on a board which can be
raised along two columns, E and I, and which are fixed by means of the
screws KK. Round the vessel VV is a second larger coil, G, fixed on the
columns SS'. The vessel VV rests on the lower plane. In the centre of
the coil is a bar of soft iron, x^ which makes an electromagnet.

The vessel VV contains acidulated water, and in the liquid are two
cylindrical copper plates e and i, soldered to copper wires, e' and i\ which
convey the current of a battery of four cells through the rods E and I. The
whole system is arranged on a larger base, on the left of which is a commu-
tator represented afterwards on a larger scale (fig, 826). With the base of
the columns E, I, S and S' are connected four copper strips, three of which
lead to the commutator and the fourth to the binding screw A, which
receives the wire from the positive pole.

The following three effects may be obtained with this apparatus :— (i), the
action of the coil G alone ; (2), the action of the electromagnet H alone ;
(3), the simultaneous action of the coil and of the electromagnet.

I. Fig. 824 represents the apparatus arranged for the first effect. The

854

Dynamical Electricity.

[869

current coming by the bindin.i; screw A attains the column S', which leads it
to the coil (}, with regard to which it is left — that is, in a contrary direction
to the hands of a watch. Then descending by the column S, it reaches the

c o m m u t a t o r,
which leads it
by the plate
marked centri-
pete to the
column E and
to the electrode
e'. The current
here traverses
the licjuid from
the circumfer-
ence to the
centre, attains
the electrode z,
the column I,
and by the inter-
\ention 'of the
plate cefitrifuge
the central piece
of the com-
mutator. This
transmits it finally to the negative binding screw, which leads it to the battery.
The liquid then commences a direct rotatory motion — that is to say, in the
same direction as the coil. If the direction of the current in the liquid is
centrifugal — that is, proceeds from the centre to the circumference — the
rotation is inverse ; that is, in the opposite direction to that of the coil.
In both cases the rotations may be shown to those at a distance by means
of small flags, f f^ fixed on discs of cork which float on the liquid, and
which are coated with lampblack to prevent adherence by capillary attraction
between the discs and the electrodes e and /.

II. To experiment with the electromagnet alone, the positive wire of the
battery is connected with the binding screw C, and the binding screws D and
B are joined by a copper wire. The current first passes into the electromagnet
H, then, reaching the commutator by the binding screw B, passes into the
centripetal plate, whence it rises in the column E, traverses the liquid in the
same direction as at first, reascends by the column I, and from thence to
the centre of the commutator and the negative binding screw, which leads it
to the battery. If the north pole of the electromagnet is at the same height
as the glass vessel, as in the figure, the Ampcrian currents move in the
opposite direction to the hands of a watch, and the floats then move in the
same direction as above ; and if the electromagnet is raised until the neutral
line is at the same heij^ht as the vessel, the floats stop ; if it is above ihcm,
the floats move again, but in the opposite direction.

III. To cause the coil and the electromagnet to act simultaneously, the.
positive wire of the battery is attached at C, and the binding screws D and
A are connected by a conductor. Hence, after having traversed the coil H,

-871] Directive Actio?i of tlie Earth on Vertical Currents. 855

the current arrives from D, and the binding screw A, whence it traverses
exactly the same circuit as in the first experiments. The effects are the
same, though more intense ; the action of the coil and the electromagnet
being in the same direction.

A simpler form of this experiment was devised by Clerk Maxwell. At
the bottom of a small beaker, a copper disc is placed with an insulated
tongue bent at right angles, and connected with a similar zinc disc supported
about an inch above the copper. Dilute acid is placed so as to cover both
discs, and some fine sawdust having been added to the liquid the whole is
placed on the pole of an electromagnet. The rotation of the liquid is then
shown by that of the sawdust.

S70. Bertln's commutator. — Commutators are apparatus by which the
direction of currents may be changed at pleasure, or by which they may be
open or closed. Bertin's has the advantage of at once showing the direc-
tion of the current. It consists of a small base of hard wood on which is an
ebonite plate, which, by means of the handle in (fig. 826), is turned about a
central axis, between two stops, c and c'. On the disc are fixed two copper
plates, one of which, c, is always positive, being connected by the axis and
by a plate, + , with the binding screw P, which receives the positive electrode
of the battery ; the other, zV, bent in the form of a horseshoe, is in metallic
connection with a plate below the disc against which it moves with friction ;
this plate is in connection with the negative electrode N. On the opposite
side of the board are two binding screws, b and b' , to which are adapted two
elastic metal plates, r and r'.

These details being
premised, the disc being
turned as shown in the
figure, the current coming
by the binding screw P
passes into the piece ^,
the plate r and the bind-
ing screw ^, which by a
second plate, or by a cop-
per wire, leads it to the
apparatus shown in fig.
825, or any other. Then Fijr. 826.

returning to the binding

screw b\ the current attains the plate /■', the piece i e, and ultimately the
binding screw N, which returns it to the battery.

If the disc is turned so that the handle is halfway between c and c', the
pieces o and i e being no longer in contact with the plates r and ;■', the cur-
rent does not pass. If w is turned as far as c, the plate 0 touches r', and r
touches c ; the current thus passes first to b' and returns by iJ ; it is therefore
reversed.

871. Directive action of tbe earth on vertical currents. — The earth,
which exercises a directive action on magnets (690), acts also upon currents,
giving them in some cases a fixed direction, in others a continuous rotatoiy
motion.

The first of these two actions may be thus enunciated : Every vertical

856

Dynainical Electricity.

[871-

currcnt movable about an axis parallel to itself , places itself under the direc-
tive action of the earth in a plane through this axis perpendicular to the
7nagnctic meridian, and stops after some oscillations, 07i the east of its axis
of rotatio7i wheii it is descending, and on the west when it is ascending.

This may be demonstrated by means of the apparatus represented in fig.
828, which consists of two brass vessels of somewhat different diameters.
The larger, a, about 13 inches in diameter, has an aperture in the centre,
through which passes a brass support, b, insulated from the vessel a, but
communicating with the vessel K. This column terminates in a small cup.

Fig. 828.

in which a light wooden rod rests on a pivot. At one end of this rod a fine
wire is coiled, each end of which dips in acidulated water, with which the
two vessels are respectively filled.

The current arriving by the wire m passes to a strip of copper, which is
connected underneath the base of the apparatus with the bottom of the
column b. Ascending in this column, the current reaches the vessel K, and
the acidulated water which it contains ; it ascends from thence in the wire
c, redescends by the wire e, and, traversing the acidulated water, it reaches
the sides of the vessel a, and so back to the battery through the wire n.

The current being thus closed, the wire e moves round the column b, and
stops to the east of it, when it descends, as is the case in the figure ; but if
it ascends, which is eflTected by transmitting the current by the wire «, the
wire e stops to the west of the column b, in a position directly opposite to
that which it assumes when it is descending.

If the rod with a single wire, in fig. 82S, be replaced by one with two wires
as in fig. S29, the rod will not move, for as each wire tends to place itself on
the east of the column a, two equal and conlraiy effects are produced, which
counterbalance one another.

872. Action of the earth on horizontal currents movable about a
vertical axis. — The action of the earth on horizontal currents is not direc-
tive, but gives them a continuous rotatoiy motion from the east to the wcsty "
whcfi the horizontal current moves away from the axis of rotation, and from
the west to the east when it is directed towards this axis.

-874]

Structure of a Solenoid.

857

This may be illustrated by means of the apparatus represented in fig. 829,
which only differs from that of fig. 828 in having but one vessel. The
current ascending by the
column rt, traverses the
two wires cc, and de-
scends by the wires bb,
from which it regains
the pile ; the circuit bccb
then begins a continuous
rotation either from the
east to the west, or from
the west to the east, ac-
cording as in the wires

cc the current goes from the centre, as is the case in the figure, or goes
towards it, which is the case when the current enters by the wire /// instead
of by ;/. But we have seen (871) that the action of the earth on the vertical
wires bb is destroyed ; hence the rotation is that produced by the action on
the horizontal branches cc. This rotatory action of the terrestrial current
on horizontal currents is an instance of the rotation of a finite horizontal by
an infinite horizontal current (S64).

873. Directive action of the earth on closed currents movable about
a vertical axis. — If the current on which the earth acts is closed, whether
it be rectangular or circular, the result is not a continuous rotation, but a
directive action, as in the case of vertical currents (871), in virtue of which
the current places itself in a plane perpe7idi-
cular to the magftetic meridia?i, so that it is
ascending on the east of its axis of rotation,
and descefiding on the west.

This property, which can be shown by
means of the apparatus represented in fig.
830, is a consequence of what has been said
about horizontal and vertical currents. For
in the closed circuit BA, the current in the
upper and lower parts tends to turn in oppo-
site directions, from the law of horizontal
currents (872), and hence is in equilibrium ;
while in the lateral parts the current on the
one side tends towards the east, and on the
other side to the west, from the law of vertical currents.

From the directive action which the earth exerts on
sary, in many experiments, to neutralise this action,
arranging the movable circuit symmetrically about its axis of rotation, so
that the directive action of the earth tends to turn the two branches in
opposite directions, and hence destroys them. This condition is fulfilled in
the circuit in fig. 822. Such circuits are hence called astatic circuits.

874. Structure of a solenoid. — A solenoid is a system of equal and
parallel circular currents formed of the same piece of covered copper wire
and coiled in the fomi of a helix or spiral, as represented in fig. 831. A sole-
noid, however, is only complete when part of the wire BC passes in the

currents, it is neces-
This is effected by

858

Dynamical Electricity.

874-

direction of the axis in the interior of the heHx. With this arrangement,
when the circuit is traversed by a current, it follows from what has been
said about sinuous currents (86 1) that the action of a solenoid in a longi-
tudinal direction, AB, is counterbalanced by that of the rectilinear current
BC. This action is accordingly null in the
A^^^^^Xpv-NTV'y-v'^r^v^ir-ir^jr^-N direction of the length, and the actioti of

(. ^ Q A-A y y A IfrruVlYPCr ^ '^ solenoid in a direction perpendicular to

^ its axis is exactly eqiiivatent to that of a

'^' "^^* series of equal parallel curretits.

875. Action of currents on solenoids. — What has been said of the
action of fixed rectilinear currents on finite rectangular, or circular currents

(864), applies evidently to
each of the circuits of a sole-
noid, and hence a rectilinear
current must tend to direct
these circuits parallel to
itself. To demonstrate this
fact experimentally, a sole-
noid is constructed as shown
in fig. 832, so that it can be
suspended by two pivots in
the cups a and c of the appa-
ratus represented in fig. 830.
The solenoid is then mov-
able about a vertical axis,
and if a rectilinear current
QP be passed beneath it, which at the same time traverses the wires of
the solenoid, the latter is seen to turn and set at right angles to the lower
current — that is, in such a position that its circuits are pai-allel to the fixed
current ; and, further, the current in the lower part of each of the circuits is
in the same direction as in the rectilinear wire.

If, instead of passing a rectilinear current below the solenoid, it is passed
vertically on the side, an attraction or repulsion will take place, according
as the two currents in the vertical wire, and in the nearest part of the
solenoid, are in the same or in contrary directions.

876. Directive action of the earth on solenoids. — If a solenoid be
suspended in the two cups (fig. 833), not in the direction of the magnetic
meridian, and a current be passed through tlie solenoid, the latter will
begin to move, and will finally set in such a position that its axis is in the
direction of the magnetic meridian. If the solenoid be removed, it will,
after a few oscillations, return, so that its axis is in the magnetic meridian.
Further, it will be found that in the lower half of the coils of which the
solenoid consists, the direction of the current is from east to west ; in other
words, the current is descending on that side of the coil turned towards the
cast and asce7tding on the Mcst. The directive action of the earth on
solenoids is accordingly a consequence of that which it exerts on circular
currents. In this experiment the solenoid is directed like a magnetic needle,
and the nortJi pole, as in magnets, is that end which points towards the
north, and the south pole that whicli jioints towards tlie south. This cxperi-

Fig. 832.

-879J

Ampere's TJieory of Magnetism.

859

ment may be made by means of a solenoid fitted on a De la Rive's floating
battery (867),

Fig. S33.

877. Mutual action of magnets and solenoids. — Exactly the same
phenomena of attraction and repulsion exist between solenoids and magnets
as between magnets themselves. For if one of the poles of a magnet be pre-
sented to a movable solenoid, traversed by a current, attraction or repulsion
will take place, according as the poles of the magnet and of the solenoid are
of contrary or of the same name. The same phenomenon takes place
when a solenoid traversed by a current and held in the hand is presented to
a movable magnetic needle. If one pole of a long bar magnet be presented
to the centre of the floating coil (fig. 823), then if the direction of the current
in the coil is the same as that of the amperian current (879) in that pole of the
magnet, the coil will be attracted to the magnet, and, encircling it, will move
towards the middle, where it is stationary ; if the currents are opposite, then the
coil will first of all be repelled, it will then turn round, and proceed as before.

878. ivzutual action of solenoids. — When two solenoids traversed by a
powerful current are allowed to act on each other, one of them being held
in the hand and the other being movable about a vertical axis, as shown
in fig. 833, attraction and repulsion will take place just as in the case of two
magnets. These phenomena are readily explained by reference to what has
been said about the mutual action of the currents, bearing in mind the direc-
tion of the currents in the extremities presented to each other.

879. iimpere's theory of mag-netism. — Ampere propounded a theory,
based on the analogy between solenoids and magnets, by which all magnetic
phenomena may be referred to electrodynamical principles.

Instead of attributing magnetic phenomena to the existence of two fluids.
Ampere assumed that each individual molecule of a magnetic substance is
traversed by a closed electric current, and further that these molecular cur-
rents are free to move about their centres. The coercive force, however,
which is little or nothing in soft iron, but considerable in steel, opposes this
motion, and tends to keep them in any position in which they happen to be.
When the magnetic substance is not magnetised, these molecular currents,
under the influence of their mutual attractions, occupy such positions that
their total action on any external substance is nil. Magnetisation consists
in giving to these molecular currents a parallel direction, and the stronger

Fig. 834.

860 Dynaniicixl Rlectvicity. [879-

the magnetising force the more perfect the paralleHsm. The limit of mag-
netisation is attained when the currents are completely parallel.

The resultant of the actions of all the molecular currents is equivalent to
that of a single current which traverses the outside of a magnet. For by

inspection of fig. 834, in which
the molecular currents are re-
presented by a series of small
internal circles in the two ends
of a cylindrical bar, it will be
seen that the adjacent parts of
the currents oppose one another
and cannot exercise any external
electrodynamic action. This is
not the case with the surface ;
there the molecular currents at
ab are not neutralised by other
currents, and as the points abc
are infinitely near, they form a series of elements in the same direction
situated in planes perpendicular to the axis of the magnet, and which con-
stitute a true solenoid

The direction of these currents in magnets can be ascertained by con-
sidering the suspended solenoid (fig. 832). If we supposed it traversed by a
current, and in equilibrium in the magnetic meridian, it will set in such a
position that in the lower half of each coil the current flows from east to
west. We have then the following rule : — When the 7iorth pole of a magnet
is looked at, the direction of tJie amperian currents is opposite to that of the
hands of a watch ; and wJien the south pole is looked at, the direction is the
same as that of the Iiands.

880. Terrestrial current. — In order to explain terrestrial magnetic
effects on this supposition, the existence of electrical currents is assumed,
which continually circulate round our globe from east to west perpendicular
to the magnetic meridian. The resultant of their action is a single current
traversing the magnetic equator from east to west. They are supposed by
some to be thermo-electric currents due to the variations of temperature
caused by the successive influence of the sun on the difterent parts of the
globe from east to west.

These currents direct magnetic needles ; for a suspended magnetic
needle comes to rest when the molecular currents on its under-surface are
parallel and in the same direction as the terrestrial currents. As the
molecular currents are at right angles to the direction of its length, the
needle places its greatest length at right angles to east and west, or north
and south. Natural magnetisation is probably imparted in the same way to
iron minerals.

88 r. Kail's experiment. — In the action of magnets on currents which
has been described in the foregoing sections, we have been concerned with
the action of the magnet on the body which conveys the current.

Professor Hall of Baltimore has made the following experiment to
determine whether the path of a current itself in the body of a conductor is
or is not deflected when it is exposed to the direct action of a magnetic field.

-881] HalFs Experiment. 86 1

A strip of gold leaf AB, 9 centimetres in length by 2 centimetres broad (fig.

835), was fastened on a glass plate, which was placed between the poles of

an electromagnet in such a manner that the plane of the strip was at right

angles to the lines of force of the magnetic field. The ends of this strip A

and B were in connection with the poles

of a Bunsen's cell. Two wires leading to

a Thomson's galvanometer a and b were

connected with two equipotential points

at the opposite edges of the strip ; that

is to say, in two points, found by trial,

in which there was no deflection of / 5I

the galvanometer (738). When now the -5^' X,

electromagnet was excited by passing a

current through it, a distinct deflection "' ^'

was produced in the galvanometer, showing that the path of the current in

the conducting strip had been deflected. This deflection was permanent,

and could not therefore be due to induction, and its direction was reversed

when the current in the magnet was reversed.

The magnetic field acts thus upon the current in the gold leaf in such a
manner as to displace it from one edge towards the other, and to cause a
small portion to pass through the circuit of the galvanometer.

The electricity is displaced in the direction of the electromagnetic force
T, that is, from a\.o b through the galvanometer in the case of iron, zinc, and
cobalt, but from b \.o a through the galvanometer, with nickel, gold, and
bismuth. ~0f all metals, bismuth shows the phenomenon in the highest
degree.

862 Dynamical Electricity. [882-

CHAPTER V. .

MAGNETISATION BY CURRENTS. ELECTROMAGNETS.
ELECTRIC TELEGRAPHS.

882. Magrnetisation by currents. — From the influence which currents
exert upon magnets, turning the north pole to the left and the south pole to
the right, it is natural to think that by acting upon magnetic substances in
the natural state the currents would tend to separate the two magnetisms.
In fact, when a wire traversed by a current is immersed in iron filings, they
adhere to it in large quantities (fig. 836), each particle sets particularly to the

wire ; they become detached as soon as the current ceases, and there is no
action on any non-magnetic metal.

In like manner an iron or steel bar is magnetised when placed at right
angles, and near to a current ; the effect is increased by coiling an insulated
copper wire round a glass tube, in which there is an unmagnetised steel bar.
If a current be passed through the wire, even for a short time, the bar be-
comes strongly magnetised.

If, as we have already seen (791), the discharge of a Leydenjar be trans-
mitted through the wire, by connecting one end with the outer coating, and
the other with the inner coating, the bar is also magnetised. This is a
convenient way of illustrating the identity between frictional and voltaic
electricity.

If in this experiment the wire be coiled on the tube in such a manner
that when it is held vertically the downward direction of the coils is from
right to left on the side next the observer, this constitutes a riglit-handcd or
dcxtrorsal spiral or Iiclix (fig. 837), of which the ordinary screw is an

Eig. 837-

example. In a Icft-iutiidcd ox si /i isi rorsal /w/ix ihc coiling is in the opposite
direction, that is, from left to right (fig. 83S).

In a right-handed spiral the north pole is at the end at which the current
emerges, and the south pole at the end at which it enters ; the reverse is the
case in a left-handed spiral. But whatever the direction of the coiling, the
polarity is easily found by the following rule : 1/ a person s7(.'ii/uiiifio iti tlic

-883]

Electromagnets.

863

cuniiil look (if the axis of the spiral^ the north pole is always on his left. If
the wire be not coiled regularly, but if its direction be reversed, at each
change of direction a consequent pole (681) is formed in the magnet. The

^^^m^^^i^i^i^^s^^;^^^

simplest method of remembering the polarity produced is as follows : What-
ever be the nature of the helix, either right or left handed, if the end facing
the observer has the current flowing in the direction of the handsof a watch,
it is a south pole, and vice versa. The same polarity is produced whether
or not there is an iron core with the helix.

The nature of the tube on which the helix is coiled is not without influence.
Wood and glass have no effect, but a thick cylinder of copper may greatly
affect the action of the current unless the copper be slit longitudinally. This
action will be subsequently explained. The same is the case with iron,
silver, and tin.

In order to magnetise a steel bar by means of electricity, it need not be
placed in a tube, as shown in figs. 837 and 838. It is sufficient to coil round
it a copper wire, covered with silk,
cotton, or gutta-percha, in order to in-
sulate the circuits from one another.
The action of the current is thus mul-
tiplied, and a feeble current is suffi-
cient to produce a powerful magneti-
sing effect.

8S3. Electromag'nets. — - IClcctro-
jiiao/iets arc bars of soft iron which,
under the influence of a voltaic current,
become magnets ; this magnetism is
only temporary, for the coercive force
of perfectly soft iron is ////, and as soon
as the current ceases to pass through
the wire, the bar reverts to its normal
magnetic, but unmagnetised state. If,
liowever, the iron is not quite pure it
retains more or less traces of magneti-
sation. Electromagnets have the
horse-shoe form, as shown in fig. 839,
and a copper wire, co\ered with silk or
cotton, is rolled several times rounil
them on the two branches so as to

form two bobbins, A and B. In order _ ^^

that the two ends of the horse-shoe i^- kv„u u _

may be of opposite polarity, the wind- ^ '■^" "'"

ing on the two limbs A and B must be such that if the horse-shoe were
straightened out, it would be in the same direction. Such an arrangement
as this is called a magnetising spiral.

'^'f'tllUljiJ*

864 Dynamical Electricity. [883-

Electromagnets, instead of being made in one piece, are constructed of
two cylinders firmly screwed to a stout piece of the same metal. Such are
the electromagnets in Morse's telegraph (889) and the electromagnetic motor
(899). The helices on them must be such that the current shall flow in the
same direction as the hands of a watch as seen from the south pole, and
against the hands of a watch as seen from the north pole.

The most powerful permanent magnets are obtained by means of electro-
magnets. For this purpose the steel bar is placed in a ring consisting of several
turns of insulated wire through which a strong current is passed, and the bar
is moved backwards and forwards in the coil, finishing where it had begun
in the middle of the bar ; the current is then opened. Or starting with the
middle, one half of the bar is moved 15 or 20 times over one pole of an elec-
tromagnet such as fig. 839, and the other half is passed in the same way over
the other limb.

The following are the principal results which have been obtained in refer-
ence to electromagnets : —

The magtietising force of a spiral is proportional to the product of the
number of turns of the wire into the strength of the current which traverses
it. With a given battery, the greatest magnetising power is obtained when
the resistance in the magnetising spiral is equal to the sum of the other re-
sistances in the circuit, those of the battery included, and the length and dia-
meter of the wire must be so arranged as to satisfy these conditions.

Provided the bar projects sufficiently at each end of the spiral, the width
of the coils has no influence on the magnetism produced.

Taking into account the resistance, the electromagnetic force is indepen-
dent of the nature and thickness of the wire. Thus the strength of the cur-
rent, and the number of coils being the same, thick and thin wires produce
the same effect.

The relation between the strength of the magnetism developed in soft
iron and the strength of the current cannot be expressed in a simple manner.
At first the electromagnetism increases somewhat more rapidly than in pro-
portion to the strength of the current, but the rate becomes less until it
reaches a maximum which is not exceeded however strong be the current.
The existence of this maximum, which varies for each bar, is a support for
the theory of molecular magnets, or molecular currents which have been laid
down (879). The maximum is attained when all the currents in the magnets
have set in their final position.

Soft iron and steel differ greatly as to their retention of magnetisation ;
thus for the same strength of current the temporary magnetisation (or that
observed while the current lasts) was 0*499 in the case of soft iron, 0-248 for
steel, and 0-246 for cast iron ; while that remaining after the current ceased
was o, 0T58, and o'Oi7 respectively. In other words, soft iron retained none
of the magnetisation, and cast iron 7 per cent. ; while steel retained 64 per
cent, of that which had been evoked in it.

The magnetism which a magnet retains after the current ceases to act is
called ihc pcriiuvtc/if or rcDiaiicnt magnetism. The latter term is frequently
employed to denote the small quantity left in soft iron in which its presence
is undesirable. The term residual is also used in this sense.

The limiting value of the magnetism which can be imparted to the

-883] Electromagnets. 865

strongest magnets is 40 C.G.S. units per gramme, according to \^'eber ; with
sewing needles as much as 85 and with thin knitting- needles as much as 106
have been obtained. With ordinary bar magnets the value is usually much
less than 40.

During magnetisation the \-olume of a magnet does not vary. This has
been established by placing the bar to be magnetised with its helix in a sort
of water thermometer, consisting of a flask provided with a capillary tube.
On magnetising, no alteration in the position of the water is observed. But
the dimensions vary ; the diameter is somewhat lessened, and the length
increased : according to Joule to the extent of about 075000 j i^ the bar is
magnetised to saturation. Bidwell has shown that if the magnetisation is
carried beyond the point at which the magnetic elongation of the rod reaches
a maximum, the length of the rod, instead of remaining unchanged, steadily
diminishes, the curve expressing the relation between the length and the
magnetising force descending in a straight line which shows no tendency to
become horizontal.

The iron used for an electromagnet must be pure, and be made as soft as
possible by being reheated and cooled a great many times ; it is polished by
means of a file, so as to avoid twisting. If this is not the case, the bar re-
tains, after the passage of the current, a quantity of residual magnetism. A
bundle of soft iron wires loses its magnetism more rapidly than a massive
bar of the same size. According to Stone, iron wires may be materially
improved for electromagnetic experiments by forming them into bundles
by tying them round with wire ; these bundles are then dipped in melted
parafifine and set fire to.

Remanent magnetism is greater in long magnets — those, that is to say, in
which the diameter is small in proportion to the length. It is decidedly
greater in soft iron when the magnetising current is not opened suddenly, as
is usually the case, but is gradually brought to zero by inserting successively
greater resistances. By suddenly opening the current it has occasionally
been found with thick rods of very soft iron that a reversed remanent mag-
netism is met with, which is called abttornial magnetisation.

This is easily understood from the tendency of molecular magnets to re-
vert to this primitive condition (879). In doing this they experience a certain
friction or resistance, and when the magnetisation gradually diminishes this
hinders the complete reversal of the molecules ; but with a sudden cessation
the molecules, from the greater vis viva of their reversal, will sooner come
back to their original position, or even pass it, and come to rest on the
opposite side.

The weight attached to the keeper which a magnet can support is known
as its lifting ox portative force. If the armature is prevented from coming
in contact with the magnet by interposing a non-magnetic substance an attrac-
tion is excited ; this is proportional to the square of the cm-rent strength so
long as the magnetic moment does not attain its maximum. Two unequally
strong electromagnets attract each other with a force proportional to the
square of the sum of both currents.

The relation between the portative and the magnetising force is not so
simple ; according to the researches of Bidwell it seems that for small
magnetisation the portative force increases less rapidly than the current

3 K

866 Dynamical Electricity. [883-

strcngth up to a certain point, when the strength of the field was about 270-
units and the weight supported was ) 0,800 grammes per square centimetre.
P'rom this point the magnetising current and the load increased in exactly
ihe same proportion. When the field had an intensity of 1,074 C.G.S. units
the greatest weight supported was 15,100 grammes per square centimetre^
or 52 pounds per square inch.

If the current be broken while the electromagnet is supporting even a
heavy weight attached to the keeper, it frequently happens that the keeper
does not become at once detached ; if now the magnet is gently tapped so as
to set the molecules in vibration, the keeper at once falls ; this phenomenon is
due to what is called magnetic hysteresis.

If a bar magnet be suspended by a string so that its axis is in the prolon-
gation of that of a spiral, and a current be now passed, it will be seen that
the magnet will be attracted or repelled according as the direction of the
supposed current in the magnet is the same as that of the current in the
spiral or not. In the case of the attraction, and if the magnet be not too-
bng and be sufficiently free to move, it will be drawn within the spiral. The
force with which the magnet is drawn in is nearly proportional to the strength
of the current and to the number of turns of the wire.

If the experiment be made with a bar of soft iron, it is drawn in, and there
is a remarkable difference in the strength, which is proportional to the square
of the magnetising force of the spiral.

Magnetism is not uniformly distributed in the section of electromagnets ;
the external layer exhibits a stronger magnetisation than the inner ones^
and with feeble forces there is only a magnetic excitation in the outer layer.
The magnetism in solid and in hollow cylinders of the same diameters is
the same, provided in the latter case there is sufficient thickness of iron for
the development of the magnetisation. With currents below a certain
strength, wide tubes of sheet-iron are far more powerfully magnetised than
solid rods of the same length and weight ; but with more powerful currents
the magnetism of the latter preponderates.

This may be illustrated by the following experiment : Two identical
magnetising spirals are joined by a wire and placed vertically a little dis-
tance apart ; from one end of the beam of an ordinary balance a solid soft
iron rod is suspended so that it is half way within the spiral, and this is
counterpoised by a sheet-iron cylinder of the same length and weight but
of greater diameter, which is also halfway within the other spiral.

If now the same weak current is transmitted through both spirals the
cylinder is drawn down, but if a stronger one is passed it is the rod which
is sucked in.

884. Vibratory motion and sounds produced by currents. — When a
rod of soft iron is magnetised by a strong electric current, it gives a very
distinct sound, which, however, is only produced at the moment of closing
or opening the current. This phenomenon, first observed by Page in
.America, and by Delezenne in France, was ]xirticularly investigated by
l)e la Rive, who attributed it to a vibratory motion of the molecules of
iron in consequence of a rapid succession of magnetisations and demag-
netisations.

Wiicn the current is broken and closed at very short intervals, Dela Rive

-885] Reis's Telephone. 867

observed tliat, whatever be the shape or magnitude of the iron bars, two
sounds may always be distinguished ; one, which is musical, corresponds to
that which the rod would give by vibrating transversely ; the other, which
consists of a series of harsh sounds, corresponding to the interruptions of
the current, was compared by De la Rive to the noise of rain falling on a
metal roof The most marked sound is that obtained by stretching, on a
sounding-board, pieces of soft iron wire, well annealed, from i to 2 mm. in
diameter and i to 2 yards long. These wires, being placed in the axis of one
or more bobbins traversed by powerful currents, send forth a number of
sounds, which produce a surprising effect, and much resemble that of a
number of church bells heard at a distance. Rods of zinc, copper, or brass
give no note even with strong currents.

Wertheim obtained the same sounds by passing a discontinuous cur-
rent, not through the bobbins surrounding the iron wires, but through the
wires themselves. The musical sound is then stronger and more sonorous
in general than in the previous experiment. The hypothesis of a molecular
movement in the iron wires at the moment of their magnetisation, and of
their demagnetisation, is confirmed by the researches of Wertheim, who
found that their elasticity is then diminished.

885. Rels's telephone. — The essential features of this instrument (fig.

840) are a sort of box, B, one side of which is closed by a membrane C,

while there is

a mouthpiece, ,'' Z7nt

A, in another T°--j

side. On the ^;Jj ^

membrane is a a_, b

piece of thin jl

metal-foil C,

which is con- :=;

nected with a

wire leading to

one pole of the

battery G, the _. „

, "^ , r f^'S- 840.

other pole of

which is put to earth. Just above the foil, and almost touching it, is a metal
point D, which is connected by the line wire (886) with one end of a coil of
insulated wire surrounding an iron wire, the other end of which is put to earth.
When the mouthpiece is spoken or sung into the sounds set the mem-
brane in vibration ; this alternately opens and closes the current, and these
makes and breaks being transmitted through the circuit to the electromagnet
F, produce the corresponding sounds.

3 K 2

868 Dynamical Electricity. [886-

ELECTRIC TELEGRAPH.

886. Electric telegraphs. — These are apparatus by which signals can be
transmitted to considerable distances by means of voltaic currents propa-
gated in metallic wires. Towards the end of the last century, and at the
beginning of the present, many philosophers proposed to correspond at a
distance by means of the effects produced by electrical machines when pro-
pagated in insulated conducting wires. In i8ii, Soemmering invented a
telegraph, in which he used the decomposition of water for giving signals.
In 1820, at a time when the electromagnet was unknown, Ampere proposed
to correspond by means of magnetic needles, above which a current w^as sent,
as many wires and needles being used as letters were required. In 1834,
Gauss and Weber constructed an electromagnetic telegraph, in which a voltaic
current transmitted by a wire acted on a magnetised bar the oscillations of
which under its influence were observed by a telescope. They succeeded in
thus sending signals from the Observatory to the Physical Cabinet in Got-
tingen, a distance of a mile and a quarter, and to them belongs the honour of
having first demonstrated experimentally the possibility of electrical com-
munication at a considerable distance. In 1837, Steinheil in Munich, and
Wheatstone in London, constructed telegraphs in which several wires each
acted on a single needle ; the current in the first case being produced by an
electromagnetic machine, and in the second by a constant battery.

Every electric telegraph consists essentially of three parts : i, a circuit
consisting of a metallic connection between two places, and an electromotor
for producing the current ; 2, a coinmiinicator for sending the signals from
the one station ; and, 3, an indicator for receiving them at the other station.
The manner in which these objects, more especially the last two, are effected
can be greatly varied, and we shall limit ourselves to a description of the
three principal methods.

One form of electromotor still sometimes used in England is a modifica-
tion of Wollaston's battery. It consists of a trough divided into compart-
ments in each of which is an amalga-
mated zinc plate and a copper plate ;
these plates are usually about 4^, inches
in height by 3! in breadth. The com-
partments are filled with sand, which is
moistened with dilute sulphuric acid.
This battery is inexpensive and easily
worked, only requiring from time to

time the addition of a little acid ; but

it has very low electromotive force and

consideiable resistance, and when it has

^ ' been at work for some time the effects

' '^- '''• of polarisation begin to be perceived.

On the telegraphs of the South-Eastern Railway, the platinised graphite.

(811) battery, invented l^y Mr. C. V, Walker, has been used with success.

On circuits on which there is constant work some form of Daniell's battery

-887] Wheatstone and Cooke's TekgrapJi. 869

Is used, and for other circuits Leclanche's cell is coming into more extended
use. In France, Daniell's battery is used for telegraphic purposes.

The connection between two stations is made by means of galvanised iron
wire suspended by porcelain supports (fig. 841), which insulate and protect
them against the rain, either on posts or against the sides of buildings. In
England and other moist climates special attention is required to be paid to
the perfection of the insulation. In towns, wires covered with gutta-percha
are placed in tubes laid in the ground. Submarine cables, where great
strength is required combined with lightness and high conducting power,
are formed on the general type of one of the Atlantic cables, a longitudinal
view of which is given in fig. 842, while fig. 843 represents a cross section.

Fig. S4.'. Fig. 843.

In the centre is the core,^\i\<^ is the conductor ; it consists of seven copper
wires, each i mm. in diameter, twisted in a spiral strand and covered with
several layers of gutta-percha, between each of which is a coating of Chat-
tertoiis compound — a mixture of tar, resin, and gutta-percha. This forms
the insulator proper, and it should have great resistance to the passage of
electricity, combined with low specific inductive capacity (748). Round the
insulator is a coating of hemp, and on the outside is wound spirally a pro-
tecting sheath of steel wire, spun round with hemp.

At the station which sends the despatch, the line is connected with the
positive pole of a battery, the current passes by the line to the other station,
and if there were a second return line, it would traverse it in the opposite
direction to return to the negative pole. In 1837, Steinheil made the very
important discovery that the earth might be used for the return conductor,
thereby saving the expense of the second line. For this purpose the end of
the conductor at the one station, and the negative pole of the battery at the
other, are connected with large copper plates, which are sunk to some depth
in the ground. The action is then the same as if the earth acted as a
return wire. The earth is, indeed, far superior to a return wire ; for the
added resistance of such a wire would be considerable, whereas the resist-
ance of the earth beyond a short distance is absolutely 7iil. The earth really
dissipates the electricity, and does not actually return the same current to
the battery.

8S7. "Wbeatstone and Cooke's sing^le needle telegrraph. — This con-
sists essentially of a vertical multiplier (821) with an astatic needle, the
arrangement of which is seen in fig. 845, while fig. 844 gives a front view
of the case in which the apparatus is placed. A (fig. 845) is the bobbin,
consisting of about 400 feet of fine copper wire, wound in a frame in two
connected coils. Instead of an astatic needle, Mr. Walter has found it ad-
vantageous to use a single needle formed of several pieces of very thin steel

870

Dynamical Electricity.

[887-

strongly magnetised ; it works with the bobbin, and a light index joined to
it by a horizontal axis indicates the motion of the needle on the dial.

The signs are made by transmitting the current in different directions
through the multiplier, by which the needle is deflected either to the right
or left, according to the will of the operator. The instrument by which this
is effected is a commutator or key, G, fig. 846 ; its action is shown in fig. 847,
while fig. 846 shows on a large scale how two stations are connected. It
consists of a cylinder of boxwood with a handle, which projects in front of
the case (fig. 844). On its circumference parallel to the axis are seven brass
strips (fig. 846), the spaces between which are insulated by ivory ; these

strips are connected at the end by metallic wires, also insulated from each
other, in the following manner : a with b and f,/with d., and c with g. Four
springs press against the cylinder ; x and y arc connected with the poles of
the battery, ;;/, with the earth plate, and // witli one end of the multiplier, N.
When not at work the cylinder and the handle are in a vertical position,
as seen on the left of the diagram. The circuit is thus open, for the pole
springs, x and/, are not connected with the metal of the commutator. But
if, as in the figure on tlie right, the key is turned to the right, the battery
is brouglit into the circuit, and the current passes in the following direc-
tion : + r^o\Q, x'a'b'fi'Wq"i^, conductor y/M//^/t7//E/, earth /'E'wV'^>', --
pole. The coils N and N' are so arranged that by the action of the current

-888]

Dial Telegraphs.

871

the motion of the needle corresponds to the motion of the handle. By
turning the handle to the left the current would have the following direction :
+ pole x'df in'E'p', c:ivth p'E//ical>/iM^, conductor /'^'MV/'^^'c?/', -pole, and
thus the needle would be deflected in the opposite direction.

The signs are given by differently combined deflections of the needle
as represented in tlic alphaljct on tlic dial (fig. 844). \ denotes a deflection

Fig. S46.

of the upper end of the needle to the left, and /a deflection to the right ;
I, for instance, is" indicated by two deflections to the left, and M by two to
the right. D is expressed by right-left-left, and C by right-left-right-left, tS:c.

require great practice

These signs are somewhat complicated and
usually not more than 12 to 20 words can be sent
in a minute. The single-needle telegraph was for-
merly sometimes replaced by the double-needle
one, which is constructed on the same principle,
but there are two needles and two wires instead
of one.

888. Dial telegrrapbs. — Of these many kinds
e.xist. Figs. 848 and 849 represent a lecture-
model of one form, constructed by Froment, and
which will serve to illustrate the principle. It
consists of two parts — the Xtj for transmitting
signals (fig. 848), and the indicator (fig. 849) for
receiving them. The first apparatus is connected
with a battery, Q, and the two apparatus are
in communication by means of metal wires, one of which, AOD (fig. 848),
goes from the departure to the arrival station, and the other, HKLI (fig.

Fig.- 847-

8/2

Dynamical Electricity

[888-

849), from the arrival to the departure. In practice, the latter is replaced
by the earth circuit. Each apparatus is furnished with a dial with 25 of

the letters of the alphabet, on which a noodle iinnos. Tlie needle at the
departure station is moved by hand, that of the ani\al by olcclricit)-.

-888] Dial Telegraph. 873

The path of the current and its effects are as follows : from the battery it
passes through a copper wire, A (fig. 848), into a brass spring, N, which
presses against a metal wheel, R, then by a second spring, M, into the wire
O, which joins the other station. Thence the current passes into the bobbin
of an electromagnet, b, not fully shown in fig. 849, but of which fig. 847
represents a section, showing the front of the apparatus. This electromagnet
is fixed horizontally at one end, and at the other it attracts an armature of
soft iron, a, which forms part of a bent lever, movable about its axis, <?, while
a spring, r, attracts the lever in the opposite direction.

When the current passes, the electromagnet attracts the lever ci;C, which
by a rod, z, acts on a second lever, d, fixed to a horizontal axis, itself con-
nected with a fork, F. When the current is broken the spring r draws the
lever r^C, and therewith all the connected pieces ; a backward-and-forward
motion is produced, which is communicated to the fork F ; this transmits
it to a toothed wheel, G, on the axis of which is the needle. From the
arrangement of its teeth, the wheel G is always moved in the same direction
by the fork.

To explain the intermittent action of the magnet, we must refer to fig.
848. The toothed wheel, R, has 26 teeth, of which 25 correspond to letters
of the alphabet, and the last to the interval reserved between the letters Z
and A. When holding the knob P in the hand the wheel R is turned, the end
of the plate >N from its curvature is always in contact with the teeth ; the
plate M, on the contrary, terminates in a catch cut so that contact is alter-
nately made and broken. Hence, the connections with the battery having
been made, if the needle P is advanced through four letters, for example, the
current passes four times in N and M, and is four times broken. The electro-
magnet of the arrival station will then have attracted four times, and have
ceased to do so four times. Lastly, the wheel G will have turned by four
teeth, and as each tooth corresponds to a letter, the needle of the arrival
station will have passed through exactly the same number of letters as that
of the departure station. The piece S, represented in the two figures, is a
copper plate, mo\able on a hinge, which serves to make or to break the
current at will.

From this explanation it will be readily intelligible how communications
are made between different places. Suppose, for example, that the first ap-
paratus being at London and the second at Brighton, there being metallic
connection between the two towns, it is desired to send the word signal to
the latter town : as the needles correspond on each apparatus to the interval
retained between Z and A, the person sending the despatch moves the
needle P to the letter S, where it stops for a very short time ; as the needle
in Brighton accurately reproduces the motion of the London needle, it stops
at the same letter, and the person who receives the despatch notes this letter.
The one at London, always continuing to turn in the same direction, stops
at the letter I, the second needle immediately stops at the same letter ; and
continuing in the same manner with the letters G, N, A, L, all the word is
soon transmitted to Brighton. The attention of the observer at the arrival
station is attracted by means of an electric alarum. Each station must
further be provided with the two apparatus (figs. 848 and 849), without which
it would be impossible to answer.

•874

Dynamical Electricity.

[889-

889. — Morse's telegrapb. — The telegraphs hitherto described leave no
trace of the despatches sent, and if any errors have been made in copying
the signals there is no means of remedying them. These inconveniences
are now met with in the case of the writing telegraphs., in which the signs
themselves are printed on a strip of paper at the time at which they are
transmitted.

Of the numerous printing and writing telegraphs which have been devised,
that of Morse, first brought into use in North America, is best known. It
has been almost universally adopted on the Continent. In this instrument
there are three distinct parts : the receiver., the sender., and the relay ; figs.
850, 851, 852, and 853 represent these apparatus.

Receiver. We will first describe the receiver (fig. 850), leaving out of sight
for the moment the accessory pieces, G and T, placed on the right of the
figure. The current which enters the indicator by the wire, C, passes into an
electromagnet, E, which when the current is closed attracts an armature of
soft iron. A, fixed at the end of a horizontal lever movable about an axis, x ;
when the current is open the lever is raised by a spring r. By means of two
screws, m and v, the amplitude of the oscillations is regulated. At the other
end of the lever there is a pencil, <?, which writes the signals. For this
purpose a long band of strong paper, ///, rolled round a drum, R, passes

i'"ii;. £50.

between two copper rollers with a rough surface, //■, and turning in contrary
directions. Drawn in the direction of the arrows, the band of paper becomes
•i*elled on a second drum, Q, which is turned by hand. A clockwork motion
placed in the box, HI), works the rollers, between which the band of paper
passes.

-889]

Morse's TelegrapJi.

875

The paper being thus set in motion, whenever the electromagnet works,
the point o strikes the paper, and, without perforating it, produces an inden-
tation the shape of which depends on the time during which the point is in
contact with the paper. If it only strikes it instantaneously, it makes a dot
(-) or short stroke ; but if the contact has any duration, a dash ( — ) of corre-
sponding length is produced. Hence, by varying the length of contact of
the transmitting key at one station, a combination of dots and dashes may
be produced at another station, and it is only necessary to give a definite
meaning to these combinations.

In order to make an indentation a considerable pressure is required, which
necessitates the employment of a strong current, and the newer instruments
(fig. 851) are based on the use of ink-wriic7's. The paper band passes
close to, but not touching, a metal disc with a fine edge, r, which turns
against a small ink-roller^ a, all being rotated by the same mechanism.
When the end A is attracted, the bent plate at the other end presses the
paper against the disc which is inked by contact with the ink-roller, and
thus produces a mark on the paper, which is either short or long according
to the duration
of the contact.
The signs are
thus more le-
gible, and are
produced by
far weaker cur-
rents.

The same
telegraphic al-
phabet is now
u n i \- e r s a 1 1 y
used wherever

telegraphic communication exists ; and the signals for the single-needle instru-
ment (fig. 844) as well as those used for printing have been modified, so that
they now correspond to each other. Thus a beat of the top of the needle to
the left \ is equixalent to a dot : and a beat to the right / to a dash. The
figure on the next page gives the alphabet.

The Jlag signals used in military operations are similarly used. A swing
of the flag from its upright vertical position to the right or left has the same
meaning as the corresponding motion of the top end of the needle. So too
long or short obscurations of the limelight used in signalling by night, or
of the heliograph (523), correspond to dashes and dots.

Sender or key. This consists of a small mahogany base, which acts as
support for a metal lever ab (fig. 852), movable about a horizontal axis which
passes through its middle. The extremity a of this lever is always pressed
upwards by a spring beneath, so that it is only by pressing with the finger
on the key B that the lever sinks and strikes the button x. Round the base
are three binding screws, one connected with the wire P, which comes from
the positi^•e pole of the battery ; the second connected with L, the line wire ;
and the third with the wire A, which passes to the indicator, for of course

8/6

Dynamical Electricity.

[889-

two places in communication are each provided with an indicator and com-
municator.

These details known, there are two cases to be considered, i. The key

SCs'GLE

SLVGia;

PRINTIKG.

-VEEDLE.

PH1NTD.G.

N-EEniZ.

A -_

As^

///

J Is

IIJ

E -

\\v

I/s

SNNX

vn/

I --

vsx/

.///

s//

/.J

! ./.

A//

/Av

arranged so as to receive a message from a distant station ; the end
b is then down, as represented in the figure, so that the current which

arri\es by the line wire L,
►B and ascends in the me-

tallic piece m, descends
in the wire A, which leads
it to the indicator of the
station at which the ap-
l^aratus is placed. i. A
message is to be trans-
milted ; in this case the
1. !■ key B is pressed so that

1 .^. tj. tlie lever comes in contact

with the button x. The
current of the local battery, which comes by the wire P, ascending then in
the lever, descends by in and joins the wire L, which conducts it to the
station to which the despatch is addressed. According to the length of time
during which B is pressed, a dot or a line is ])r()duccd in the recei\er to
wliich the current proceeds.

Relay. In describing the receiver wc have assumed that the current of
the line coming by the wire C (fig. 850) entered directly into the electro-
magnet, and worked the armature A, producing a despatch ; but when the

-889]

Morse's Telegraph.

S77

current has traversed a distance of a few miles its strength has diminished
so greatly that it cannot act upon the electromagnet with sufficient force to
print a despatch. Hence it is necessary to have recourse to a relay — that is,
to an auxiliary electromagnet which is still tra\ersed by the current of the
line, but which serves to introduce into the communicator the current of a
local battery of four or five elements placed at the station, and which is only used
to print the signals transmitted by the wire.

For this purpose the current entering the relay by the binding screw, L
(fig. 8 53), passes into an electromagnet, E, whence it passes into the earth
by the binding screw T. Now, each time that the current of the line passes
into the relay, the electromagnet attracts an armature, A, fixed at the bottom
of a vertical lever, ^z^, which oscillates about a horizontal axis.

At each oscillation the top of the lever p strikes against a button ;;,
and at this moment the current of the local battery which enters by the bind-
ing screw c^ ascends the column ;«, passes into the lever/, descends by the rod
o, which transmits it to the screw Z : thence it enters the electromagnet of the
indicator, whence it emerges by the wire Z, to return to the local battery from
which it started. Then, when the current of the line is open, the electro-
magnet of the relay does not act, and the le"\er/, drawn by a spring r, leax^es
the button ;/, as shown in the drawing, and the local current no longer
passes. Thus the relay transmits to the indicator exactly the same phases of
passage and intermittence as those effected by the manipulator in the station
which sends the despatch.

With a general battery of 25 Daniell's elements the current is usually
strong enough at upwards of 90 miles from its starting-point to work a relay.
For a longer distance a new current must be taken, as will be seen in the
paragraph on the change of current {vide infra).

Wo7idng of the three apparatus. The three principal pieces of Morse's
apparatus being thus known, the following is the actual path of the current.

The current of
the line coming by
the wire L(fig. 850)
passes at first to
the piece T intended
to serve as light-
ning - conductor,
when, from the in-
fluence of atmos-
pheric electricity in
time of storm, the
conducting wires
become charged
with so much elec-
tricity as to give
dangerous sparks.

This apparatus consists of two copper discs, rt'and/ provided with teeth on
the sides opposite each other, but not touching. The disc d is connected
with the earth by a metal plate at the back of the stand which supports this
lightning conductor, while tlic disc/ is in the current. The latter coming by

8/8 Dynamical Electricity. [889-

the line L enters the lightning-conductor by the binding screw fixed at the
lower part of the stand on the left ; then rises to a commutator, ;?, which con-
ducts it to a button, r, whence it reaches the disc /by a metal plate at the
back of the stand ; in case a lightning discharge should pass along the wire,
it would now act inductively on the disc ^, and emerge by the points without
danger to those about the apparatus. Moreover, from the disc/, the current
passes into a very fine wire insulated on a tube, e. As the wire is melted
when the discharge is too strong, the electricity does not pass into the
apparatus, which still further removes any danger.

Lastly, the current proceeds from the foot of the support to a screw on
the right, which conducts it to a small galvanometer, G, serving to indicate
by the deflection of the needle whether the current passes. From this
galvanometer the current passes to a key (fig. 852), which it enters at L,
emerging at A to go to the relay (fig. 853). Entering this at L, it works
the electromagnet, and establishes the communication necessary for the
passage of the current of the local battery, as has been said in speaking of
the relay.

Change of ciirrejit. To complete this description of Morse's apparatus it
must be observed that in general the current which arrives at L, after having
traversed several miles, has not sufficient force to register the despatch, nor
to proceed to a new distant point. Hence in each telegraphic station a
new current must be taken, that of the postal battery., which consists of 20 to
30 Daniell's elements, and is not identical with the local battery.

This new current enters at P (fig. 850), reaches a binding screw which
conducts it to the column H, and thence only proceeds further when the
armature A sinks. A small contact placed under the lever then touches the
button V : the current proceeds from the column H to the metallic mass
BD, whence by a binding screw and a wire, not represented in the figure, it
reaches, lastly, the wire of the line, which sends it to the following post, and
so on from one point to another.

890. Cowper's writing- telegraph. — This very remarkable invention is
a true telegraph, in that it faithfully reproduces at a distance an exact fac-
simile of a person's handwriting. The following is a general idea of the
principle of the instrument.

Two line wires are required, which are severally connected at the re-
ceiving station with two galvanometers, whose coils are at right angles to
each other. At the sending station is a vertical pencil with two light rods,
jointed to it at right angles to each other. One of these contact rods guides
a contact piece which is connected by a wire with one pole of a battery, the
other pole of which is to earth. This contact piece slides over the edges of
a series of contact plates insulated from each other, between<^ach of which
a special resistance is interposed, and the last of the contact pimp's is con-
nected with one line wire. The other contact piece slides over a second
series of such plates connected with the other line wire.

Let us consider one contact alone ; as it moves over the contact plates in
one direction or the other, it l)rings less or more resistance into the circuit,
and thercljy alters the strength of the current. The effect of this is that the
needle of the corresponding galvanometer is less or more deflected. Now the
end of this needle is connected by a light thread with a receiving pen, which

-891] Induction in Telegraph Cables. 879

is a capillary tube full of ink. An oscillation of the needle would produce an
up-and-down motion of the pen, and if simultaneously a band of paper passed
under the pen, being moved regularly by clockwork, there would be produced
on it a series of up-and-down strokes. A corresponding effect would be pro-
duced by the action of the needle of the other galvanometer, except that its
strokes would be backwards and forwards instead of up and down.

Now the action of the writing pen is that it varies simultaneously the
strengths of the two currents, and they produce a motion of the receiving
pen which is compounded of the two movements described above, and
which is an exact reproduction, on a smaller scale, of the original motion.
The following line is a facsimile.

Both the paper written in pencil at the sending station and that written
in ink at the receiving station move along as the writing proceeds, and the
messages have only to be cut off from time to time.

Experiments made with this instrument show that it will write through
resistances equal to 36 miles.

891. Induction inteleg:rapb cables. — In the earliest experiments on the
use of insulated subterranean wires for telegraphic communication it was
found that difficulties occurred in their use which were not experienced with
overhead wires. This did not arise from defective insulation, for the better
the insulation the greater the difficulty. It was suspected by Siemens and
others that the retardation was due to statical induction, taking place be-
tween the inner wire through the insulator and the external moisture ; and
Faraday proved that this was the case by the following experiments among
others. A length of about 100 miles of gutta-percha-covered copper wire
was immersed in water, the ends being led into the chamber of observation.
When the pole of a battery containing a large number of cells was momen-
tarily connected with one end of the wire, the other end being insulated, and
a person simultaneously touched the wire and the earth contact, he obtained
a violent shock.

When the wire, after being in momentary contact with the battery, was
placed in connection with a galvanometer, a considerable deflection was
observed ; there was a feebler one 3 or 4 minutes after, and even as long as
20 or 30 minutes afterwards.

When the insulated galvanometer was permanently connected with one
end of the wire, and then the free end of the galvanometer wire joined to the
pole of the battery, a rush of electricity through the galvanometer into the
wire was perceived. This speedily diminished and the needle ultimately
came to rest. When the galvanometer was detached from the battery and
put to earth, the electricity flowed as rapidly out of the wire, and the needle
was momentarily deflected in the opposite direction.

These phenomena are not difficult to explain. The wire with its thin
insulating coating of gutta-percha becomes statically charged with electricity
from the batter)'. The coating of gutta-percha through which the inductive
action takes place is only yV of an inch in thickness, and the extent of the
coatings is very great. The surface of the copper wire amounts to 8,300

88o Dynamical Electricity. [891-

square feet, and that of the outside coating is four times as much. The
potential can only be as great as that of the battery, but from the enormous
surface the capacity, and therefore the quantity, is very great. Thus the
wires, after being detached from the battery, showed all the actions of a
powerful electric battery. These effects take place but to a less extent with
wires in air ; the external coating is here the earth, which is so distant that
induction and charge are very small, more especially in the long lines.

Hence the difficulty in submarine telegraphy. The electricity which
enters the insulating wire must first be used in charging the large Leyden
jar which it constitutes, and only after this has happened can the current
reach the distant end of the circuit. The current begins later at the distant
end, and ceases sooner. The electricity is not projected like the bullet from
a gun, but rather like a quantity of water flowing from a large reservoir into
a canal in connection with large basins which it has to fill as well as itself
If the electrical currents follow too rapidly, an uninterrupted current will
appear at the other end, which indicates small differences in strength, but
not with sufficient clearness differences in duration or direction. Hence in
submarine wires the signals must be slower than in air wires to obtain clear
indications. By the use of alternating currents — that is, of currents which
are alternately positive and negative — these disturbing influences may be
materially lessened, and communication be accelerated and made more
certain, iDut they can never be entirely obviated.

In the Atlantic Cable, instruments on the principle of Thomson's reflect-
ing galvanometer (822) are used for the reception of signals ; the motions of
the spot of light to the right and left forming the basis of the alphabet.

892. Syphon recorder — Sir W. Thomson has invented an extremely
ingenious instrument called the syphon recorder, by which the very feeble

signals transmitted through long
lengths of submarine cables are ob-
served and also recorded.

A light rectangular coil of iron .$•
(fig. 854), connected with the line wire
by the screws^ and q, hangs by a bi-
polar suspension between the two poles
of a powerful electromagnet AB, so
that its plane is in the right line joining
l'/'\ '' i I 'v ' '"Z^^^^ '•'^^ poles. The space inside the coil

' ' 11, is occupied by a mass of soft iron /,

by which the strength of the fluid is
greatly increased. When a current
is passed this coil thereby becomes
a magnet, and is deflected cither to
the right or the left according to the
direction of the current ; its move-
ments are almost deadbeat, as the
damping is considerable.

A veiy light capillary tube c dips
with its short end in a reservoir of ink, while the other end is in front of a
jjajjcr riI)bon which is moved along at a uniform rate like the ribbon in a

Fi-. 85

-893]

Duplex TelegrapJiy.

88i

Morse's recorder. In order to get rid of friction against the paper, this ink
is electrified, and spurts out in a continuous series of fine drops against the
paper, marking on it a straight line so long as no current passes in the coil.
This syphon is, however, connected by a system of silk threads with the coil,
and according as this is deflected either to the right or the left the end of
the syphon is deflected too, and accordingly traces a wavy line (fig. 85 5) on

\rXr^f\T-yKr-^f' —

op q r s t n V 7v x y z

Fig. 855.

the paper, which represents deflections right or left of the central line, that
are, in short, the Morse signals (889).

The electrification of the ink is effected by a small electrostatic induction
machine ; this is worked by clockwork, which at the same time pays out the
paper ribbon.

893. Duplex telegraphy — By this is meant a system of telegraphy by
which messages maybe simultaneously sent in opposite directions on one and
the same wire, whereby the working capacity of a line is practically doubled.

Several plans have been devised for accomplishing this very important
improvement ; no more can here be attempted than to give a general account
of the principle of the method in one or two cases.

Let m (fig. 856) represent the electromagnet of a Morse's instrument
which is wound round with two equal coils in opposite directions ; these coils
are represented by the full and dotted lines, and one of them, which may be
called the li7ie coil, is joined to the line LL', which connects the two stations.
The other coil,
that repre-

sented by the
dotted line,
which may be
called the

equating coil,
is in connec-
tion with the
earth at E by
means of an
adjustable re-
sistance, or ar-
tificial line, R.
By this means
the resistance
of the branch Fig. 856.

rtRE may be made equal to that of the branch a'LL'a. The battery b has
one pole to earth at E, and the other pole, by means of a make-and-break
key, c, can be connected at a, where the two oppositely wound coils bifurcate.
The back contact of the key is also connected with earth.

3 L

882 Dynamical Electricity. [893-

The station at B is arranged in a similar manner, as is represented by
corresponding letters with affixes.

Now when B depresses his key and sends a current into the line, inasmuch
as the electromagnet of his instrument is wound with equal coils in opposite
directions, the armature is not attracted, for the core is not magnetised because
the currents in the two coils counteract one another. Thus, although a
current passes from B, there is no indication of it in his own instrument — a
condition essential in all systems of duplex. telegraphy.

But with regard to the effect on A, there are two cases, according as he
is or is not sending a message at the same time. If A's key is not down,
then the current will circulate round the core of the electromagnet and will
reach the earth by the path Lrt^-E ; the core will therefore become magnet-
ised, the armature attracted, and a signal produced in the ordinaiy way.

If, however, at the moment at which B has his key down, A also depresses
his, then it will be seen that, as currents are sent in opposite directions from
both A and B, they neutralise one another, no current passes in the line
a\AJa' : it is, as it were, blocked. But though no current passes in the line
coil, a current does pass at each station to earth, through the equating coil,
which, being no longer counterbalanced by any opposite current in the line
coil, magnetises the core of the electromagnet, which thus attracts the arma-
ture and produces a signal.

We have here supposed that A and B both send, for instance, the same
currents to line : the final effect is not different if they send opposite currents
at the same time. For then, as they neutralise each other in the line LL',
the effect is the same as if the resistance of the line were diminished. More
electricity flows at line from each station through the line coil being no longer
balanced by the equating coil ; the current of the line coil preponderates and
then works the electromagnet.

Hence, in both these cases, each station, so to speak, produces the signal
which the other one wishes to selid.

Another method is based on the principle of Wheatstone's bridge (955).
At each station is a battery P (fig. 857), one pole of which is to earth while
the other is connected with the key M.
The wire from M bifurcates at A into the
two branches B and C, between which is
connected the galvanometer ttr the receiv-
ing instrument. The branch ,AB goes to
line and AC to earth. There arc exactly
corresponding parts at the other station.
Now, from the principle of the bridge, the
resistances AB and AC may be adjusted
n such a manner that the potentials at
the points B and C are equal when the
key is depressed and the current sent ;
accordingly no current passes in the bridge,
and the galvanometer is at rest ; but the current from A passing to line
bifurcates at B', traversing the galvanometer and going to earth ; hence a
signal is received at that station.

Other methods of duplex telegraphy arc based on the principle of

\\>s^\VaV^\V;<;\<\\v

Fig. 857.

-896] The Sounder. 883

leakage ; but for these, as well as for quad ruplex telegraphy, special manuals
must be consulted.

894. Earth currents. — In long telegraph circuits more or less powerful
currents are produced, even \\hcn the battery is not at work. This arises
from a difference of potential being established in the earth at the two places
between which the communication is established. These currents are some-
times in one direction and sometimes in another, and are at times so power-
ful and irregular as quite to interfere with the working of the lines. Lines
running NE and SW are most frequently affected ; lines running NW and
SE are less so, and the currents are far weaker. Their strength often
amounts to as much as 40 millamperes, which is a stronger current than is
required for working ordinary telegraph instruments.

These currents do not seem to be due to atmospheric electricity, for they
cease if a wire be disconnected at one of its ends, and they appear in under-
ground wires.

According to Wild, they are the prime cause of magnetic storms, but not
of the periodical variations in the magnetic elements.

895. Bain's electrochemical teleg^raph. — If a strip of paper be soaked
in a solution of ferrocyanide of potassium and be placed on a metal surface
connected with the negative pole of a battery, on touching the paper with a
steel pointer connected with the positive pole, a blue mark due to the forma-
tion of some Prussian blue will be formed about the iron, so long as the current
passes. The first telegraph based on this principle was invented by Bain.
The alphabet is the same as Morse's, but the despatch is first composed at
the departure station on a long strip of ordinary paper. It is perforated
successively by small round and elongated holes, which correspond respec-
tively to the dots and marks. This strip of paper is interposed between a
small metal wheel and a metal spring, both forming part of the circuit. The
wheel, in turning, carries with it the paper strip, all parts of which pass
successively between the wheel and the plate. If the strip were not per-
forated, it would, not being a conductor, constantly offer a resistance to the
passage of the current ; but, in consequence of the holes, eveiy time one of
them passes, there is contact between the wheel and the plate. Thus the
current works the relay of the station to which it is sent, and traces in blue,
on a paper disc, impregnated with ferrocyanide of potassium, the same series
of points and marks as those on the perforated paper.

896. The sounder. — The sound produced when the armature of the elec-
tromagnet in a Morse's instrument is attracted by the passage of the current
is so distinct and clear that many telegraph operators have been in the
habit of reading the messages by the sounds thus produced, and at most of
checking their reading by comparison with the signs produced on the paper.

Based on this fact a form of instrument invented in America has come
into use for the purpose of reading by sound. The sounder, as it is called,
is essentially a small electromagnet on an ebonite base, resembling the relay
in fig. 853. The armature is attached to one end of a lever, and is kept at
a certain distance from the electromagnet by a spring. When the current
passes, the armature is attracted against the electromagnet with a sharp
click, and when the current ceases it is withdrawn by the spring. Hence the
interval between the sounds is of longer or shorter duration according to the

31-2

884

Dynamical Electricity.

[896-

will of the sender, and thus in effect a series of short or long intervals which
represent short and long sounds can be produced which correspond to the
dots and dashes of the Morse alphabet. Such instruments are simple, easily-
adjusted, and portable, not occupying more space than an ordinary field-glass.
They are coming into extended use, especially for military telegraph work.

897. Electric alarum. — One form of these instruments is represented in
fig. 858. On a wooden board arranged vertically is fixed an electromagnet,
E ; the line wire is connected with the bind-
ing screw, w, with which is also connected
one end of the wire of the electromagnet ;
the other end is connected with a spring, r,
to which is attached the armature, a ; this
again is pressed against by a spring, C, which
in turn is connected with the binding screw
n, from which the wire leads to earth.

Whenever the current passes, the arma-
ture a is attracted, carrying with it a hammer,
P, which strikes against the bell T and makes
it sound. The moment this takes place, con-
tact is broken between the armature a and
the spring C, and the current bemg stopped
the electromagnet does not act ; the spring
r, however, in virtue of its elasticity, brings
the armature in contact with the spring C,
the current again passes, and so on as long
as the current continues to pass.

898. Electrical clocks. — Electrical
clocks are clockwork machines, in which an
eiectromagnet is both the motor and the regulator, by means of an electric
current regularly interrupted, in a manner resembling that described in the
preceding paragraph. Fig. 859 represents the face of such a clock, and fig.
860 the mechanism which works the needles.

An electromagnet, B, attracts an armature of soft iron, P, movable on a
pivot, rt. The armature P transmits its oscillating motion to a lever, s, which
by means of a ratchet, ;/, turns the wheel A. This, by the pinion, D, turns
the wheel C, which by a series of wheels and pinions moves the hands. The
small one marks the hours, the large one the minutes ; but as the latter does
not move regularly, but by sudden starts from second to second, it follows
that it may also be used to indicate the seconds.

It is obvious that the regularity of the motion of the hands depends on
the regularity of the oscillations of the piece P. For this purpose, the oscil-
lations of the current, before passing into the electromagnet B, are regulated
by a standard clock, which itself has been previously regulated by a seconds
pendulum. At each oscillation of the pendulum there is an arrangement by
which it opens and closes the current, and thus the armature P beats seconds
exactly.

To illustrate the use of these electrical clocks, suppose that on the railway -
from London to Birmingham each station has an electric clock, and that
from the London station a conducting wire passes to all the clocks on the

-899]

Electromagnetic Machines.

line as far as Birmingham. When the current passes in this wire all the
clocks will simultaneously indicate the same hour, the same minute, and the
same second ; for electricity takes an inappreciable time to go from London
to Birmingham.

Fig. 859.

899. Electromag'netic machines.— Numerous attempts have been made
to apply electromagnetism as a motive power in machinery. Fig. 861 repre-
sents an engine of this kind constructed by Froment. It consists of four
powerful electromagnets, ABCD, fixed on an iron frame, X. Between these
electromagnets is a system of two iron wheels movable on the same hori-
zontal axis, with eight soft iron armatures, M, on their circumference.

The current arrives at K, ascends in the wire E, and reaches a metallic
arc, O, which serves to pass the current successively into each electromagnet,
so that the attractions exerted on the armatures M shall always be in the
same direction. Now this can only be the case provided the current is
broken in each electromagnet just when an armature comes in front of the
axis of the bobbin. To produce this interruption the arc O has three branches
c, each terminating with a steel spring, to which a small sheave is attached.
Two of these establish the communication respectively with one electro-
magnet, and the third with two. On a central wheel, a, there are cogs, on
which the sheaves alternately rest. Whenever one of them rests on a cog,
the current passes into the corresponding electromagnet, but ceases to pass
when there is no longer contact. On emerging from the electromagnets the
current passes to the negative pole of the battery by the wire H.

In this manner, the armatures M being successively attracted by the four
electromagnets, the system of wheels which carries them assumes a rapid
rotatoiy motion, which by the wheel P and an endless band is transmitted to a
sheave, Q, which sends it finally to any machine, a grinding-mill for example.

In his workshops Froment had an electromotive engine of one-horse
power. But, though an interesting application of the transformation of
energy, these machines will never be practically applied in manufactures,

Dynamical Electricity.

[899-

for the expense of the acids and the zinc which they use veiy far exceeds
that of the coal in steam-engines of the same force.

Thus a machine devised by Kravogl produces about 1 7 per cent, of the
useful effect due to the chemical combination of the zinc with the acid in the
battery, and therefore in utilising this force they are about equal to the best
steam-engines. But a pound of coal yields 7,200 thermal units, and a pound
of zinc only 1,200 (484) ; and as zinc is ten times as dear as coal, engines

worked by electricity, independently of any question as to the cost of con-
struction, or of the cost of the acids, are sixty times as dear to work as
steam-engines.

The energy of the electrical current may be compared with the I'is viva
of a small mass which moves with very great velocity. Hence it can be
understood that at present the most advantageous employment of electricity
is to be found, not so much in the transformation of its vis viva into the
relatively slow movement of large masses, as in the rapid transmission of a
small power to great distances, as in the electric telegraph.

900]

Induction by Currents.

887

CHAPTER' VI.

VOLTAIC INDUCTION.

900. Induction by currents. — We have already seen (744) that by
induction is meant the action which electrified bodies exert at a distance
on bodies in the natural state. Hitherto we have only had to deal with
electrostatical induction ; we shall now see that dynamical electricity pro-
duces analogous effects.

Faraday discovered this class of phenomena in 1832, and he gave the
name of currents of induction or induced currc7its to instantaneous currents
developed in conductors under the influence of metallic conductors traversed
by electric currents, or by the influence of powerful magnets, or even by
the magnetic action of the earth ; and the currents which give rise to them
he called inducing currents.

The inductive action of a current at the moment of opening or closing
may be shown by means of a bobbin with X.\\o wires. This consists (fig. 862)

of a cylinder of wood or of cardboard, on which a quantity of silk-covered
No. 16 copper wire is coiled ; on this is coiled a considerably greater length
of fine copper wire, about No. 35, also insulated by being covered with silk.
This latter coil, which is called the secondary coil, is connected by its ends
with two binding screws, «, b, from which wires pass to a galvanometer,
while the thicker wire, \.\v& prima fy coil, is connected by its extremities with
two binding screws, c and d. One of these, d, being connected with one pole
of a batteiy, when a wire from the other pole is connected with c, the current
passes in the primary coil, and in this alone. The following phenomena are
then observed : —

888

Dynamical Electricity,

[900-

i. At the moment at which the thick wire is traversed by the current,
the galvanometer, by the deflection of the needle, indicates the existence in
the secondary coil of a current invei'se to that in the primaiy coil, that is,
in the contrary direction ; this is only instantaneous, for the needle imme-
diately reverts to zero, and remains so as long as the inducing current passes
through cd.

ii. At the moment at which the current is opened — that is, when the wire
cd ceases to be traversed by a current — there is again produced in the wire
ab an induced current instantaneous like the first, but direct^ that is, in the
same direction as the inducing current.

901. Production of induced currents toy continuous ones. — Induced
currents are also produced when a primary coil traversed by a current is
approached to or removed from a secondary one ; this may be shown by the
following apparatus (fig. 863), in which B is a hollow coil consisting of a

great length of fine wire, and A a coil consisting of a shorter and thicker
wire, and of such dimensions that it can be placed in the secondary coil.
The coil A being traversed by a current, if it is suddenly placed in the coil
B, a galvanometer connected with the latter indicates by the direction of its
deflection the existence in it of an inverse current ; this is only instantaneous ;
the needle rapidly returns to zero, and remains so as long as the small
bobbin is in the large one. If it is rapidly withdrawn, the galvanometer
shows that the wire is traversed by a direct current. If, instead of rapidly
introducing or replacing the primaiy coil, this is done slowly, the galvano-
meter only indicates a weak current, which is the feebler the slower the
motion.

If, instead of varying the distance of the inducing current, its intensity
Ije varied that is, cither increased by bringing additional batteiy power into

-903] Inductive Action of the Ley den Discharge. 889

the circuit, or diminished by increasing the resistance, an induced current
is produced in the secondary wire, which is inverse if the intensity of the
inducing current increases, and direct if it diminishes.

902. Conditions of induction. Iienz's law. — P'rom the experiments
which have been described in the previous paragraphs the following prin-
ciples may be deduced : —

I. The distance remaining the same, a co7itinuoiis a?id constant curreitt
docs not induce any current in an adjacent conductor.

W. A current, at the moment of being closed, produces in an adjacent con-
ductor an inverse current.

III. A current, at the moment it ceases, produces a direct current.

IV. A current which is removed, or whose strength dimittishes, gives
rise to a direct induced' current.

V. A current which is approached, or whose strength increases, gives rise
to aft ifiverse induced current.

VI. On the induction produced between a closed circuit and a current in
activity, when their relative distance varies, Lenz has based the following
law, which is known as Lenz's law : —

If the relative position of two conductors A and B be changed, of which
A is traversed by a curretit, a current is induced in B in such a direction
that, by its electrodynamic actioji on the curretit in A, it wotdd have imparted
to the conductors a motion of the contraty kind to that by which the inducing
action was produced.

Thus, for instance, in V., when a current is approached to a conductor, an
inverse current is produced ; but two conductors traversed by currents in
opposite directions repel one another, according to the received laws of
electrodynamics (858). Conversely when a current is moved away from a
conductor, a current of the same direction is produced ; now two currents in
the same direction attract one another.

On bringing the inducing wire near the induced as well as in removing it
away, work is required ; hence a quantity of heat proportional to the work
consumed must result, as Edlund's investigations have shown. On the
other hand, when induction results from the opening and closing of the cir-
cuit (II. and III.) no work is lost, but the inducing current loses as much
heat as is produced in the induced circuit.

903. Inductive action of the Iieyden discliargre. — Figure 864 represents
an apparatus devised by Matteucci, which is very well adapted for showing
the development of induced currents produced either by the discharge of a
Leyden jar or by the passage of a voltaic current.

It consists of two glass plates about 12 inches in diameter, fixed vertically
on the two supports A and B. These supports are on movable feet, and
can either be approached or removed at will. On the anterior face of the
plate A are coiled about 30 yards of copper wire C, a millimetre in diameter.
The two ends of this wire pass through the plate, one in the centre, the other
near the edge, terminating in two binding screws, like those represented in
;;/ and 7i on the plate B. To these binding screws are attached two copper
wires, c and d, through which the inducing current is passed.

On the face of the plate B, which is towards A, is enrolled a spiral of
finer copper wire than the wire C. Its extremities terminate in the binding

890

Dynamical Electt icity.

[903-

screws m and «, on which are fixed two wires, h and z, intended to transmit
the induced current. The two wires on the plates are not only covered with
silk, but each circuit is insulated from the next one by a thick layer of shellac
varnish.

In order to show the production of the induced current by the discharge
of a Leyden jar, one end of the wire C is connected with the outer coating,
and the other end with the knob of the Leyden jar, as shown in the figure.
When the spark passes, the electricity traversing the wire C acts by induc-
tion on the wire on the plate B, and produces an instantaneous current
in this wire. A person holding two copper handles connected with the
wire i and h receives a shock, the intensity of which is greater in pro-
portion as the plates A and B are nearer.

JUJJAHUIN i -
Fig. 864.

The experiment may also be made by simply twisting together two
lengths of a few feet of gutta-percha-covered copper wire. The ends of one
length being held in the hand, an electric discharge is passed through the
other length.

The above apparatus can also be used to show the production of induced
currents by the influence of voltaic currents. For this purpose the current
of a battery is passed through the inducing wire C, while the ends of the
other wire, h and z, are connected with a galvanometer. At the moment at
which the current commences or finishes, or when the distance of the two
conductors is varied, the same phenomena are observed as in the case of the
apparatus represented in fig. 863.

904. Induction by magrnets. — It has been seen that the influence of a
current magnetises a steel bar ; in like manner a magnet can produce induced
currents in metal circuits, Faraday showed this by means of a coil with a
single wire of 200 to 300 yards in length. The two ends of the wire being
connected with a galvanometer, as shown in fig. 865, a strongly magnetised
bar is suddenly inserted in the bobbin, and the following phenomena are
observed : —

i. At the moment at which the magnet is introduced, the galvanometer
indicates in the wire the existence of a current, the direction of which isr
opposed to that which circulates round the magnet, considering the latter as
a solenoid on Ampere's theory (87Q).

-905] Inductive Action of Magnets on Bodies in Motion. 891

ii. When the magnet is withdrawn, the needle of the galvanometer, which
has returned to zero, indicates the existence of a direct current.

The inductive action of magnets may also be illustrated by the follow-
ing experiment : a bar of soft iron is placed in the above bobbin and a strong-
magnet suddenly brought in contact with it ; the needle of the galvanometer
is deflected, but returns to zero when the magnet is stationary, and is de-
flected in the opposite direction when it is removed. The induction is here
pi^oduced by the magnetisation of the soft iron bar in the interior of the
bobbin under the influence of the magnet.

The same inductive effects are produced in the wires of an electromagnet,
if a strong magnet be made to rotate rapidly in front of the extremities of

the wire in such a manner that its poles act successively by influence on the
two branches of the electromagnet ; or also by forming two coils round a
horseshoe magnet, and passing a plate of soft iron rapidly in front of the
poles of the magnet ; the soft iron becoming magnetic reacts by influence on
the magnet, and induced currents are produced in the wire alternately in
different directions.

The inductive action of magnets is a confirmation of Ampere's theory
of magnetism. For as, on this theory, magnets are solenoids, all the ex-
periments which have been mentioned may be explained by the inductive
action of currents which traverse the surface of magnets ; the induction of
magnets is, in short, an induction of currents. And it is a useful exercise
to see how on this view the inductive action of magnets falls under Lenz's
law (902).

905. Inductive action of magrnets on bodies in motion. — Arago was
the first to observe, in 1824, that the number of oscillations which a mag-
netised needle makes in a given time, under the influence of the earth's
magnetism, is very much lessened by the proximity of certain metallic
masses, and especially of copper, which may reduce the number in a given
time from 300 to 4. This observation led Arago in 1825 to the discovery of

892 Dynamical Electricity. [905-

an equally unexpected fact — that of the rotative action which a plate of
copper in motion exercises on a magnet.

This phenomenon may be shown by means of the apparatus represented
in fig. 866. It consists of a copper disc, M, movable about a vertical axis.
On this axis is a sheave, B, round which is coiled an endless cord, passing
also round the sheave A. By turning this with the hand, the disc M may
be rotated with great rapidity. Above the disc is a glass plate, on which is

Fig. 866.

a small pivot supporting a magnetic needle, ab. If the disc be now rotated
with a slow and uniform velocity, the needle is deflected in the direction of
the motion, and stops at an angle of from 20° to 30° with the direction of the
magnetic meridian, according to the velocity of the rotation of the disc.
But if this velocity increases, the needle is ultimately deflected more than
90° ; it is then carried along, describes an entire revolution, and follows the
motion of the disc until this stops.

Babbage and Herschel modified Arago's experiment by causing a horse-
shoe magnet placed vertically to rotate below a copper disc suspended on
silk threads without torsion ; the disc rotated in the same direction as the
magnets. The effect decreases with the distance of the disc, and varies
with its nature. The maximum effect is produced with metals ; with wood,
glass, water, &c., it disappears. Babbage and Herschel found that, represent-
ing this action on copper at 100, the action on other metals is as follows :
zinc 95, tin 46, lead 25, antimony 9, bismuth 2. Lastly, the effect is enfeebled
if there are non-conducting breaks in the disc, especially in the direction of
the radii ; but it is the same if these breaks arc soldered with any metal.

Faraday made an experiment the reverse of Arago's first obser\ation ;
since the presence of a metal at rest stops the oscillations of a magnetic
needle, the neighbourhood of a magnet at rest ought to stop the motion of a
rotating mass of metal. Faraday suspended a cube of copper to a twisted
thread, which was placed between the poles of a powerful electromagnet.
When the thread was left to itself, it began to spin round with great velocity,,
but sto])ped the moment a powerful current passed through the electromagnet.

Faratlay was the first to give an explanation of all these phenomena of

-906] Induction by the Action of the EartJi. 893

magnetism by rotation. They depend on the circumstances that a magnet
or a solenoid can induce currents in a solid mass of metal. In the above case
the magnet induces currents in the disc when the latter is rotated ; and con-
\-ersely when the magnet is rotated while the disc is primarily at rest. Now
these induced currents, by their electrodynamic action, tend to destroy the
motion which gave rise to them ; they are simple illustrations of Lenz's law ;
they act in the same way as friction would do.

i. For instance, let AB (fig. 867) be a needle oscillating over a copper
disc, and suppose that in one of its oscillations it goes in the direction of the
arrows from N to M. In approaching the point M, for
instance, it develops there a current in the opposite
direction, and which therefore repels it ; in moving away
from N it produces currents which are of the same kind,
and which therefore attract, and both these actions
concur in bringing it to rest.

ii. Suppose the metallic mass turns from N towards
M, and that the magnet is fixed ; the magnet Avill repel
by induction points such as N which are approaching A, . ^'

and will attract M which is moving away ; hence the motion of the metal
stops, as in Faraday's experiment.

iii. If in Arago's experiment the disc is moving from N to M, N ap-
proaches A and repels it, while M, moving away, attracts it ; hence the needle
moves in the same direction as the disc.

If this explanation is true, all circumstances which favour induction will
increase the dynamic action ; and those which diminish the former will
also lessen the latter. We know that induction is greater in good conductors,
and that it does not take place in insulating substances ; but we have seen
that the needle is moved with a force which is less, the less the conducting
power of the disc, and it is not moved when the disc is of glass. Dove found
that there is no induction on a tube split lengthwise in which a coil is
introduced.

906. Induction by the action of the earth. — Faraday discovered that
terrestrial magnetism can develop induced currents in metallic bodies in
motion, acting like a powerful magnet placed in the interior of the earth in
the direction of the dipping needle, or, according to the theoiy of Ampere,
like a series of electrical currents directed from east to west parallel to the
magnetic equator. He first proved this by placing a long helix of copper
wire covered with silk (such as A, fig. 863) in the plane of the magnetic
meridian parallel to the dipping needle ; by turning this helix 180° about an
axis perpendicular to its length in its middle, he observed that at each turn
a gahanom.eter connected with the two ends of the helix was deflected. The
apparatus depicted in fig. 868, and known as DelezeiuK^s circle^ serves for
showing the currents produced by the inductive action of the earth. It
consists of a wooden ring, RS, about two feet in diameter, fixed to an axis,
oa, about which it can be turned by means of a handle, M. The axis oa is
itself fixed in a frame PQ, movable about a horizontal axis. By pointers
fixed to these two axes the inclination towards the horizon of the frame PQ,
and therefore of the axis oa, is indicated on a dial, b, while a second dial, c,
gives the angular displacement of the ring. This ring has a groove in which

894

Dynamical Electricity.

[906-

is coiled a great length of insulated copper wire. The two ends of the wire
terminate in a commutator analogous to that in Clarke's apparatus (912), the
object of which is to pass the current always in the same sense, although its
direction, SR, changes at each half-turn of the ring. On each of the rings
of the commutator are two brass plates, which transmit the current to two
wires in contact with the galvanometer. Suppose that the ends of the
wire on the coil are directly connected with wires leading to a galvanometer
at some distance, and the apparatus so placed that its axis of rotation oa
is at right angles to the magnetic meridian, and the plane of the ring, RS,
at right angles to the hne of dip. If, now, the frame be quickly turned
through 180°, the needle will be momentarily deflected, to the right for
instance ; if, while the needle on its return is just passing its position of

rest, the frame is rapidly turned to its original position, it will be deflected
to the left to a greater angle than at first, for the needle is already in motion ;
by repeating the operation, that is, reversing the swing when the needle is
passing its position of rest, the deflections will increase to a maximum, which
is a measure of the earth's magnetism. This method of amplifying an
originally small motion is known as the method of multiplication.

If the axis of rotation, oa., is vertical and the ring is rotated as above
described, only the horizontal component of the earth's magnetism can act,
and the angular deflection is then a measure of the horizontal component H.
Similarly, if the axis is horizontal and in the plane of the magnetic meridian,
and if the rotation is made through 180° from the horizontal position, only
the vertical component V acts, and is thus measured by the deflection.

Hence, from two such sets of observations wc may determine the inclina-

tion in any place, for tan i =

To experiment with the currents produced by continuous rotation the
wires are connected with the commutator.

907. Current of self-induction. Extra current. — If a closed circuit
traversed by a \c)Itaic current \)e broken, a scarcely perceptible spark is ob-

907]

Currejit of Self-induction. Extra Curretit.

895

tained if the wire joining the two poles be short. Further, if the obsei-ver
himself form part of the circuit by holding a pole in each hand, no shock is
perceived unless the current is very strong. If, on the contrary, the wire is
long, and especially if it makes a great number of turns so as to form a
coil with very close folds, and still more if a soft iron bar be inserted in the
coil, the spark, which is inappreciable when the current is closed, acquires a
great intensity when it is opened, and an observer in the circuit receives a
shock which is the stronger the greater the number of turns.

Faraday referred this strengthening of the current when it is broken to
an inductive action which the current in each winding exerts upon the others :
an action in virtue of which there is produced in the bobbin a direct current
q{ self-induction — that is, one in the same direction as the principal one. This
is known as the extra current, or curre?it of self-induction.

To show the existence of this current on breaking, Faraday arranged the
experiment as seen in fig. 869. Two wires from the poles E E' of a battery
are connected with two binding screws, D and F, with which are also con-
nected the two ends of a coil B, with a long fine wire. On the path of the

wires at the points A and C are two other wires, which are connected with a
galvanometer, G. Hence the current from the pole E branches at A into
two currents, one which traverses the galvanometer, the other the bobbin,
and both joining the negative pole E'.

The needle of the galvanometer being then deflected from G to a' by the
current which goes from A to C, it is brought back to zero, and kept there by
an obstacle which prevents it from turning in the direction Qa\ but leaves it
free in the opposite direction. On breaking contact at E, it is seen that the
moment the circuit is open the needle is deflected in the direction Qa ;
showing a current contrary to that which passed during the existence of the
current — that is, showing the current from C to A. But the battery current
having ceased, the only remaining one is the current AFBDCA ; and since
in the part C A the current goes from C to A, it must traverse the entire circuit
in the direction AFBDC — that is, the same as the principal current. This

896 Dynamical Electricity. [907-

currcnt, which thus appears when the circuit is made, is the extra current
or ciirre7it of self-induction.

908. Extra current on opening- and on closing-. — ^The coils of the spiral
act inductively on each other, not merely on opening but also on closing
the current. Hence, in accordance -with the general law of induction, each
spiral, acting on each succeeding one, induces a current in the opposite
direction to its own — that is, an inverse current : this, which is the extra
current on closing., or the inverse extra current, being of contrary direction
to the principal one, diminishes its intensity and lessens or suppresses the
spark on closing.

When, however, the current is opened, each turn then acts inductively
on each succeeding one, producing a current in the same direction as its own,
and which therefore greatly heightens the intensity of the principal current.
This is the extra current oji opefiing, or direct extra current.

To observe the direct extra current, the conductor on which its effect is
to be traced may be introduced into the circuit, by being connected in any
suitable manner with the binding screws A and C in the place of the galvano-
meter. It can thus be shown that the direct extra current gives violent
shocks and bright sparks, decomposes water, melts platinum wires, and
magnetises steel needles. The shock produced by the current may be
tried by attaching the ends of the wire to two files, which are held in the
hands. On moving the point of one file over the teeth of the other, a
series of shocks is obtained, due to the alternate opening and closing of the
current.

The above effects acquire greater intensity when a bar of soft iron is
introduced into the bobbin, or, what is the same thing, when the current is
passed through the bobbin of an electromagnet ; and still more is this the
case if the core, instead of being massive, consists of a bundle of insulated
straight wires. Faraday explained this strengthening action of soft iron as
follows : If inside the spiral there is an iron bar, on opening the circuit
when the principal current disappears, the magnetism which it evokes in the
bar disappears too ; but the disappearance of this magnetism acts like the
disappearance of the electrical current, and the disappearing magnetism in-
duces a current in the same direction as the disappearing principal current,
the effect of which is thus heightened.

In the experiments just described the effects of the two extra currents
accompany those of the principal current. Edlund has devised an in-
genious arrangement of apparatus by which the action of the principal cur-
rent on the measuring instruments can be completely avoided, so that only
that of the extra current remains.

The plan of this experiment is represented in fig. 870, in which A is a
battery the poles of which are connected with b and c. M is a differential
reflecting galvanometer the exactly equal coils of which terminate in cp and
fh. Wires connect b with // and/, and in like manner c is connected with
e and/ The current from A divides at c, passing round the galvanometer
the adjustment of the resistances is such that the primary current A does not
deflect the needle of the galvanometer. This current is denoted by the un-
feathered arrow.

A coil being introduced at S, and an equivalent resistance T between c

-911]

Properties of Induced Currents.

897

and c ; in order that this latter might have no self-induction, it was coiled
on two glass rods 10 feet apart.

When the resistances had been adjusted so that they were equal, and the
current at q was broken, an extra current was produced in the coil S, which,
circulating in the same direction round both windings in
the galvanometer as represented by the feathered arrows,
deflected it. When the current was closed, the extra cur-
rent passed through both coils in the same direction,
which was opposite that of the feathered arrows, and as
the deflections in the two cases were the same it followed
that the currents on opening and closing are equal and
opposite.

Edlund also showed that the electromotive force of
the extra current is proportional to the strength of the
primary current.

909. Induced currents of different orders. — Spite
of their instantaneous character, induced currents can
themselves, by their action on closed circuits, give rise
to new induced currents, these again to others, and so
on, producing induced cin-7-cnts of different orders.

These currents, discovered by Henry, may be ob-
tained by causing to act on each other a series of bobbins,
each formed of a copper wire covered with silk, and
coiled spirally in one plane, like that represented in
plate A, fig. 864. The currents thus produced are alter-
nately in opposite directions, and their intensity decreases
in proportion as they are of a higher order.

910. Properties of induced currents. — The preced-
ing experiments that induced currents have all the pro-
perties of ordinary currents. They produce violent physiological, luminous,
calorific, and chemical efiects, and finally give rise to new induced currents.
They also deflect the magnetic needle, and magnetise steel bars when
they are passed through a copper wire coiled in a helix round the bars.

The direct induced current and the inverse induced current have been
compared as to their chemical action ; the violence of the shock ; the deflec-
tion of the galvanometer ; and the magnetising action on steel bars. In these
respects they differ greatly : they are equal in their chemical action ; they are
about equal in their action on the galvanometer ; but while the shock of the
direct current is very powerful, that of the inverse current is scarcely percept-
ible. The same difference prevails with reference to the magnetising force.
The direct current magnetises to saturation, while the inverse current does
not magnetise.

911. iviairneto-electrical machine.— After the discovery of magneto-
electrical induction, several attem.pts were made to produce an uninterrupted
series of sparks by means of a magnet. Apparatus for this purpose were
devised by Pixii and Ritchie, and subsequently by Saxton, Ettingshausen,
and Clarke. Fig. 871 represents that invented by Clarke. It consists of
a owerful horseshoe magnetic batter}'. A, fixed against a vertical wooden
support. In front of this are two coils, B B', movable round a horizontal

.3 M

898

Dynamical Electricity.

[911-

ron joined at one

axis. These coils are wound on two cylinders of soft

end by a plate of soft iron, V, and at the other by a similar plate of

brass. These two plates are fixed on a copper axis, terminated at one

end by a commutator, qi, and at the other by a pulley, which is moved

by an endless band passing round a large wheel, which is turned by a

handle.

Each coil consists of about 1,500 turns of very fine copper wire covered
with silk. One end of the wire of the coil B is connected on the axis of

Fig. 871.

rotation with one end of the wire of the coil 15', and the two other ends
of these wires terminate in a copper washer, (^, which is fixed to the axis,
but is insulated by a cylindrical envelope of ivory. In order that in each
wire the induced current may be in the same direction, it is coiled on the
two coils in different directions— that is, one is right-handed, the other
left-handed.

When now the electromagnet turns, its two branches become alternately
magnetised in contrary directions under the influence of the magnet A, and
in each wire an induced current is produced, the direction of which changes
at each half-turn.

Let us follow one of the coils— 15, for instance— while it makes a com*'
plcte revolution in front of the poles a and b of the magnet ; calling the
poles of the electromagnet successively a' and b'. Let us further consider

911]

Magneto-electrical Machine.

899

the latter when it passes in front of the north pole of the magnetic battery
(fig. 871). The iron has then a south pole, in which, as we know, the Am-
porian currents move like the hands of a watch. The contrary seems to be
represented in fig. 873, but it must be remembered that the coils are seen
here as they are in fig. 871 ; and hence, when viewed at the end which
faces the magnet, the Amperian currents seem to turn like the hands of a
watch. These currents act inductively on the wire of the bobbin, producing
a current in the same direction (902, iii.), for the bobbin moves away trom
the pole <?, its soft iron is demagnetised, and the Amperian currents cease.
The intensity of the induced currents in the coil decreases, until the right

Fig. 873.

Fig. 874

Fig. S75.

Fig. 876.

line joining the axes of the two coils is perpendicular to that which joins the
poles a and b of the magnet. There is now no magnetisation in the bar,
laut quickly approaching the pole b^ its soft iron is then magnetised in the
opposite direction — that is, becomes a north pole (fig. 874). The Amperian
currents are then in the direction of the arrow a' ; and as they are com-
mencing, they develop in the wire of the bobbin an inverse current (901)
which is in the same direction as that developed in the first quarter of the
turn. Moreover, this second current adds itself to the first ; for while the
coil moves away from «, it approaches b. Hence, during the lower half-
turn from a to b., the wire was successively traversed by two induced currents
in the same direction, and if the rotatory motion is sufificiently rapid, we

3 M 2

900

D)niamical Electricity.

[911-

might admit during this half-turn the existence of a single current in the
wire.

The same reasoning applied to the figures 875 and 876 will show that
during the upper half-turn the wire of the coil B is still traversed by a
single current, but in the opposite direction to that of the lower half-turn.
What has been said about the coil B applies obviously to the coil B' ; yet,
as one of these is right-handed and the other left-handed, the currents are
constantly in the same direction in the two coils during each upper or lower
half-revolution. At each successive half-turn they both change, but are in
the same direction as regards each other ; the term ' direction ' having here
reference to figs. 873-876.

912. Commutator.— The object of this apparatus (fig. 877), of which fig.
878 is a section, is to bring the two alternating currents always in the same
direction. It consists of an insulating cylinder of ivory or ebony, J, in the
axis of which is a copper cylinder, k^ of smaller diameter, fixed to the arma-
ture V, and turning with the coils. On the ivory cylinder is first a brass
ferrule, q, and in front of it two half-ferrules, 0 and o\ also of brass, and
completely insulated from one another. The half-ferrule o is connected with
the ferrule ^ by a tongue, .i". On the sides of a block of wood, M, there are
two brass plates, 7;/, ;z, on which are screwed two elastic springs, b and c^ which
press successively on the half-ferrules 0 and o\ when rotation takes place.

We have al-
ready seen that
the two ends of
the wire of the
coil, those in
the same direc-
tion with respect
to the currents
passmg through
them at any
time, which will
be found to be
tliose farthest
away from the
armature \', ter-
minate in the
metallic axis k,
and therefore on
the half-ferrule
o ; while the
'^"'S- ^^^• other two ends,

both in the same direction with respect to the current, are joined to the
ferrule i]^ and therefore to the half- ferrule 0. It follows that the pieces
0 o' are always poles of alternating currents which are developed in the
coils : and, as these are alternately in contrary directions, the pieces o.
and 0' are alternately positive and negative. Now, taking the case in
which the half-ferrule 0' is positive, the current descends by the spring b,
follows the plate ///, arrives at n by the wire /, ascends in c, and is closed

-912]

Covunutator.

901

by contact with the piece 0 ; then when, in consequence of rotation, 0
takes the place of o\ the current retains the same direction ; for, as it is
then reversed in the coils, o has become positive and 0' negative, and so
forth, as long- as the coil is
turned.

With the two springs b
and c alone, the opposite
currents from the two pieces
0 and o' could not unite
when ni and ;/ are not joined ;
this is effected by means of
a third spring, a (fig. 880),
and of two appendices, z",
only one of which is visible
in the figure. These two
pieces are insulated from one F'g- 878.

another on an ivory cylinder, but communicate respectively with the pieces
0 and o'. As often as the spring a touches one of these pieces it is con-
nected with the spring b^ and the current is closed, for it passes from b
to a, and then reaches the spring c by the plate n. On the contrary, as
long as the spring a does not touch one of these appendices the current is
broken.

For physiological effects the use of the spring a greatly increases the
intensity of the shocks. For this purpose two long spirals of copper wire
with handles,/ and/', are fixed at n and m. Holding the handles in the
hands, so long' as the spring a does not touch the appendices z, the current
passes through the body of the experimenter, but without appreciable effect ;
while each time that the plate a touches one of the appendices z, the current,
as we have seen above, is closed by the pieces, b, a, and c, and ceasing then
to pass through the wires >!p, nip', produces in this and through the body a
direct extra current which causes a violent shock.

This is renewed at each half-turn of the electromagnet, and its intensity
increases with the velocity of the rotation. The muscles contract with such
force that they do not obey the will, and the two hands cannot be detached.
With an apparatus of large dimen-
sions a continuance of the shock
is unendurable.

All the effects of voltaic cur-
rents may be produced by the in-
duced current of Clarke's machine.
Fig. S72 shows how the apparatus
is to be arranged for the decom-
position of water. The spring a
is suppressed, the current being
closed by the two wires which re-
present the electrodes.

For physiological and chemical effects the wire rolled on the coils is
fine, and each about 500 or 600 yards in length. For heating effects, on the
contrary', the wire is thick, and there are about 25 to 35 yards on each coil.

Fis. S79.

902 Dynamical Electricity. i_912~

Figs. 879 and 880 represent the arrangement of the bobbins and the com-
mutator in each case. The first represents the inflammation of ether, and
the second the incandescence of a wire, c, in which the current from the
plate a to the plate c always passes in the same direction.

Pixii's and Saxton's electromagnetic machine differs from Clarke's in
having the electromagnet fixed while the magnet rotates.

Wheatstone devised a compendious form of the mag'neto-electrical
machine, for the purpose of using the induced spark in firing mines (794).

Breguet's apparatus for the same purpose consists of a powerful horse-
shoe magnetic battery, to the ends of which are screwed soft iron cores,
round which are coils of fine wires ; to these are connected the wires leading
to the mine to be fired. The ends of the soft cores are connected by a
soft iron keeper ; and when, by a suitable mechanism, this is suddenly
detached from the cores, a powerful momentary induction current is pro-
duced in the coils, which is sufficient to fire more than one fuse, through
even a considerable length of wire.

913. Magrneto-electrical machine. — The principle of Clarke's apparatus
has received in the last few years a remarkable extension in large magneto-
electrical machines, by means of which mechanical work is transformed into
powerful electrical currents by the inductive action of magnets on coils in mcftion.

The first machine of this kind was invented by Nollet, in Brussels, in
1850. It consists (fig. 881) of a cast-iron frame, 5^ feet in height, on the
circumference of which eight series of five powerful horseshoe magnetic
batteries, A, A, A, are arranged in a parallel order on wooden cross-pieces.
These batteries, each of which can support from 120 to 130 pounds, are so
arranged that if they are considered either parallel to the axis of the frame,
or in a plane perpendicular to this axis, opposite poles always face one
another. In each series the outside batteries consist of three magnetised
plates, while the three middle ones have six plates, because they act by both
faces, while the first only acts by one.

On a horizontal iron axis going from one end to the other of the frame
four bronze wheels are fixed, each correspondmg to the intervals between
the magnetic batteries of two vertical series. There are 16 coils on the
circumference of each of these — that is, as many as there are magnetic poles
in each vertical series of magnets. These coils, represented in fig. 882, differ
from those of Clarke's apparatus in having 12 wires, each i li yards in length,
instead of a single wire, by which the resistance is diminished. The wires
of these coils are insulated by means of bitumen dissolved in oil of turpentine.
They are not wound upon solid cylinders of iron, but on iron tubes, split
longitudinally ; this device renders the magnetisation and demagnetisation
more rapid when the coils pass in front of the poles of the magnet. Further,
the discs of copper which terminate the coils are slit in the direction of the
radius, in order to prevent the formation of induced currents in these discs.
The four wheels being respectively provided with 16 coils each, there are
altogether 64 coils arranged in 16 horizontal series of four, as seen at D on
the left of the frame. The Tength of the wire on each coil being 12 times
\\h yards, or 138 yards, the total length in the whole apparatus is 64 times*
138 yards, or 8,832 yards.

The wires are wound on all the coils in the same direction ; and not only

-913]

Magneto-electrical MacJiine.

903

on the same wheel, but on all four, all wires are connected with one another.
For this purpose the bobbins are joined, as shown in fig. 883 ; on the first
wheel the twelve wires of the first coil, x, are connected on a piece of
mahogany fixed on the front face of the wheel with a plate of copper, in,
connected by a wire, O, with the centre of the axis which supports the
wheels. At the other end, on the other face of the wheel, the same wires are

%i :ii,ii;!if;iv:i!:::,;"i":v,,i;3S

m^" \

Fig. 881.

soldered to a plate indicated by a dotted line which connects them with the
coilj/ ; from this they are connected with the coil s' by a plate, /, and so on,
for the coils /, tt, . . . up to the last, v. The wires of this coil terminate in
a''plate, 11, which traverses the first wheel, and is soldered to the wires of the
first coil of the next wheel, on which the same series of connections is re-
peated ; these wires pass to the third wheel, thence to the fourth, and so on
to the end of the axis.

904

Dynamical Electi'icity.

[913-

The coils being- thus arranged, one after another, like the elements of a
battery connected in a series (825), the electricity is of high potential. But
they may also be arranged by connecting the plates alternately, not with
each other, but with two metal rings, in such a manner that all the ends of

Fig. 882. Fig. 8S3.

the same name are connected with the same ring-. Each of these rings
is then a pole, and this arrangement may be used where a high degree of
potential is not required.

From these explanations it will be easy to understand the manner in
which electricity is produced and propagated in this apparatus. An endless
band, receiving its motion from a steam-engine, passes round a pulley fixed
at the end of the axis which supports the wheels and the coils, and moves
the whole system with any desired rapidity. Experience has shown that to
obtain the greatest degree of light the most suitable velocity is 235 revolu-
tions in a minute. During this rotation, if we at first consider a single
coil, the tube of soft iron on which it is coiled, in passing in front of the
poles of the magnet, undergoes at its two ends an opposite induction, the
efifects of which are added, but change from one pole to another. As these
tubes, during one rotation, pass successively in front of sixteen poles
alternately of different names, they are magnetised eight times in one
direction and eight times in the opposite direction. In the same time there
are thus produced in the bobbin eight direct induced currents and eight
inverse induced currents ; in all, sixteen currents in each revolution. With
a velocity of 235 turns in a minute, the number of currents in the same time
is 235 X 16 = 3,760 alternately in opposite directions. The same phe-
nomenon is produced with each of the 64 coils ; but as they are all wound
in the same direction, and are connected with each other, their effects accu-
mulate, and there is the same number of currents, but they are more intense.

To utilise these currents in producing the electric light, the connections
are made as shown in fig. 884. On the posterior side the last coil, x\ of
the fourth wheel terminates by a wire, G, on the axis MN, which supports
the wheels : the current thus passes to the axis, and thence over all the
machine, so that it can be taken from any desired point. In the front
the first coil, x, of the first wheel communicates, by the wire O, not with
the axis itself but with a steel cylinder, <■, fitted in the axis, from which, how-
ever, it is insulated by an ivory collar. The screw ^, to which the wire Q
is attached, is likewise insulated by a piece of ivory. From the cylinder c
the current passes to a fixed metal piece, K, from which it passes to the

-914] Siemens' Armature. 905

wire H, which transmits it to the binding screw a of fig. 881. The binding
screw b communicates with the framework, and therefore with the wire of
the last coil x' (fig. S84). From the two binding screws a and h the current
passes by two copper wires to two carbons, the distance of which is regu-
lated by means of an apparatus analogous in principle to that already
described (835).

In this machine the currents are not rectified so as to be in the same
direction^— it produces alternate currents ; hence each carbon is alternately

IMl

w " iir' 'r -^ ^

Fig. SS4.

positive and negative, and in fact they are consumed with equal rapidity
if a suitable lamp be used ; but when they are to be used for electro-metal-
lurgy, or for magnetising, they must be rectified, which is effected by means
of a suitable commutator (912).

This type of machine may claim a description here as that by which
magneto-electrical currents were first applied on a large scale for technical
purposes. Such machines, are, however, being superseded by various im-
proved forms of machines, which for the same power are simpler, less costly,
and occupy a smaller space. Of the newer forms of magneto-electrical
machine that of Meriten's is stated to give the best results.

Q14. Siemens' armature. — Dr. Siemens devised a cylindrical armature
for magneto-electrical machines, in which the insulated wire is wound length-
wise on the core, instead of transversely, as is usually the case.

It consists of a soft iron rod or cylinder, AB (fig. 8S5), from one foot to
three feet in length. A deep groove is cut in this cylinder and on the ends,

in which is coiled the insulated wire, as shown in section in fig. 887. To
the two ends of the cylinder, brass discs, E and D, are secured. With E is
connected a commutator C, consisting of two pieces of steel insulated from
each other, and connected respectively with the two ends of the wire. On
the other disc is a pulley,^, round which passes a cord, so that the bobbin
moves veiy rapidly on the two pivots.

9o6 Dynamical Electricity [914-

When a voltaic current circulates in the wire, the two cylindrical seg-
ments A and B are immediately magnetised, one with one polarity and the
other with the opposite. On the other hand, if instead of passing a voltaic
current through the wire of the coil, the coil itself be made to rotate rapidly
between the opposite poles of magnetised masses, as the segments A and
B become alternately magnetised and demagnetised, their induction pro-
duces in the wire a series of currents alternately positive and negative, as in
Clarke's apparatus (910). When these currents are collected in a commutator
which adjusts them (912), that is, sends all the positive currents on one
spring and all the negative on another — these springs become electrodes,
from one of which positive electricity starts, and from the other negative. If
these springs are connected by a conductor, the same effects are obtained as
when the two poles of a voltaic battery are united.

This armature has the great advantage that a large number of com-
paratively small magnets may be used instead of one large one. As, weight
for weight, the former possess greater magnetic force than the latter, they
can be made more economically. And as the armature is enclosed by and
is very near the magnets, it experiences the action of the field in its greatest
strength.

915. "Wild's magneto-electrical luachine. — Mr. Wild constructed a
magneto-electrical machine in which Siemens' armature is used along with
a new principle— that of the multiplication of tlie current. Instead of uti-
lising directly the current produced by the introduction of a magnet, Mr. Wild
passes It into an electromagnet, and by the induction of this latter a more
energetic current is obtained ; the electromagnet thus excited plays the part
of the permanent magnets, but is more powerful,

This machine consists first of a battery of 12 to 16 magnets, P (fig. 886),
each of which weighs about 3 pounds, and can support about 20 pounds.
Between the poles of the magnets two soft iron keepers CC are arranged,
separated by a brass plate, O. These three pieces are joined by bolts, and
the whole compound keeper is perforated longitudinally by a cylindrical
cavity, in which works a Siemens' armature, //, about 2 inches in diameter.
The wire of this armature terminates in a commutator, which leads the
positive and negative currents to two binding screws, a and b. This com-
mutator is represented on a larger scale in fig. 887. At the other end is a
pulley by which the armature can be turned at the rate of 25 turns in a
second. The wire on the armature is 20 yards long.

Below the support for the magnets and their armatures are two large
electromagnets, Bl>, which are called ihojictd nuii^ncts, since to them is due
the production of the magnetic field. Each consists of a rectangular soft
iron plate, 36 inches in length by 26 in breadth and i.^ inch thick, on which
arc coiled about 1,610 feet of insulated copper wire. The wires of these
electromagnets are joined at one end, so as to form a single circuit of 3,200
feet. One of the other ends is connected with the binding screw a, and the
other with b. At the top the two plates arc joined hy a transverse plate of
iron, so as to form a single electromagnet.

At the bottom of the electromagnets BB are two iron armatures, scpanitcd-
l)y a brass plate, 0,and in the entire length is a cylindrical channel in which
works a Siemens' armature, w, as above : this armature, however, is above a

-915J

Jl'i/d's Mao;neio-electrical Machine.

,07

yard in length, nearly 6 inches in diameter, and its wire is 100 feet long.
The ends are connected with a commutator, from which the adjusted currents
pass to two wires, r and s. The armatui'c m is rotated at the rate of 1,700
turns in a minute.

|inil|i|iV''«tr"^

111 II

'* »IL » «a^_

illl^Pt«V

Fig. 886.

• Fig. 887 shows on a larger scale a cross section of the coil of the armatures
CC, and of the plates AA, on which the wire of the electro-magnets BB is
coiled.

These details being premised, the following is the working of the
machine : — When the armatures n and m are rotated by means of a steam-
engine with the velocity mentioned, the magnets produce in the first arma-

9o8

Dynamical Elettricity,

[915-

ture induced currents, which, adjusted by the commutator, pass into the
electromagnet BB, and magnetise it. But as these impart to the lower
armatures, CC, opposite polarities^the induction of these latter produces in
the armature ;;/ a series of positive and negative currents far more powerful

Fig.

than those of the upper armature ; so that when these are adjusted by a
commutator and directed by the wires ;- and s, very powerful effects are
obtained.

These effects are still further intensified if, as Mr. Wild has done, the
adjusted current of the armature ;// is passed into a second electromagnet,
whose armatures surround a third and larger Siemens' armature turning with
the two others. Mr. Wild thus produced currents of a strength far exceeding
anything which up to that time had been attained ; he was able, for instance,
to melt easily an iron wire a foot long and more than 0'2 inch in diameter.

916. Bynamo-electrlcal macbines. — A great advance was made by the
discovery of the principle of the reaction of a current on itself— a discovery
made by Dr. Werner Siemens and Sir C. Wheatstone independently of each
other, and almost simultaneously. If a momentary voltaic current be passed
through the wires of the rotating armature of such a machine as the above,
a trace of residual magnetism (715) will be left in the core. The rotation of
this armature induces a current in the electromagnets BB ; this in turn
reacts on the armature, increases its magnetism, which again increases the
strength of the electromagnets, and so forth. We have in this an analogy
with Holtz's machine (759), in which the electricity of the plate and the con-
ductors reciprocally strengthen each other. It is not even necessary to
specially magnetise the iron at the outset ; the trace of residual magnetism
always present in iron (715) is sufficient to start the apparatus, which then
goes on increasing with the velocity of the rot;ition, and which indeed is
only limited by the heating of the wires and the bearings, and by the diffi-
culty of properly insulating the coils when such powerful currents are used.

Apparatus which transform mechanical work into electricity without the
use of permanent magnets, or of extraneous electromagnets, are known
as dynamo-clcctrical machitics or brief!)- dyntuitos^ in contradistinction tor'
ina_Q;nctfl-elccfrical machines, in which the magnetism is not furnished by
the play of the machine itself, but is got from permanent magnets. It must

-916]

Dynamo-electrical MacJiines.

909

not, however, be supposed that in the one the electricity is produced at the
expense of the magnetism, and in the other at the expense of the work.
There is really no distinction of this kind between them ; in both kinds of
machine electricity is produced at the cost of work ; and for this reason
both are indeed dynamo-electrical machines, and the distinction of the two
kinds is only one of convenience.

The earliest machine of this kind was that invented by Mr. Ladd. It con-
sists essentially of two Siemens' armatures, rotating with great velocity, and
of two iron plates, A A (fig. 889), surrounded by an insulated copper wire.

r^i

Fig. 889.

The electromagnets BB are not joined so as to form a single one, but
are two distinct electromagnets, each having at the end two hollow cylin-
ders, CC, in which are fitted two Siemens' armatures, in and « : the current
of the armature n passing round the electromagnets reverts to itself. The
wire of the armature m passes into the apparatus which is to utilise the
current — for instance, two carbon points, D.

The residual magnetism in the armature plates and their keepers is sufficient
to start the machine. If, then, the armatures m and n be rotated by means of
two bands passing round a common drum, the magnetism of the hollow cylin-
ders CC, acting upon the armature ;/, excites induction currents, which, ad-
justed by a commutator, pass round the electromagnets BB, and more strongly
magnetise the cylinders or shoes CC. These in their turn reacting more
powerfully on the armature ;/, strengthen the current ; we thus see that n and
B continually and mutually strengthen each other as the velocity of the rota-
tion increases. Hence, as the iron of the armature m becomes more and
more strongly magnetised under the influence of the electromagnets BB, a

9IO

Dynamical Electricity

[916-

Fig.

gradually more powerful induced current is developed in this armature, which
is directed, commutated or not, according to the use for which it is designed.

In a machine exhi-
bited at the Paris Exhi-
bition of 1867 the plates
A A were only 24 inches
in length by 12 inches in
width. With these small
dimensions the current is
equal to that of 25 to 30
Bunsen's cells. It can
work the electric light and
keep incandescent a plati-
num wire a metre in length
and 0-5 mm. in diameter.
The above form of the
machine is worked by
steam power. Mr. Ladd
devised a more compact
form, which may be
worked by hand. This
is represented in fig. 890.
The two armatures are
fixed end to end, and the
coils are wound on it at
right angles to each other,
as shown in the figure.
The current from this can
raise to white heat 18
in. of platinum wire o-oi
in. in thickness, and with
an inductorium (921) con-
taining 3 miles of second-
ary wire 2-in. sparks can
be obtained.

917. Pacinotti's ringr.
Cramme's magneto-

electrical maclilne. — .V
remarkable improvement
in magneto- and dynamo-
electric machines is
tlie application of a ling
inductor. This was in-
vented by Prof Pacinotti
in 186?, and is known
as Paciiwtti's 7-i)ig. It
was applied by him to-
an electromagnetic motor, but he showed that it could be used as a mag-
neto-electrical motor. The same principle was discovered several years

Fig. 891.

-917j

Paa'iiotti's Rino;. GTamine^s Machine.

911

Fig. 392.

later, it would appear quite independently, by M. Gramme, and utilised

by him in the construction of a new form of magneto-electrical machine.

This differed from all previous forms in giving at once direct, and what are

practically continuous currents, and

which, having regard to the size of the

machine, M^ere more powerful than any

hitherto obtained. A laboratory form

of Gramme's machine is represented in

fig. 891, in about | of the real size. On

a base is fixed vertically a powerful

Jamin's magnetic battery, A (fig. 891),

constructed of 24 steel plates, each i mm.

in thickness, then separately magnetised

to saturation. To the poles are

affixed two soft iron armatures a and ^,

between which an axle is rotated by

means of a wheel and rackwork. On

this axle is a ring on which are wound

a series of thirty coils. The ring or

core is not solid, but itself consists of a coil of a number of turns of soft iron

wire, as seen in fig. 892, and in this way the changes in its magnetisation

which take place are far more rapid, and the heating effect due to these

rapid changes is less ; the wire is continuous, and the two ends are soldered

together.

On this core are wound the coils BCD ; they are united by thin brass
knee-plates, ;//;?, to each of which are soldered the copper wires of two suc-
cessive coils, so as to form a continuous whole. The plates are insulated
from each other, and are fixed on a wooden block <?, mounted on the axis
of rotation. The branches mn of the knee-plates form a sheath about this
axis, and two flat brushes of copper wire, fixed to the binding screws c and z,
are in contact with the upper and lower parts of this
sheath, and receive the currents which originate in the
coils.

In order to understand the action of Gramme's ma-
chine, let us now consider the condition of a soft iron
ring which is placed between the two opposite poles of
a powerful permanent magnet, at the opposite ends of
a diameter of the ring (fig. 893). The parts nearest the
magnet will be of the opposite polarity to that of the in-
ducing magnet. We may consider that under its in-
fluence each half of the ring is converted into a magnet
with its two poles and neutral line. The same poles of
the ring face each other, and the effect is not altered if
the ends touch. Let us now suppose the ring fixed,
and that a thin coil moves round it, starting from the neutral line,
nears the pole j^, a current on approach will be induced in the coil
opposite direction to that which, on Ampere's hypothesis, circulates round
the end of the pole s ; as it passes over the other half s, a leaving current
is produced, which is in the same direction as that Avhich circulates round .\- ;

912 Dynamical Electricity. [917-

but it must be remembered that as these poles face one another, their
Amperian currents are in opposite directions, the result of which is that the
currents induced on approaching s and on leaving s are in the same direc-
tion ; in other words, as the coil circulates in front of the double pole it
will be traversed by a continuous current in the same direction, the strength
of which increases from the neutral point till it comes in front of the poles,
and then diminishes until it is at the neutral point again. The same process
repeats itself in the coil as it approaches the other pole, except that the
current is negative, so that if the collectors are adjusted one on each side of
the neutral point they will collect the opposite currents, and they can be
utilised in an external circuit. What is here true of one coil is true of all
others as they pass in front of the poles ; and as they are all connected
together we get, not so much a series of separate impulses, as a continuous
series of currents. This continuous character of the currents is improved
by the fact that the collector brushes are so arranged as to touch more than
one of the knee-pieces at once.

The ring of course does actually rotate with the coils, and the polarity of
each part is continually changing ; but although this is the case, the position
of the poles remains fixed in space, and the effect is as we have said. It
must be added that the poles of the magnet also act directly on the coils ;
and if we consider the ring as non-magnetic, and only the direct action of
the poles on the coils to operate, it will be seen to be in the same direction
as the action of the ring. Both effects concur then in increasing the strength
and also continuity of the currents.

This apparatus is very powerful ; the smallest size made can decompose
water, and heat to redness an iron wire 20 centimetres in length and a
millimetre in diameter. Masc&rt and Angot determined the electromotive
force of different Gramme's machines by placing in the circuit of the
machine, but in opposition to it, a number of Daniell's elements. The
velocity of rotation was then increased until a galvanometer in the circuit
was not deflected. When this was the case, seeing that the resistance
traversed by the opposing currents was the same, it is clear that the electro-
motive force due to the machine rotating at the given speed is exactly equi-
valent to that of the corresponding number of elements. Thus, for instance,
the current from 3 Daniell's cells was found to neutralise that of a particular
hand Gramme's machine rotating with a velocity of 10-2 turns per second.
The average electromotive force due to this machine was found equal to 0-27
of a Daniell for a velocity of i turn per second. With another the ratio
was 0-31, and with others again as much as o-8 of a Daniell.

It will be seen from the description that the action of the ring inductor is
not inconsistent with the application of the dynamo-electrical principle ; and
in the larger machines it is applied, and the rotation effected, by steam or
gas engines or by water power. The dimensions and details of the construc-
tion vary with the purpose for which the machine is designed. Thus in a
machine which is to be used for electrolysis, the coils in the ring inductor
are made up of a comparatively short length of insulated upper bands, while
for the electric light a long length of fine insulated wire is used.

Gramme's machine is reversible ; for while by its means motion is con-
verted into electricity, it can in like manner convert electricity into motion.

-918]

Siemens' Dynamo-electrical Machine.

913

This may be seen by connecting the binding screws c and / with the poles
of a Grove's battery. This iron core then becomes magnetised by the
action of the current passing through the coils ; the whole system rotates
rapidly under the influence of the magnetised bundle.

918. Siemens' dyoamo-electrlcal machines. — Fig 894 represents the
essential features of one of the small-sized vertical machines made by
Messrs. Siemens. A character-
istic is the cylindrical or drum
armature, which may be re-
garded as an extension of that
already described (914). The
electromagnets MM and M'M'
with double poles feed the mag-
netism of the soft iron arma-
tures NN, which are bent so
as to almost completely encircle
the inductor ; they are in de-
tached pieces, so that air can
freely circulate between them,
and thereby the temperature be
kept down.

The inductor itself, D, con-
sists of a drum-shaped frame of
soft iron wire covered with a
layer of insulating material, and
fixed to an axle which rests in the strong upright supports, and is rotated by
means of power transmitted to the sheave A. The wire is coiled on this ;
one end is attached to a plate which forms part of the collector, as in
Gramme's machine ; it passes lengthwise round the drum in several turns,
and the other end is attached to a similar piece on the collector, which is
diametrically opposite the first. The wire is continuous, the connection of
the individual strands being effected by means of the collector. On the
collector rest two pairs of brushes, b b, and b' b' ; they are connected re-
spectively with insulated binding screws ; from these the current passes
through the wires of the electromagnet, and thence to the terminals,/^',
where it may be utilised in the external circuit.

The advantage of this construction is that from the length of the inductor
the wires are moving in a more extended field ; and being on the surface,
and quite close to the armature of the field magnets, are more under their
influence.

A small machine of this kind, which does not occupy a space of more
than three cubic feet, and rotating with a velocity of 15 turns in a second,
which is effected by U horse-power, can produce a light of 1,400 candles.
The larger sizes produce far more powerful effects, but require of cb"urse
greater power to work them.

Machines of this class give continuous currents. A kind is constructed
for alternating currents ; it consists of a combination of two machines, one
of which is on the dynamo principle, as in the above case, while the other is
analogous to the magneto-electrical machine.

914 Dynamical Electricity. [919-

919. Brush dynamo-electrical machine. — The armature of this ma-
chine (fig. 895) is ring-shaped, and has some resemblance to Gramme's,
but the coiling is different. The section of the ring is rectangular (fig. 896),.

and there are deep rectangular grooves in it, in which are the coils of wire
eight in number. The projecting cheeks thus formed between the coils form
polar appendices, which are intended to act laterally on the coils. These
cheeks are traversed by deep horizontal grooves, and also by a large and
deep vertical groove, which almost divides the ring into two parts. By this

means the formation of local cur-
rents is hindered, and a greater
cooling surface is obtained.

The ring rotates between the
four poles of two very powerful
electromagnets, M and M', whose
soft iron armatures are prolonged
in pole plates, N and S, double poles
*''«-^96. Fig. 897. being adjacent. "

On the collector are four rings (fig. 897-. Each ring consists of two seg-
ments, A B, separated from each other at one end by an air space, while
between the others is a smaller segment, C, called the ' insulator.' During
the rotation one pair of coils is in the neutral position, in which no electro-
motive force is being developed in it. In this position the coils only repre-
sent a resistance, and their presence in the circuit is a pure loss. The
contacts are so arranged that the moment the pair is in this position, which
is at each quarter of a rotation, one of the brushes touches the insulator,
and is thus not only removed from the circuit, but, not being closed, no
current can circulate in it.

One end of each coil is connected with one end of the coil exactly
opposite it, the other ends being connected with one of the four commutator
rings where they are connected to isolated segments. From these segments
the current of the two coils is taken off by brushes arranged horizontally and

-919a]

Classification of Dvnaino Machines.

915

in connection with curved spring bands, which lead it to the binding screws,
from which it passes into thd external circuit.

In a machine of this kind which gives 16 arc lights the ring is half a
metre in diameter, and each of the 8 coils contains 275 metres of cotton-
covered copper wire 2 mm. in diameter, and weighing 10 kg. Each pair of
coils has a resistance of ih ohms, and the electromagnets have a resistance
of 6 ohms^o that the total internal resistance is 12 ohms.

In any such machines, the strength of the current which it produces is
proportional to the strength of the magnetic field, and with a given armature
to the speed of rotation, or to the number of lines of force cut in a given
time (826) ; and is inversely as the resistance of the circuit. The strength
of the magnetic field in a magneto machine depends on the strength of the
permanent magnets which form the field, and when these are electromagnets
and are separately excited, on the strength of the magnets by which they are
excited. With dynamo machines the strength of the field magnets is a func-
tion of the current which it itself produces in the coils of the electromagnet,
and the strength of this current depends on the resistance of the circuit, the
external part of which is liable to frequent variations from accidental causes.
Hence dynamo machines are more irregular in their action than magneto
machines, which are therefore to be preferred where steadiness is required.
With both classes of machines the most favourable results are obtained
with the larger sizes.

919^?, Classification of dynamo machines. — The principal types of
dynamo machines arc depicted in figs. 898-901. Fig. 898 represents a machine
in which the wires from a separate
machine excite the field magnets, and
this type is known as the separately
excited machine ; Wild's machine (fig.
886) is an example of this class.

Fig. 899 represents the original
form of the dynamo ; the current from
the armature passes directh- from (ine
brush into the wire of the field magnet,
from thence into the external circuit,
returning to the armature by the other
brush ; such machines are said to be
series wound. This mode of winding
has the defect that variations or breaks
in the external resistance ha\e a much greater effect on the current than in
magneto machines ; for the E.M.F. in these is constant for a given speed of
rotation, and alterations in the external resistance only affect the current in
accordance with Ohm's law. With the series machine the E.M.F. itself
is lessened if the external resistance is doubled, for instance, for a weaker
current now circulates in the field magnets, and the magnetic field in which
the armature rotates is thereby \\eaker. Accordingly the current becomes
much less than half what it was. If, further, the current is completely stopped,
the field magnets almost entirely lose their magnetism, and a considerable
time elapses before their magnetism is again excited. Complete stoppages
also reverse the polarity of the magnets in consequence of the production of

3 N 2

Fig. 809.

gi6

Dynamical Electricity.

[919a-

Fig. 900.

Fig. goi.

polarisation currents, and accordingly when a steady current is required as
in electroplating, or in charging an accumulator (849), such machines are
not used.

A third type is that represented in fig. goo, and is known as the shmit
wound dynamo ; the current at the armature divides at B, one portion passes

through the wire of the field magnet,
which is long and thin, and the other
through the external circuit — for in-
stance, an electroplating bath. If a
total break occurs in this circuit the
effect is that a more powerful current
passes through the field magnets,
which are thus again in readiness to
act when the circuit is restored. An
increase in the resistance of the ex-
ternal circuit has but small effect ; for
if the E.M.F. remained constant, the
current would only diminish in accord-
ance with Ohm's law, and as a rela-
tively larger proportion now goes through the field magnets, the latter are
more strongly excited, and the current again increased ; the latter is, in
short, lessened in a smaller degree than that in which the resistance is
increased. Such machines are used for electroplating and other qlectrolytic
work.

The <;^;;//(?z^/;^/ w^?/;/c/ dynamo is represented in fig. 901. Consider one
wire as in the ordinary series wound machine, and in addition to this a
second long thin wire from B passing round the field magnets to the other
brush at B'. This machine is used for feeding a number of glow lamps which
are inserted in parallel, and for which it is essential that the difference of
potential is constant. If now a number of these lamps are removed the re-
sistance in the circuit of the stout wire is increased, and the current would
be lessened, partly from Ohm's law and partly from the weaker magnetism,
whereby the difference of potential would be less, and possibly to such an
extent that the lamps would not glow ; but with the compound winding a
greater proportion of the current now passes through the thin wire, and thus
acts more strongly on the magnetism. By a suitable choice of the resistances,
and the relative number of turns of the wires, the increase of the magnetisation
can be made so great that the diminution in the difference of potential is
thereby compensated.

920. Applications of magrneto and dynamo-electrical macbines. —
Magneto-electrical machines with lonstant currents arc a triumph of modern
times; from their discovery, together with that of the dynamo principle (946),
is dated the introduction of electricity for industrial purposes. Great improve-
ments have of late been made in magneto-electrical machines, both in the
economy and simplicity of their construction, and also in their power ; for
details on these matters we must refer to special technical works.

The energy of any electrical current or |)ortion of an electrical current is
measured by the product of the electromotive force, E, or difference of poten-
tials at the ends of the portion considered, into the strength of the current

-920J Applications of Dynamo-electrical lilacJiines. 917

itself. The magnitude represented by an electromotive force of a volt, V,
multiplied by a current strength of an ampere, A, is called a volt-ampere^
and from its great practical utility has got a special name, that of Watt
(964). A volt-ampere is equivalent to a watt, but the two are not identical ;
the former is the measure of the electrical, and the latter of the mechanical
effect which can result from the electrical, that is, can be transformed into it.
A horse-power is equal to 746 watts, or a watt is 0-0134 of a horse-power.
Hence, if we know the number of watts produced in any circuit, this divided
by 746 gives at once the equivalent in horse-power. The kilowatt is the
Board of Trade unit of electrical energy ; it is 1000 watts or i^ horse-power.

A magneto-electrical machine may be compared to a pump forcing water
through a pipe against friction ; the electrical current corresponds to the
volume of water passing in a second, and the electromotive force corresponds
to the difference in pressure on the two sides of the pump. Just as the
power of a pump is measured by the product of the pressure, and volume of
water per second, so the product of the electromotive force and current is
power, and the ratio of this power to the mechanical power expended in
driving the magneto-electrical machine is the efficie?icy of the magneto-
electrical machine. The peculiarity of the dynamo-electrical machine is
this, that the electromotive force, or the element corresponding to difference
of pressure in the case of a pump, depends directly on the current passing.
It does not increase indefinitely with increase of current, but increases to a
certain limit, and then remains constant.

Dr. Hopkinson made a series of experiments with a machine of Siemens'
construction, where special arrangements were made for determining the
speed at which the machine was driven, the driving power, the resistances
in the circuit, and the difference in potential between the two ends of a known
resistance in the circuit. He thus found that to drive the machine in open
circuit at a speed of 720 rotations required an expenditure of 0-28 horse-
power. Exclusive of friction, the efficiency of the machine was found to be
about 90 per cent., so that in this respect little improvement can be expected.

If the relation between the electromotive force measured in volts (814),
and the strength of the current measured in amperes (814), for a given speed
of rotation be expressed by a curve, it is found that this curve has the form
of a slanting straight line starting from the origin, and then begins to bend
away, approaching a horizontal line. The point at which it begins to bend
away is when the electromotive force is about two-thirds of its maximum,
and this is called by Hopkinson the criticat current : it has this physical
meaning, that below this point any change in the speed of rotation, with a
steady external resistance, or any change in the external resistance, with a
constant speed of rotation, produces considerable changes in the current.

The principal application which has been made of the currents produced
by dynamo machines is to the production of the electrical light (837). In
this respect it may be said that the arrangements for producing the electricity
are more perfect than those for producing the light ; for while over 90 per
cent, of the mechanical power used appears in the form of current, only about
half of that which is transmitted to the machine appears in the electrical arc.

For electrodes of a definite material, kept at a definite distance apart,
and under the ordinary atmospheric pressure, the difference of potential is

91 8 Dynamical Electricity. [920-

approximatcly constant tor a constant speed of rotation. The product of
difference of potential into the current passing, is the work developed in the
arc, and the ratio of this, to the mechanical power expended in driving the
machine, is the efficiency of tJte electrical arc.

Comparing together the relative costs of producing a certain degree of
illumination— ci;, by means of gas ; b., by the electrical arc with alternating-
currents ; c, by one with continuous currents, the machines for the production
of the last two being worked by a gas engine — it was found that the ratio
was as ii6 : 62 : 15 ; when the machine was heated by coal instead of gas
the cost was as 116 : 50 : 10, it being assumed that four pounds of coal pro-
duced one horse-power per hour. The actual cost of lighting the British
Museum with a light representing 18,800 candles was six shillings an hour,
of which the carbons cost nearly one-half.

Hopkinson gives the following illustration of the luminous effect produced
by converting energy into heat in a closed space. One hundred and twenty
feet of what is called 15-candle gas (509) produce a light of 360 standard candles
for an hour. The heat produced in this combustion is equivalent to about 60
millions of foot-pounds (484). If this gas be burned in a gas-engine (476) about
8 million foot-pounds of work will be done outside the engine, or 4 horse-
power for an hour (472). This power is sufficient to drive an A Gramme
machine for an hour ; the amount of energy which is converted into current
is 6,400,000 foot-pounds, of which about one-half, or 3,200,000, appear in the
form of energy in the electric arc. Viewed horizontally this radiates a light
of 2,000 candles, and two or three times as much when viewed from below.
Hence about 3 million foot-pounds changed into heat in the electric arc will
affect our eyes six times as powerfully as 60 millions changed into heat in a
gas burner.

Both for arc and incandescent lamps the relative efficiency is greater the
higher the illuminating power. Thus with ;i Swan lamp of 16 candles the
work required for each candle-power is 272 candles for a horse-power, or
about 2^^ watts, while with a 32-canclle lamp the number of candles equiva-
lent to a horse-power is 415.

Although the temperature of the electric arc is exceedingly high'(838), yet
from the small amount of racHating surface the heating effect is far less than
that produced by other sources of equal illumination. Thus Siemens found
that an electric arc light of 4,000 candles radiated 142-5 thermal units in a
minute, while to produce this light by gas would require 200 Argand burners,
•which would emit 15,000 units, or over a hundred times as much. So too it
has been found that incandescent lamps produce less than five per cent, of
the heat from other sources of equal intensity as regards this light.

Siemens made a series of experiments on the influence of the electrical
light on vegetation. The light was produced by a dynamo-electrical machine
of his construction, and was equal in illuminating powcrto 1,400 candles. Of
a series of four sets of quickly growing plants in pots, one set was left in the
dark, and two other sets were exposed to the action of the daylight and of
the electric light separately; while the fourth was exposed to the joint action
of the two lights. The first set sowed withered and died ; those exposed to .
the electric light grew and flourished, but not so vigorously as those exposecf
to daylight alone ; those, however, which had been exposed to the conjoint

-920] Applications of Dynamo Machines. gig

action of both lights, showed the most vigorous growth. Plants did not
seem to require a period of repose, but made increased and vigorous pro-
gress if subjected at daytime to sunlight, and by night to the electric light.

The electric light was also found beneficial in promoting the formation of
aromatic and saccharine substances on which the ripening of fruits depends.

Abney found that the luminosity and also thj actinic action of the light
produced by the electric arc increased more rapidly than in direct ratio to
the velocity of rotation, and the horse-power required to produce it. This
increase was slowest for red light, more rapid with blue, and most rapid
of all with tlie actinic action. With a speed of 565 rotations, and an ex-
penditure of 9 horse-power, the actinic action was equal to that of 1 1,000
candles.

Cohn f )und that the electrical light is more favourable for the pure per-
ception of colour than any other light of equal luminosity.

Electrical furnace. — It is probable that the temperature which can be
produced by the oxyhydrogen flame is limited and has been already reached,
ani that we must look to the electrical arc for the production of higher
temperatures than those at which carbonic acid and water are decomposed.^
Direct experiments by Siemens with the electric arc show not only that it
produces a very high temperature withm a contracted space, but also that
it will conveniently and economically produce such larger effects as will
render it useful for many purposes in the arts, like the fusion of platinum
and steel. He constructed an arrangement by which the electric arc was,
formed within a crucible made of the most refractory materials ; the one
electrode passed through the bottom of the crucible and the other through
the lid, and there was an arrangement by which the distance of the elec-
trodes could be automatically regulated ; another important point was to
constitute the positive pole of the material to be fused, as it is at this pole
that the heat is principally developed, the arrangement formed in short an
electrical furnace. A dynamo machine capable of producing a current of
36 amperes, and which produces a light equal to 6,000 candles, fused a
kilogramme of steel within half an hour. vSiemens calcu ated that the heat
in his furnace represented J of the horse-power expende.l in working the
machine ; and as a good engine onl-/ utilises about ,'. of the combustible
value of the coal employed m working it, it follows that the electrical
furnace utilises l^ of the energy residing in the fuel under the engine. The
electrical furnace is theoretically more economical than the ordinary air
furnaces. Not only is the furnace thus a source of intense heat, but in
certain operations the reducing action of the electrodes plays an important
part, as in Cowle's method for the direct production of aluminum bronze.
A charge of 35 kgr. powdered corundum, an aluminous mineral mixed with
powdered charcoal and twice its weight of granulated copper, was placed
between carbon electrodes in a suitable vessel. On passing a powerful
current the alumina was reduced and united directly with the copper to
form aluminum bronze. The current actually employed was one of 5,000
amperes with an E.M.F. of 50 volts, or with a power of 500,000 watts-
second. The current was continued for an hour and a half, and produced
about 82 kgr. of the alloy. Each kgr. of akiminum in the alloy represents
a work of 44 horse-power for an hnir.

920 Dynamical Electricity. [920a-

920(?. Electrical transmission of power. — When a magneto or dynamo
machine is couple 1 up with a second one, on working the first the second
is put in rotation, and in a direction opposed to that of the first. Two such
machines coupled in this way are called Xho^ generator and the motor. This
motor may be geared up with any machine, such as a saw wheel, a lathe, or
a pump, which is thereby made to do its special work. On this depends
the possibility of transmitting by electricity to great distances power from a
common centre, and of thereby utilising natural sources of power, such as
waterfalls, windmills, and the like.

The efficiency of any magneto machine, as we have seen, is the ratio of
the energy 7v' developed in the machine to the mechanical power w, expended
in producing it. Apart from friction, more than 90 per cent, of the power
can be thus converted ; if such a machine works on short circuit the whole
of this energy would appear as heat ; when external work is done, such as in
producing the electric light, the energy is shared between the various parts of
the circuit, and the amount of this energy in any part can be easily obtained
if we know the fall of potential between the part in question and the current
wiiich is passing.

When a motor is connected with a generator at work, the former is set
in motion, and in a direction opposed to that of the generator ; it thereby
developes an electromotive force expressed in volts of v, opposed to that of

VA
the (generator V. The total work W of the venerator in unit time is

746

horse-power. Part of this work appeals in the heating of the conducting

vA.
wires, and the rest in the form of the energy of the motor w, which is

746

h.p., where t> is the difference of potentials at the two terminals of the

machine. The ratio ^-' = ^, that is, the work of the motor, is to that of

W V
tlie generator in the ratio of their electromotive forces, in other words, to
the differences of potentials at the respective terminals. In practice the best
conditio 1 of working is to arrange so that the generator has twice the electro-
motive force of the motor, the current being, of course, the same in each.

In some experiments as much as 4.} horse-power has been electrically
transmitted through eight miles of an ordinary galvanised iron telegraph line
4 mm. in diameter, and with an efficiency of o\er 30 per cent, of the
mechanical power employed.

The magneto-electrical machine has been applied to propelling car-
riages along a railway. A narrow-gauge railway was laid down, and upon
this a train of three or four carriages was laid, and on the first of these
a medium-sized dynamo machine, so fixed and connected with the axle of
one pair of wheels as to give motion to the same. The two rails, being laid
ujjon wooden sleepeis, were sufficiently insulated to serve for electrical con-
du( tors. Between the two rails a bar of iron was fixed on wooden supports,
through which the current was conveyed to the train by brushes fixed to the
di i\ ing carriage, while the return circuit was completed through the rails.
At the station the centre bar and rails were electrically connected with '
liie poles of a dynamo machine like that on the carriage, and which was
worked from a fixed steam-engine on the ground. The magneto machine

-921]

Inductorium. RuJinikorff' s Coil.

921

exerted 5 horse-power, and it travelled with a velocity of 15 to 20 miles
an hour.

Another application is to what is called tclpJicragc. by which is meant
a means of propelling- light carriages or buckets along a single metal rope
or rod, supported on posts at some height above the ground. A working-
line has been already constructed and used with success, and this method of
electrical haulage will probabl)- be of great service in con\eying minerals in
mountainous countries, from the facility with which it can be constructed on
uneven ground, and particularly in those cases in which water supply is
available.

921. Inductorium. RubrnkorfTs coil. — These are arrangements for
producing- induced currents, in which a current is induced by the action of
an electric current, whose circuit is alternately opened and closed in rapid
succession. These instruments, known as mductoriutns, or induction coils,
present considerable variety in their construction, but all consist essentially
of a hollow cylinder in which is a bar of soft iron, or bundle of iron wires,
with two helices coiled round it, one connected with the poles of a battery,
the current of which is alternatelj' opened and closed by a self-acting arrange-
ment, and the other serving for the development of the induced current. By
means of these apparatus, and with a current of three or four Grove's cells,
physical, chemical, and physiological effects are produced equal and superior
to those obtainable with electrical machines and even the most powerful
Leyden batteries.

Of all the forms those constructed by Ruhmkorff are the most powerful.
Fig. 902 is a representation of one, the coil of which is about 14 inches in

P'ig. 902.

length. The pritnary or inducing wire is of copper, and is about 2 mm. in
diameter, and 40 or 50 yards in length. It is coiled directly on a cylinder of
cardboard which forms the nucleus of the apparatus, and is enclosed in an
insulating cylinder of glass, or of caoutchouc. On these is coiled the sccondaiy
or induced wire, which is also of copper, and is about \ mm. in diameter.
.\ great point in these apparatus is the insulation. The wires are not merely
insulated by being in the first case covered with silk, but each individual
coil is separated from the rest by a layer of melted shellac. The length of
the secondary wire varies greatly ; in the largest size hitherto made, that of
the late Mr. Spottiswoode, it is as much as 280 miles, while the primary was

922

Dynamical Electricity.

[921-

II 64 yards. With these great lengths the wire is thinner, about \ mm.
The thinner and longer the wire the higher the potential of the induced
electricity.

The following is the working of the apparatus :— The current arriving by
the wire P at a binding screw, «, passes thence in the commutator C, to be
afterwards described (fig. 905), thence by the binding screw b it enters the
primary wire, where it acts inductively on the secondary wire ; having tra-
versed the primary wire, it emerges by the wire s (fig. 903). Following the
direction of the arrows, it will be seen that the current ascends in the
binding screw z, reaches an oscillating piece of iron, <?, called the hnmtiier,
descends by the anvil h, and passes into a copper plate, K, which takes it
to the commutator C. It goes from there to the binding screw c, and finally
to the negative pole of the battery by the wire N.

The current in the primary wire only acts inductively on the secondary
wire (901), when it opens or closes, and hence must be constantly in-
terrupted. This is effected by means of the oscillating hammer o (fig. 903).
In the centre of the bobbin is a bundle of soft iron wires, forming together a
cylinder a little longer than the bobbin, and thus projecting at the end as
seen at A. When the current passes in the primary wire this hammer, o,
is attracted ; but immediately, there being no contact between o and h, the
current is broken, the magnetisation ceases, and the hammer falls ; the
current again passing, the same series of phenomena recommences, so that
the hammer oscillates with great rapidity.

922. Condenser. — In proportion as the current passes thus intermittently
in the primary wire of the bobbin, an induced current, alternately direct

and inverse, is produced at each
interruption in the secondary wire.
But as this is perfectly insulated,
the induced current requires such a
strength as to produce very power-
ful effects. Fizeau increased this
strength still more by interposing
a condenser in the primary circuit.
This condenser (fig. 904) con-
sists of sheets of tinfoil placed over
each other and insulated by larger
slieets of stout paper, 7/, soaked in
paraffinc or resin. The sheets of
tinfoil project at the end of the
paper, one set at j s' s'\ and the other at the other end, at e e' e", so that
when joined by a binding- screw the odd numbers form one coating of a
condenser, and the even numbers the other coating. In large condensers,
tlic surface of each condenser is as much as 75 square yards. The whole
Ixing placed in a box at the base of the apparatus, one of the coatings,
the positive, is connected with the binding screw z, which receives the
current on emerging from the bobbin ; and the other, the negative, is con-
nected with the binding screw w, which communicates by the plate K with
the commutator C, and with the battery.

To understand the effect of the condenser, it must Ijc observed that at

Fig. 903.

Fig. 904.

-923] Condenser of Rulimkorff's Coil. ' 923

each break of the inducing current an extra current is produced in the same

direction, which, continuing in a certain manner, prolongs its duration. It

is this extra current which produces the spark that passes at each break

between the hammer and the anvil ; when the current is strong this spark

rapidly alters the surface of the hammer and an\il, though they are of

platinum. By interposing

the condenser in the inducing /~

circuit, the extra current, in- ^ ^I

stead of producing so strong

a spark, passes into the , _ _

condenser — the positive s^^ ~ --

electricity in the coating « ^0^

connected with /, and the

negative in that connected

with ;//. But the opposite electricities combining quickly by the thick wire of

the primary coil, by the battery, and the circuit C K ?n, give rise to a current

contrary to that of the battery, which instantaneously demagnetises the

bundle of soft iron : the induced current is thus shorter and more intense.

The binding screws m and ?? on the base of the apparatus are for receiving

this extra current.

The commutator or key serv^es to break contact or send the current in
either direction. The section in fig. 905 is entirely of brass, excepting the
core. A, which is of ebonite : on the two sides are two brass plates, C C.
Against these press two elastic brass springs, joined to two binding screws,
a and c, with which are also connected the electrodes of the battery. The
current arriving at a rises in C, thence by a
screw, _y, it reaches the binding screw b and the
bobbin : then returning by the plate K, which
is connected with the hammer, the current goes
to C by the screw x, descends to c, and rejoins
the battery by the wire N. If, by means of the
milled head, the key is turned 180 degrees, it
is easy to see that exactly the opposite takes
place ; the current reaches the hammer by the
plate K and emerges at b. If, lastly, it is only

turned through 90 degrees, the elastic plates ■" . :-!a JSjJiM'^

rest on the ebonite A instead of on the plate Fig. 905.

C C, and the current is broken.

The two wires from the bobbin at 0 and o' (fig. 902) are the two ends of
the secondary wire. They are connected with the thicker wires P P', so
that the current can be sent in any desired direction. With large coils the
hammer cannot be used, for the surfaces become so much heated as to melt.
But P'oucault invented a mercury contact-breaker which is free from this
inconvenience, and which is an important improvement. Very powerful
discharges were obtained by Spottiswoode from his coil by disconnecting
the contact-breaker and sending into it the alternate currents of a powerful
magneto-machine.

923. Efifects produced by Ruhinkor£°'s coil. — The high potential of
the electricity of induction coils has long been known, and many luminous

924 ' Dynamical Electricity. [923-

and heating effects have been obtained by their means. But it is only
since the improvements which Ruhmkorff introduced into his coil, that
it has been possible to utilise all the potential of induced currents, and to
show that these currents possess po\verful statical as well as dynamical
properties.

Induced currents are produced in the coil at each opening and breaking
of contact. But these currents are not equal either in duration or in
potential. The direct current, or that on opening, is of shorter duration, but
higher potential ; that of closing of longer duration, but lower potential.
Hence if the two ends P and P' of the fine wire (figs. 902 and 903) are con-
nected, as there are two equal and contrary quantities of electricity in the
wire the two currents neutralise each other. If a galvanometer is placed in
the circuit, only a very feeble deflection is produced in the direction of the
direct current. This is not the case if the two ends P and P' of the wire are
separated. As the resistance of the air is then opposed to the passage of the
currents, that which has highest potential — that is, the direct one or that on
opening — passes in excess, and the more so the greater the distance of P
and P' up to a certain limit at which neither passes. There are then at P
and P' nothing but potentials which are alternately contrary.

A striking distance of i mm. (788) corresponds to an electromotive force
of 5,490 volts, and the striking distance of I inch which is furnished by even
a small machine represents a potential of over 70,000 volts. How enormous
must then be the potential of Spottiswoode's larger machine.

The physiological effects of Ruhmkorff's coil are very powerful ; in fact,
shocks are so violent that many experimenters have been suddenly pros-
trated by them. A rabbit may be killed with two of Bunsen's elements, and
a somewhat larger number of couples would kill a man.

The heating effects are also easily observed ; an air thermometer is
heated by the alternating currents ; if a veiy fine iron wire is interposed
between the two ends P and P' of the induced wire, this iron wire is imme-
diately melted, and burns with a bright light. A curious phenomenon may
here be observed, namely, that when each of the wires P and P' terminates
in a very fine iron wire, and these two are brought near each other, the wire
corresponding to the negative pole alone melts, showing that its temperature
is higher.

The chemical effects are very varied ; thus, according to the shape and
distance of the platinum electrodes immersed in water, and to the degree of
acidulation of the water, either luminous effects may be produced in water
without decomposition, or the water may be decomposed and the mixed
gases disengaged at the two poles, or the decomposition may take place, and
the mixed gases separate either at a single pole or at both poles.

Gases may also be decomposed or combined by the continued action of
llie spark from the coil. If the current of a Ruhmkorff's coil be passed
through an hermetically sealed tube containing air, as shown in fig. 906,
nitrogen and oxygen combine to form nitrous acid.

The luminotts effects of Ruhmkorff's coil are also \cry remarkable, and
vary according as they take place in air, in vapour, or m very rarefied
vapours. In air the coil produces a very bright loud spark, which, with the
largest sized coil hitherto made, that of Mr. Spottiswoodc, has a length of 42

Effects produced by Ruhmkorff's Coi\.

-923] njjects produced Oy Kunmkorff's Loi.. 925

inches. In vacuo the effects are also remarkable. The experiment is made
by connecting the two wires of the coil P and P' with the two rods of the
electric ^^-g (fig. 722) used for producing in vacuo the
luminous effects of the electrical machine. Exhaustion
having been produced up to i or 2 mm., a beautiful
luminous trail is produced from one knob to the other,
which is virtually constant, and has the same intensity
as that obtained with a powerful electrical machine when
the plate is rapidly turned. This experiment is shown
in figs. 911 and 912. Fig. 910 represents a remarkable
•deviation which light undergoes when the hand is pre-
sented to the &gg.

The positive pole of the current shows the greatest
brilliancy ; its light is of a fiery red, while that of the
negative pole is of a feeble violet colour ; moreover, the
latter extends along all the length of the negative rod,
which is not the case with the positive pole.

The coil also produces mechanical effects so powerful that, with the largest
apparatus, glass plates two inches thick have been perforated. This result,
however, is not obtained by a single charge, but by several successive charges.

The experiment is arranged as shown in fig. 907. The two poles of the
induced current correspond to the binding screws a and b ; by means of a

Fig. go6.

Fig. 907.

copper wire, the pole a is connected with the lower part of an apparatus for
piercing glass like that already described (fig. 728) ; the other pole is attached
to the other conductor by a wire, d. The latter is insulated in a large
glass tube, r, filled with shellac, which is run in while in a state of fusion.
Between the two conductors is the glass to be perforated, V. When this
presents too great a resistance, there is danger lest the spark pass in the coil
itself, perforating the insulating layers which separate the wires, and then
the coil is destroyed. To avoid this, two wires, e and r, connect the poles of
the coil with two metallic rods whose distance from each other can be regu-
lated. If then the spark cannot penetrate through the glass, it strikes across,
and the coil is not injured.

926

Dyn a in ical Ekctricit) '

[923

The coil can also be used to charge Leyden jars. With a large coil
giving sparks of 6 to 8 inches, and using 6 Bunsen's elements with a large

Fig. 908.

surface Ruhmkorff charged large batteries of 6 jars each, having about 3
square yards of coated surface.

The experiment with a single Leyden jar (fig. 908) is made as follows : —
The coatings of the latter are in connection with the poles of the coil by
the wires d and /, and these same poles are also connected, by means of
tlie wires e and c, with the two horizontal rods of a universal discharger

(fig. 713). Tlie jar is then being constantly charged l)y tlic wires / and c/,
sometimes in one direction and sometimes in another, and as constantly
discharged by the wires c and c ; the discharges from »i to // taking place as
sparks two or three inches in length, very luminous, and producing a deafen-
ing sound ; they can scarcely be compared with the sparks of the electrical
machine, but are rather true lightning flashes.

To charge a battery, the form of tlic experiment is somewhat varied, the
outer coating being connected with one pole of the coil by the wire d, and

-924] Stratification of the Electric Light. 927

the inner coating with the other by the rods in n, and the wire c (fig-. 909).
The rods in and ;/ are not, however, in contact. If they were — as the two
currents, the inverse and direct, pass equally — the battery would not be
constantly charged and discharged ; while from the distance between m and
;/ the direct current, that of breaking, which has higher potential, passes
alone, and it is this which charges the battery.

923 u. Transformers. — Ruhmkorff's coil, as we have seen, is an arrange-
ment by means of which we can transform electricity of low into electricity
of high potential. There is no creation of electricity ; the energy produced
in the secondary circuit is produced at the cost of that in the primary. The
apparatus acts in short as a transformer., and it is reversible, for if we connect
the long'' thin wire with a source of electricity yielding alternating discharges
at high potential, we get alternating discharges in the short thick wire of low
potential but of much stronger current. The functions of the wires are re-
versed in this case ; the thin long wire is the primary and the short thick
wire the secondary.

This modification of the principle of Ruhmkorff's coil is of great practical
importance in the transmission of electrical energy, as is illustrated by the
following example. Suppose we have a source of energy available of 50,000
watts, for example, and that this is to be transmitted to a certain distance
in the form of electrical energy there to be utilised. Since a watt is the
])roduct of two factors, a volt into an ampere, we may vary these factors
which make up the total in any way we like. Thus the energy may be trans-
mitted and a current of 500 amperes under a pressure of 100 volts. In order
to do this the resistance of the conductor through which the current travels
must be small, which could only be effected by having it of large section and
of good very thick conducting material, that is of copper ; the great weight
of such a conduction makes it both costly and inconvenient.

The energy might, however, also be transmitted in the form of a weak
current, say of 10 amperes, under a pressure of 5,000 volts ; the current
required for this purpose might be very much thinner, and therefore less
costly. But the manipulation of currents of such a potential as this has its
own drawbacks ; the insulation must be very good, and moreover the
manipulation of such currents is attended with great danger. These currents
can then be converted at the place of application into large currents, but of
much lower electromotive force, which is accomplished by means of trans-
formers or converters. One form of such an apparatus consists of a long-
length of fine iron wire coiled so as to form a ring ; the separate turns being
insulated from each other. Round this is wrapped in alternate layers sepa-
rated from each other the carefully insulated primary and secondary wires ;
the whole arrangement closely resembling the ring of Gramme's machine
,'fig. 892).

Lane Fox showed that secondary batteries could l)e used as transformers
for direct currents of high E.M.F.

Hitherto the chief applications have been to the transmission of energy for
electrical lighting.

924. Stratification of the electric light. — Quet observed, in studying
the electric light which Ruhmkorff's coil gives in a vacuum, that if some of
the vapour of turpentine, wood spirit, alcohol, or bisulphide of carbon, &c..

928

Dynamical Electricity.

[924-

be introduced into the vessel before exhaustion, the aspect of the light is
totally modified. It appears then like a series of alternately bright and dark
zones, forming a pile of electric light between the two poles (fig. 911).

In this experiment it follows, from the discontinuity of the current of
induction, that the light is not continuous, but consists of a series of dis-
charges which are near each other in proportion as the hammer o (fig. 903)
oscillates more rapidly. The zones appear to possess a rapid gyratory and
undulatory motion. Quet considers this as an optical illusion : for if the
hammer is slowly moved by the hand, the zones appear very distinct and
fixed.

Fig. 910.

Fig. 91

Fig. 912

The light of the positive pole is most frct|uently red, and that of the
negative pole violet. The tint varies, however, with the vapour or gas in the
globe.

925. Oelssler's tube«.—The brillianry and beauty of the stratification
of the electric light are most remarkable when the discharge of the Ruhm-
korff coil takes place in glass tubes containing a highly rarefied vapour or
gas. These phenomena, which were originally investigated by (lassiott, arc
produced by means of sealed glass tubes first constructed by Gcissler, of
l?onn, and generally known as Gcissler's tubes. The tubes are filled witii
different gases or vapours, and are then exhausted, so that the pressure does
not exceed half a millimetre. At the ends of the tubes two platinum wires
are soldered into the glass.

When the two platinum wires are conncctetl with the ends of a Ruhm-

-925]

Getsslcrs Tubes.

929

kortTcoil maynificent lustrous striae, separated by dark bands, are produced
all through the tube. These striae vary in shape, colour, and lustre with the
degree of the vacuum, the nature of the gas or vapour and the dimensions
of the tube. The phenomenon has occasionally a still more brilliant aspect
from the fluorescence which the electric discharge excites in the glass.

^ij?- 913 shows the striae in carbonic acid under a quarter of a millimetre
pressure ; the colour is greenish, and the striae have not the same form as
hydrogen. In nitrogen the light is orange-yellow.

Pliicker found that the light in a Geissler's tube did not depend on the
substance of the electrodes, but simply on the nature of the gas or vapour

^~-^^~.

..^ j #^^-— --"^g^^^^^T-"— --^^tti^^-s^^^ay- V

^Hl'iptfMnMViVillWIil^^

i^ii;::ss::*!ir:li:a^

1 ' ^ l

t^ ,— -Tjirr^^r^^ ■■■ BiiSl

^^^^^^^^H

in the tube. He found that the lights furnished by hydrogen, nitrogen,
carbonic oxide, &c., give different spectra when they are decomposed by
a prism. The discharge of the coil which passes through a highly rarefied
gas would not pass through a perfect vacuum, from which it follows that the
presence of a ponderable substance is absolutely necessary for the passage
of electricity.

By the aid of a powerful magnet Pliicker tried the action of magnetism
on the electric discharge in a Geissler's tube, as Davy had done with the
ordinary voltaic arc, and obtained many curious
results, one of which may be mentioned. He found
that where the discharge is perpendicular to the line
of the poles, it is separated into two distinct parts,
which can be referred to the different action exerted
by the electromagnet on the two extra currents pro-
duced in the discharge.

The light of Geissler's tubes has been applied
to medical purposes. A long capillary tube is
soldered to two bulbs provided with platinum wires ;
this tube is bent in the middle, so that the two
branches touch, and their extremities are twisted
as shown at a (fig. 914). This tube contains a highly
rarefied gas, like those previously described, and *'S- 914.

when the discharge passes a light is produced at a, bright enough to illu-
minate any cavity of the body into which the tube is introduced.

930 Dynamical Electricity. [926-

926. 3>e la Rue and IMCuller's experiments. — -These physicists have
made a very extensive and elaborate series of experiments on the stratifica-
tion of the electric light by means of the currents produced by their battery
(812). They employed for some of these experiments as many as 14,400
cells, which is by far the most powerful battery ever put together. It is
impossible to attempt here even a condensed account of these experiments ;
but the following, which are some of the results obtained, may be mentioned.

The discharge in a vacuum tube is essentially of the same nature as that
which takes place in gases under the ordinary atmospheric pressure. A
vacuum tube was interposed in the circuit of a battery of 2,400 cells, to-
gether with a very long resistance. It was found that the potentials at the
two ends of the tube are virtually the same ; now according to Ohm's law
there should be a fall of potential along the entire circuit ; it is accordingly
concluded that the discharge is not a current in the ordinary sense of the
term, but is disruptive, the electricity being carried by the molecules of the
gas. At no degree of exhaustion is air a conductor.

All the strata start from the positive pole. For a definite pressure an
aureole is formed at the positive pole ; with a diminished pressure this de-
taches itself, is succeeded by others, and so on.

One of the most curious results is the definite and stationary character of
the strice for given conditions ; they are remarkably permanent, and seem
almost as if they could be manipulated ; a single stratum may be seen fall-
ing down a tube like a feather in a vacuum, or like a drop of water. They
are not produced in the same way as drops falling, but all and each of the
little strata are so many Leyden jars.

The length of the arc found between two terminals varies with the square
of the number of cells ; thus while 1,000 cells give a spark of 0-0051 inch
under ordinary atmospheric pressure, 11,000 cells give a spark of 0-62 inch.

With an increase of exhaustion the potential necessary to cause a current
to pass diminishes to a certain pressure which represents an exhaustion of
least resistance ; from this it again increases, and the strata thicken and
diminish in number until a point is reached at which no discharge takes
place, however high be the potential.

A change in the current often produces an entire change in the colour of
the stratification, thus in hydrogen the change is from blue to pink. If the
discharge is irregular and the strata indistinct, an alteration in the strength
of the current makes the strata distinct and steady. Even when the strata
are apparently quite steady and permanent, a pulsation may be detected in
the current by means of the telephone.

In the same tube, and with the same gas, a very great variety of phe-
nomena can be produced by varying the pressure and the current. The
peculiar luminosity and form of stratification in their various forms can be
reproduced in the same tube or in others having similar dimensions.

The colour of the discharge in one and the same gas greatly depends on
the degree of rarefaction. The least resistance to the discharge in hydrogen
and when its brilliancy is greatest, is at a pressure of 0-642 mm. or 845 M
(M is a very convenient symbol for the millionth of an atmosphere). When
the rarefaction has attained 0-002 mm. or 3 M, the discharge only just passes
even with a potential of 11,330 volts ; while with an exhaustion of 0-000055

-927] Crookes's Experiments. 931

mm., the nearest approach to a perfect vacuum ever attained, not only does
this fail to produce a discharge, but the i-inch spark of an induction coil
does not pass.

Air offers a greater resistance than hydrogen ; a spark which passes in
hydrogen across a distance of 5-6 mm. will only strike across a distance of
3 mm. in air.

In air at a pressure of 62 mm., which corresponds to an atmospheric heig'^ht
of 12*4 miles, the electric discharge has the carmine tint so often seen in the
display of the aurora borealis (991) ; at a pressure of 1-5 mm., corresponding
to a height of 30'96 miles, it is salmon-coloured ; and at a pressure of 0'8 mm.,
representing a height of 33'96 miles, it is of a pale white. Under a pressure
of 0-379 mm. the discharge has the greatest brilliancy. This represents a
height of 37'67 miles, and would be visible at a distance of 585 miles ; it is pro-
bably the upper limit of the height, though on the other hand it is possible that
the discharge may sometimes take place at a height of a few thousand feet.

927. Crookes's experiments. — Dr. Crookes has made a remarkable
series of experiments on the phenomena produced when the electrical dis-

■FJ^ ^Jr L" i^ k^B

Fig. 913.

charge is produced in tubes very highly exhausted, that is, beyond the point
at which the best effects of the stratification are produced.

When the electrical discharge is passed through a Geissler's tube in
which the exhaustion is as low as 2 mm., the negative pole is surrounded
by a narrow layer, and then by a relatively dark bluish space, the rest of
the tube being filled by layers of reddish-yellow light, separated by dark
spaces ; as the rarefaction proceeds, the bluish light extends, and under cer-
tain circumstances fills the entire tube. Wherever the light strikes against
the glass it excites the brightest fluorescence. But the most remarkable

302

9Z^

Dynamical Electricity.

[927-

feature is that when the vacuum is almost complete the nature of the phe-
nomenon changes. The light now proceeds from the electrode in straight
lines, and does not follow any bends in the tubes. This rectilinear propaga-
tion is well illustrated by the following experiment of Crookes. In fig. 91 5, A,
the negative pole of the induction coil, is connected with the electrode a,
which is made of aluminum, and forms a slightly concave mirror. If the
exhaustion is not more than 2 mm. pressure, and the positive pole is con-
nected successively with the electrodes ^, <:, d^ the discharge takes place in
curved lines as shown in the figure. But when the rarefaction is exceed-
ingly great, about a millionth of an atmosphere, the appearance is that pre-
sented in fig. 915, B. With whatever electrode the positive pole is connected,
the rays proceeding in straight lines cross in the focus, and, striking against
the opposite side, excite there the most brilliant fluorescence.

If a screen of mica of any shape be interposed in the path of the rays it
stops the light on its path, and a shadow is formed at the other end of its own
shape, surrounded by a bright fluorescence.

The discharge can also produce mechanical effects. A Geisslei-'s tube is
constructed with a pair of glass rails in it, on which rolls the axis of a light
wheel, on the spokes of which are mica vanes. If now the discharge be
directed against the top of the vanes, the wheel
moves along towards the positive pole.

The experiment represented in fig. 916 shows the

very great heat which the glow light can produce.

a is the negative electrode in the form of a concave

mirror, b a strip of platinum foil. With a sufficiently

powerful induction coil the platinum can be made

white-hot or even melted.

^^^^_^^^^H Some of the most beautiful of these experiments

fe^T^J^^^^B are those made by directing the discharge on various

^B ^^^^^1 precious stones. In these circumstances diamond

^T ^^^^^H emits a splendid green fluorescence, ruby a brilliant

■ ^I^^^^^H i-cd, emerald a carmine, and so forth.

The electrical discharge does not pass through
a vacuum, as is shown by the following experiment.
A small tube containing caustic potash is fused to
a Geisslei-'s tube connected with a Sprengel pump.
By continual exhaustion while the caustic potash is
being heated, as complete a vacuum as possible is
' '*^' '^"'' made of the tube sealed. The last minute trace of

aqueous vapour is absorljcd l^y the caustic potash as it cools. In this com-
plete vacuum the discharge, however strong, no longer passes ; the vacuum
acts as a complete non-conductor.

If, however, the caustic potash is gently heated, a trace of aqueous vapour
is given off, and a green fluorescent light flashes along the tube ; as the heating
is continued and the vapour becomes denser we get the stratification, until
ultimately the electricity passes along the tube in the form of a narrow
purple line. If the tube is allowed again to cool, the phenomena reproduce
themselves in the reverse order.

The phenomena here described are rcgardctl by Crookes as due to an

-928] Rotation of Induced Currents by Magnets. 933

ttltra-gascous state, which he calls radiant matter. In gas under the ordinary
pressure the average free path of a molecule of air is 0-000095 ni™- 5 as the
gas is more rarefied the length of the path increases, so that with the high
degrees of exhaustion which Crookes employs in his later experiments — as
much as the one twenty-millionth of an atmosphere— the length of the mean
path is so much increased that its dimensions are comparable with those of
the vessel, and along with this increase the number of intramolecular shocks
diminishes in a corresponding ratio. It is to this condition, in which the
molecules move forward with their own motion, and, striking against the sides,
give rise to the fluorescence, that Crookes accounts for the effects produced.

The theoretical views to which Crookes has been led by his experiments
have met with a considerable degree of criticism, and it must be added that
none of the explanations of these singularly beautiful experiments have met
with general adoption.

928. Rotation of induced currents by mag-nets. — De la Rive devised
an experiment which shows in a most ingenious manner that magnets act on
the light in Geissler's tubes in accordance with the laws with which they
act on any other movable conductor.

This apparatus consists of a glass globe or electrical egg (fig"- 91 7), pro-
vided at one end
with two stopcocks,
one of which can be
screwed on the air-
pump, and the other,
which is a stopcock
like that of Gay
Lussac (383), serves
to introduce a few
drops of the liquid
into the globe. At
the other end a
tubulure is ce-
mented, through
which passes a soft
iron rod about |
of an inch in dia-
meter, the top of
which is about the
centre of the globe.
Except at the two
ends, this rod is en-
tirely covered with
a very thick insulat-
ing layer of shellac,
then with a glass
tube also coated with
shellac, and finally
with another glass
tube uniformly coated jvith a layer of wax. The insulating layer must be

934 Dyjianiical Electricity. [928-

at least | of an inch thick. Inside the globe, the insulating layer is sur-
rounded at ;r with a copper ring, connected with a binding screw, f, by means
of a copper wire.

The vessel having been exhausted as completely as possible, a few drops
of ether or of turpentine are introduced by means of a stopcock a; it is
again exhausted, so that the vapour remaining is highly rarefied.

A thick disc of soft iron, c, provided with a binding screw, is then placed
on one of the branches of a powerful electromagnet, and the end in of the
rod mtt is placed on this disc, while at the same time one of the ends of the
secondary wire of Ruhmkorfif' s coil is connected with the binding screw, r,
and the other with the knob, o. If then the coil is worked without setting in
action the electromagnet, the electricity of the wire s passes to the top, ;z, of
the soft iron rod, and that of the second wire to the ring x% and a more or
less irregular luminous sheaf appears on the inside of the globe round the
rod, as in the experiment of the electric &'g'g.

But if a voltaic current passes into the electromagnet, the phenomenon
is different ; instead of starting from different points of the upper surface
;z, and the ring x, the light is condensed and emits a single arc, from
n to X. Further — and this is the most remarkable part of the experiment
— this arc turns slowly round the magnetised c\iinder ;;/;?, sometimes in
one direction, and sometimes in another, according to the direction of the
induced current, or the direction of the magnetisation. As soon as the magne-
tisation ceases, the luminous phenomenon reverts to its original appearance.
This experiment is remarkable as having been devised a priori by De la
Rive to explain, by the influence of terrestrial magnetism, a kind of rotatory
motion, from east to west, observed in the aurora borealis. The rotation of
the luminous arc in the above experiment can evidently be referred to the
rotation of currents by magnets (868).

Geissler has constructed a veiy useful form of the above experiment, in
which the globe is exhausted once for all. Apart from the purpose for which
it was originally devised, it is a very convenient arrangement for demon-
strating the action of magnets on movable currents.

929. Heat developed by tbe Indactlon of powerful magrnets on bodies
In motion. — We have already seen in Arago's experiments (914) that a rota-
ting copper disc acts at a distance on a magnetic needle, communicating to it
a rotatory motion. We shall presently see that a cube of copper, rotating
with great velocity, is suddenly stopped by the influence of the poles of two
strong magnets (938). It is clear that, in order to prevent the rotation of the
needle or of the copper, a certain mechanical force must be consumed in
overcoming the resistance which arises from the inductive action of the mag-
net. Reasoning upon the theory of the transformation of mechanical work
into heat (497, it has been attempted to ascertain what quantity of heat
is developed by the action of induced currents under the influence of power-
ful magnets. Joule, with a view of determining the mechanical equivalent
of heat, coiled a quantity of copper wire round a cylinder of soft iron, and
having enclosed the whole in a glass tube full of water, he imparted to the_-
systcm a rapid rotation between the branches of an electromagnet. A
thermometer placed in the liquid served to measure the quantity of heat
produced by the induced currents in the soft iron and the wire round it.

-929] Heat Developed by Magnets on Bodies in Motion. 935

It was thus found that the heat developed was proportional to the square of
the magnetism evoked, and was equivalent to the work used in the rotation.
Foucault made a remarkable experiment by means of the apparatus
represented in fig. 918. It consists of a powerful electromagnet fixed
horizontally on a table. Two pieces of soft iron, A and B, are in contact
with the poles of the magnet, and, becoming magnetised by induction,
they concentrate their magnetic inductive action on the two faces of a
copper disc, D, 3 inches in diameter and a quarter of an inch thick ;

Fig. 918.

this disc partly projects between the pieces A and B, and can be moved by
means of a handle and a series of toothed wheels with a velocity of 1 50 to
200 turns in a second.

So long as the current does not pass through the wire of the electro-
magnet, very little resistance is experienced in turning the handle, and
when once it has begun to rotate rapidly, and is left to itself, the rotation
continues in virtue of the acquired velocity. But when the current passes, the
disc and other pieces stop almost instantaneously ; and if the handle is
turned considerable resistance is felt. If, in spite of this, the rotation be
continued, the force used is transformed into heat, and the disc becomes
heated to a remarkable extent. In an experiment made by Foucault the
temperature of the disc rose from 10° to 61°, the current being fonned by
three of Bunsen's elements ; with six the resistance was such that the rotation
could not long be continued. The currents thus produced in solid conductors,
and which are converted into heat, are often spoken of as Foucault or eddy
currents.

Such currents are of constant occurrence in magneto-electrical machines,
and weaken their force, first, by owing their existence to some part of the
work expended ; secondly, they weaken the magnetism of the armatures by
their direction ; and, lastly, they are converted into heat, which increases
the internal resistance of the machine.

936

Dynamical Electricity.

[930-

930. The Telephone. — To the number of instruments depending on in-
duction may be added this discovery,. which is equally remarkable for the
surprising character of the results which it produces, and for the sim-
plicity of the means by which they are produced. Fig. 919 represents a
perspective, and fig. 920 a section of Graham Bell's telephone.

It consists essentially of a steel magnet, of about 4 inches in length by
half an inch in diameter, enclosed in a wooden case. Round one end of this
magnet is fitted a thin flat bobbin, BB, of fine
insulated copper wire. For a magnet of this
size a length of 250 metres of No. 38 wire,
offering a resistance of 350 ohms, is well
suited.

The ends of this coil pass through longi-
tudinal holes, LL, in the case, and are con-
nected with the binding screws CC. In front
of the magnet and at a distance which can
be regulated by a screw, but which is some-
thing less than a millimetre, is the essential
feature of the instrument, a diaphragm, D, of
soft iron, not much thicker than a sheet of
stout letter-paper. This diaphragm is screwed
down by the mouthpiece E, which is similar
to, though somewhat larger than, that of a
stethoscope.

The instruments are connected b)' wires,
for one of which the earth maybe substituted,
as in ordinary telegraphic communication
(886). Each instrument can be used either
as sender or receiver, though in actual prac-
tice it is more convenient for each operator
to have two telephones, one of which is
held to the ear, while the other is used for
speaking into ; the latter being larger and
more powerful than the receiver.
The action of the instrument depends on the fact that whenever the
relative positions of a magnet and of a closed coil of wire are altered there
is produced within the coil a current or currents of electricity. This may
be illustrated by reference to fig. 865. When the magnet is suddenly
brought into the coil, a current is produced in the coil in a particular direc-
tion. There is no current so long as the coil and the magnet are stationaiy.
When, however, the magnet is suddenly withdrawn, a current is produced
in the opposite direction. Similar effects are produced if, while the magnet
is in the coil, its magnetism is by any means increased or diminished.

Now in the telephone the magnet and the coil, when once properly
adjusted, remain fi.xed. But the magnet M magnetises by induction the
soft iron membrane D in front of it, that is, converts it into a magnet.
When, by the mouthpiece being spoken into, this iron membrane vibrates
backwards and forwards, tlicsc vibrations give rise to an alteration in the
magnetism of the permanent magnet, the effect of which is that currents

930]

The Telephone.

937

Fig. 920.

are produced in alternate directions in the coil surrounding the pole.
Moreover, the alteration in the relative positions of the magnetised dia-
phragm, thus magnetised by induction, and of the coil, give rise to currents
in the same direction as the above. These alternating currents, being
transmitted through the circuit to the distant coil, alternately attract, and
cease to attract, __
the corresponding
diaphrag-m. They C
thereby put this in ^s
vibration, and when
the mouthpiece of
this telephone is
held to the ear,
these vibrations are
perceived as sound
corresponding to
that which is trans-
mitted. Hence,
whatever sound produces the vibration of the diaphragm of the sending
instrument is repeated by that of the receiver.

The reproduction of the sound in the receiving instrument is perfect as
far as articulation is concerned, but it is considerably enfeebled, as might be
expected. The sound has something of a metallic character, appearing as
if heard through a long length of tubing, while it faithfully reproduces the
characteristics of the person speaking. It does not result from a series of
sharp and distinct makes and breaks, but in each of the momentary currents
there is a continuous rise and fall, corresponding in every gradation and
inflection to the motion of the air agitated by the speaker.

Various attempts have been made to improve the loudness of the sounds
produced in the telephone, by varying the form of the various parts, and
using more powerful magnets of horseshoe and circular forms ; but experi-
ment shows that increased loudness is always produced at the expense of
distinctness.

The amplitude of the vibration of the disc is extremely small. According
to Bosscha a unit current produced a displacement of 0-034 of a mm., and as
currents of y^^Vjo ^^ ^^^'^ ^^^ perceptible, it follows that the amount of displace-
ment must be about the —-^ of the wave-length of yellow light (637).

The current in a telephone is estimated by De la Rue as not exceeding
that which would be produced by one Daniell's cell in a circuit of copper
wire 4 mm. in diameter of a length sufficient to go 290 times round the earth.
This current would have to pass 19 years through a voltameter, to produce
I cc. of detonating gas. This is about 1,000 million times less than the
currents in ordinary use. Such currents are, however, sufficient to cause
the contraction of a frog's leg (797). According to Pellat the energy con-
tained in one test unit (water gramme degree) would maintain a continuous
sound for 10,000 years.

Siemens estimates that not more than y^Joo of the mass of sound which
the sender receives is produced. That it is possible to perceive this, is due
to the great sensitiveness and range of the ear, which can endure the sound

938 Dynamical Electricity. [930-

of a cannon at a distance of 5 yards, and still perceives it at a distance
10,000 times as great. This represents a ratio of intensities of one to one
hundred millions.

From some experiments on the transmission of the sound of a high-
pitched tuning-fork (251) Rontgen concludes that no less than 24,000 currents
are transmitted in one second.

This extreme delicacy of the telephone is its drawback to speaking
through ordinary telegraph circuits. The currents in adjacent wires, the
vibration of the posts and of the insulators, or the passage of a cart over
the streets, acts by induction on the telephone circuit, and overpowers its
indications. When a telephone circuit was placed at a distance of 20 metres
from a well-insulated line, through which signals were sent by means of a
battery of a few elements, sounds were distinctly heard in the telephone.
Speaking under such circumstances is like speaking in a storm. The
powerful currents used for systems of electric lighting produce such a roar
in an adjacent telephone circuit that it is impossible to speak through the
telephone. The only effective way of diminishing the inductive action of
adjacent systems is to have two wires in close proximity to each other.
They are thus at the same distance from the inducing circuit, and as one of
the wires is used for going and the other for returning, the similar influences
must be in opposite directions, and therefore neutralise each other.

If a telephone is inserted in the circuit of a Morse's instrument, the
sound of the working is heard, and the messages can be read ; this is the
case also of the telephone in the branch circuit of a Morse. If one telephone
is joined up with the primary, and another with the secondary wire of an
induction coil, communication is almost as good as if the two apparatus were
directly united.

Telephones have been constructed in which the thin iron plate is re-
placed by a thicker one, or by an unmagnetic one ; or if the telephone is
held close to the ear, the plate can be dispensed with altogether. In the
latter two cases the sounds are only perceived when the spiral surrounding
the magnet can vibrate with it.

A telephone may be constructed with a rod of soft iron instead of a
magnet ; when the rod is held in the line of dip, and the mouthpiece is sung
into, the sounds are reproduced.

From its extreme sensitiveness, being perhaps the most delicate galvano-
scope we possess, the telephone has become of great service in scientific
research. It may be used instead of a galvanometer in a Wheatstone's
bridge. If inserted in either of the circuits of an induction coil, the number
of breaks can be determined from the height of the tone which is produced.
When inserted in the current of a Holtz's machine, the disc of which is
rotating with a uniform velocity, the height of the note varies with the re-
sistance of the circuit, and with the capacity of the condensers. It can be
shown also that the circumstances most favourable for the production of a
most distinct stratification in a Geissler's tube correspond to a definite pitch
in the telephone.

The telephone has been used to test hardness of hearing. If the mag-
netism of a telephone be e.\cited by galvanic currents which are made inter-
mittent by a vibrating tuning-fork, and if a telephone is inserted in a branch

-931]

The Microphone.

939

circuit (961), then by varying the strength of the principal current, by the
insertion of resistances, the strength of the sounds in the telephone may be
varied at will.

When a telephone is held to the ear during a thunderstorm, every lightning
flash in the sky is simultaneously heard to be accompanied by a sharp crack.

Dolbear has constructed a telephone in which the electrostatic action of
currents is used. It consists of two circular flat discs of metal rigidly fixed
to each other in an insulated case of ebonite. One of the discs is in metallic
connection with the line wire, in which is a battery and an induction coil ;
in this way, while one disc is electrified positively, the other is negatively
electrified by induction, and if the current be varied by speaking through a
transmitter in the circuit their var>'ing effects are faithfully reproduced, and
reappear as sound vibrations on the receiver.

931. The Microphone. — When the wires of an electrical circuit, in which
is interposed a telephone, are broken, and rest loosely on each other, sounds
produced near the point of contact
are reproduced and magnified in
the telephone. The micropho?te^
invented by Prof Hughes, depends
on this fact ; its arrangement may
be greatly varied ; one of the simplest
and most convenient forms is that
represented in fig. 921. A piece
of thin wood is fitted vertically on
a base of the same material ; two
small rods of gas carbon, C C, about
\ of an inch thick, are fixed hori-
zontally in the upright ; by means of
binding screws, they are in metallic
connection with the wires of a cir-
cuit in which is a small battery and
a telephone ; and in each of them
is a cavity. A third piece, D, of the same material, and about one inch long,
is pointed at each end, one of which rests in the lower cavity, while the other
pivots loosely in the upper one. When a watch is placed on the base B, its
ticking is heard in the telephone with surprising loudness ; the walking of
a fly on the base suggests the stamping of a horse ; the scratching of a
quill, the rustling of silk, the beating of the pulse, are perceived in the tele-
phone at a distance of a hundred miles from the source of sound ; while a
drop of water falling on the base has a loud crashing sound. To obtain the
best results with a particular instrument, the position of the carbon must be
carefully adjusted by trial ; and indeed the form of the instrument itself
must be variously modified for the special object in view : in some cases
great sensitiveness is required : in others great range. In order to eliminate
as far as possible the effect of accidental vibrations due to the supports, the
base should rest on pieces of vulcanised tubing, or on wadding.

It is known that the compression of a semiconductor, such as carbon,
diminishes its resistance, while a diminution in the compression in-
creases the resistance. The action of the microphone is to be ascribed

'^"tv5Tiyir/r-

f^^^^ir-

I ig. 921

940

Dynamical Electricity,

[931-

it==t

c±.

to this ; in consequence of the minute aherations in the pressure and in the
degree of contact at the break, the electrical resistance in the circuit varies
in accordance with the sound-waves, and consequently the strength of the
currents varies too. The result of this is, that what we may call undulating
currents of electricity are produced, whose amplitude, height, and form are
in exact correspondence with the sound-waves. The effect of the micro-
phone is to draw supplies of energy from the battery, which then appear in
the telephone.

932. Hugrhes's induction balance. — The principle of this apparatus may
be thus stated : — Suppose we have two exactly equal primary induction coils,
A and A', and near them two secondary coils, B and B', also exactly equal,
and connected up with a galvanometer, so that the coils act upon it in
opposite directions. If now the current of a battery be sent through the
primary coils, joined in series, the inductive effects on each of the secondary
coils will be the same, and, as their action on the galvanometer is opposed,
no deflection of the needle will be produced. If, however, a piece of iron

be introduced into the
cZiM] c-i^ coreof one of the secon-

dary coils, the equality
in the induction effects
will be destroyed, and
the needle of the gal-
A-anometer at once de-
flected.

This principle was
first applied by Bab-
bage, Herschell, and in
a special apparatus by
Dove ; but the micro-
phone and the tele-
])hone have led the
inventor of the former
to the invention of an
apparatus which has
opened. out new possi-
bilities, and has placed
in the hands of the
physicist an elegant
and powerful engine of
research, which in cer-
tain departments of in-
vestigation promises to
be of great service.
"^■'^''- The form of instru-

ment as devised by Professor Hughes is represented in fig. 922, where the
essential parts are drawn to scale, though the relative distances of the parts
are not so ; a and a' arc the two primary coils, each of which consists of 100 "
metres of No. 32 silk-covcrcd copper wire (o'oog in diameter) wound on a flat
boxwood spool 10 inches in depth ; b and <J'are two secondaiy coils, all four coils

-932] Hughes's Induction Balance. 941

being, in intention at least, exactly alike. The two primary coils are joined
in series with a battery of three or four small Daniell's cells, in which circuit
a microphone, ;«, is also inserted ; the ticking of a small clock on the table
acts as make and break.

The secondary coils are joined up with a telephone in such a manner
that their action upon it is opposed.

Now, whatever care be taken in winding the wire on the coils, it is not
possible to get at the outset an exact balance. Hence, while one of the
secondary coils, b, is at a fixed distance from <•?, the corresponding one, b\ is
not so ; its distance from a' can be slightly modified by means of a micro-
metric screw, and thus, connection with the battery circuit having been made,
a balance is obtained by slightly varying the adjustment, and the accomplish-
ment of this is known by there being silence in the telephone. But if now
any metal whatever be introduced in one of the secondary coils, a sound
is at once heard.

This arrangement is so far a simple differential one, and furnishes as yet
no means of measuring the forces brought into play, and for this purpose
Hughes uses what is called a sonometer or audiometer. This consists of
three similar coils, f, ^, and ^, placed vertically on a horizontal graduated rule
along which d can be moved. By means of a switching key or switch,
the primary coils c and e can be put in communication with the battery and
microphone circuit quite independently of the balance, and it is so ar-
ranged that the ends of the coils c and e facing each other are of the same
polarity ; the third coil, d, the secondary one, is connected with the telephone
circuit.

If these primary coils c and e were quite equal, then, when connected up
with the battery circuit, no sound would be heard in the telephone, when the
secondary d is exactly midway between them. But as the coil is moved
from this position either towards c or e a sound is heard, due to the prepon-
derance of one or the other. In practice the coils are so arranged that a
balance is obtained when the secondary circuit is near one of the coils, c
for instance ; this represents a zero of sound, and as the coil d is moved
nearer to ^ a sound of gradually increasing intensity is heard ; distances
measured off along this scale represent values of sound on an arbitrary scale.

Suppose now that a balance has been obtained in the induction balance,
and that the coil d in the sonometer is at zero ; no sound is then heard
in the telephone when the current is switched either in one or the other
circuit. But if the balance is disturbed by placing a piece of metal in the
core of b, a definite continuous sound is heard. The current is then switched
into the sonometer, and the secondary coil e is moved until the air perceives
the same sound in both circuits. The distance then along which the coil d
has been moved is thus an arbitrary measure of the effect produced.

Although by the switch the transition from one circuit to the other
can be effected with great rapidity, and the ear can appreciate minute
differences, this has not the value of a null method. Hughes has still
further improved the balance by the following device, in which the sono-
meter is dispensed with : — A graduated strip of zinc about 200 mm. in length
by 25 mm. wide, and tapering from a thickness of 4 mm. at one end to a fine
edge at the other, is made use of The metal to be tested is placed in a

Dynamical Electricity.

942 vynamicai t.Lectrtcity. [932-

plane between a and b on the left of the plate, and the strip is moved along
the top of b' until a balance is obtained.

The instrument is of surprising delicacy ; a milligramme of copper or a
fine iron wire introduced into one of the coils which has been balanced can
be loudly heard, and appreciated by direct measurement. If two shillings
fresh from the Mint be balanced, rubbing one of them or breathing on it at
once disturbs the balance. A false coin balanced against a genuine one
is at once detected. The instrument furnishes a means of testing the deli-
cacy of hearing ; such a piece of wire as the above, or a fine spiral of copper,
furnishes a kind of test object for this purpose.

933. Tasimeter. — This instrument, invented by Edison, consists essen-
tially of an arrangement by which a disc of carbon forming part of a voltaic
circuit is exposed to varying pressure. It depends on the fact that the
resistance of carbon varies very greatly with the pressure to which it is
exposed. It consists of an iron base, on which are two rigid supports (fig.
923), one of which, a^ is connected with the galvanometer, g^ by means of
a wire. An ebonite disc, rtf, is screwed into a, and in a circular cavity in
this ebonite is a small carbon disc, not shown in the figure, in the outer

Fig. 923.

surface of which is a strip of platinum in metallic connection with one pole
of an element, /. The disc of carbon is closed in the cavity by a metal
plug, f, in which is a cavity. There is a similar plug, ^, with a correspond-
ing cavity at the end of a screw, b, which works in the upright support ; in
the two cavities is placed the strip of substance, y^ with which the experiment
is made.

A gentle pressure being applied by the screw, the needle is deflected
through a few degrees, and its position, when it comes to rest, is noted.
The slightest subsequent contraction or expansion is indicated by a deflec-
tion of the needle of the galvanometer.

The sensitiveness of the instrument is ver)' great : a thin strip of ebonite
is expanded by the heat of the hand held near it, so as to aflfect a not very
delicate galvanometer. A strip of gelatine, inserted instead of the ebonite,
is expanded by the moisture of a damp strip of paper held two or three
inches away.

The apparatus seems well adapted for the qualitative observation of

-934] Edison's Loiid-spcaking Telepho7te. 943

minute changes in length ; it has been used, for instance, to show the very
small elongation of an iron rod when it is magnetised (880). Great care is
required in the preparation of the carbon disc ; the best kind seems to be
made from lampblack prepared at a low temperature, and then powerfully
compressed into a button.

934. Edison's loud-speaking: telephone. — Although depending on a
different principle, we may give a description here of this instrument.

An adjustable metal spring passes on the surface of a small cylinder,
made of chalk, moistened with solutions of caustic potash and acetate of
mercury ; both the spring and the cylinder form part of a circuit in which
is a battery and a Reis's transmitter (884). The spring is connected in a
suitable manner with a mica disc, which is the vibrating part of a mouth-
piece like that of an ordinary telephone. The cylinder can be turned at a
uniform rate, either by hand or by an automatic clockwork arrangement.

Now while the spring is pressing on the cylinder, if the latter be rotated
in a direction away from the mouthpiece, in consequence of the friction
between the spring and the surface of the cylinder, a certain pull will be
exerted on the disc, which will tend to drag it outwards. If the direction of
rotation were the opposite, the disc would be pushed inwards. Now the
amount of pull or push will depend on the friction between the point and
the surface. If a momentary current be passed, there will be a momentary
decomposition at the surface of the cylinder, its friction will be altered in
consequence of this momentary decomposition, the effect of which is that
the disc moves inwards, and a series of such intermissions of the current
produces a corresponding series of pulsations of the disc, which if sufficiently
rapid produce a sound. The friction of the surfaces in contact is in fact
modified by means of electrical decomposition, a lubricator is liberated in
correspondence with the sound-waves, and thus the sound which they repre-
sent is reproduced. The reproduction is so loud as to be heard throughout
a room, the sounding' instrument being at a distance. Although ordinaiy
speech and music can thus be transmitted, yet the sounds have a harsh
metallic character which is not pleasing, but at the same time the individual
character of the voice is preserved.

944

Dynamical Electricity.

[935-

CHAPTER VII.

OPTICAL EFFECTS OF POWERFUL MAGNETS. DL\MAGNET1SM.

935. Optical effects of powerful magrnets. — Faraday observed, in 1845,
that a powerful electromagnet exercises an action on many substances, such
that if a polarised ray traverses them in the direction of the line of the mag-
netic poles, the plane of polarisation is deviated either to the right or to the
left according to the direction of the magnetisation.

Fig. 924 represents Faraday's apparatus, as constructed by Ruhmkorff.
It consists of two very powerful electromagnets, AI and N, fi.xed on two iron

Fig. 9-4-

supports, O O', which can be moved on a support, K. The current from a
Ijattery of 10 or 12 Bunsen's elements passes by the wire A to the commu-
tator, H, the coil M, and then to the coil N, by the wire^, descends in the
wire /, passes again to the commutator, and emerges at B. The two
cylinders of soft iron, which are in the axis of the coils, are perforated by
cylindrical holes, to allow the light to pass. At b and a there arc two Nicol's
prisms, b serving as polariser and a as analyser. By means of a limb this
latter is turned round the centre of a graduated circle, P.

The two prisms being then placed so that their principal sections are
perpendicular to each other, the prism a completely extinguishes the light
transmitted through the prism b. If at f, on the axis of the two coils, a plate"
be placed with parallel faces, either of ordinary or flint glass, light supposed

-936] PhotopJionc. 945

to be monocliromatic is still extinguished so long as the current does not

pass ; but when the connections are made, the light reappears, and in order

to extinguish it the analyser must be turned through an angle which can be

read off on the limb, and which measures the rotation. By reversing the

direction of the current twice the rotation is observed. If the source of

light is not monochromatic, and if the analyser be turned from left or right,

according Jo the direction of the current, the light passes through the

different tints of the spectrum, as is the case with plates of quartz cut

perpendicularly to the axis (674). Becquerel showed that a large number of

substances can also rotate the plane of polarisation under the influence of

powerful magnets. For a given substance the direction of the rotation is

independent of the

direction in which the ~

rays of light pass ;

and also of whether

the propagation of

the light is in the

direction of the lines

of force, or in the '^' ^'^^"

opposite direction. Hence if the ray is reflected on itself (fig. 925), and

traverses the substance a second time in the opposite direction, the rotation

is doubled. By thus increasing the path of the ray by successive reflections,

the rotation may be increased in the same proportion.

TJie rotation of the plane of polarisation between ttvo points is propor-
tional to the difference of magnetic potential \v\\\ch exists bet-ween these poiftts.
This is known as Verdefs law.

If V and V are the magnetic potentials at two points on the path of the
ray, then the angle d by which the plane of polarisation has been turned is
6 = 0) (V- V) ; 0) being the rotation which for the body in question would be
due to unit difference of potential. This quantity is called VerdeCs constant.
For different rays it is nearly as the inverse square of the wave length. For
the ray D and at 0° it is o'-o4o for bisulphide of carbon and o'-oi3 for water.
It diminishes with rise of temperature.

By means of Faraday's apparatus it has been found that thin layers of
iron, cobalt, and nickel, so fine as to be transparent, exert a powerful rota-
tion of the plane of polarisation for transmitted light. The rotation for the
central rays of the spectrum in iron is 32,000 times that of glass of the same
thickness. In all the above substances the rotation is in the direction of
the magnetising current.

936. Pbotopbone. — Mr. Graham Bell, the inventor of the telephone,
has invented an apparatus by which articulate speech can be transmitted to
a considerable distance by the simple agency of a ray of light.

The essential features of the apparatus are represented in fig. 926, in
which m is the transmitter. This consists of a wooden box closed by a thin
plate of microscope glass silvered in front, which acts as mirror ; in the
back of the box is an aperture provided with a flexible tube and mouthpiece.
A powerful beam of solar or of the electrical light falls agamst a large
mirror, //, and is reflected by it on a lens, (^, by which the rays are concentrated

946 Dynamical Electi'icity. [936-

on the mirror, w, of the transmitter. An alum cell, a^ is sometimes interposed,
to cut ofif the influence of the heating rays.

From the mirror m the reflected rays pass through a lens,/, by which they
are rendered parallel, and fall on a parabolic mirror,/, at the distant station.
Here they are concentrated on what may be called a selcnitun r/ieostate, s,
which is interposed in a circuit consisting of a few Leclanche cells and a
telephone, /.

The action depends on the alterations in the resistance of selenium
produced by the action of light. The construction of the rheostate is as
follows : — A number of discs of thin sheet brass are taken, separated from
each other by thin discs of mica of somewhat smaller diameter, and, the
whole having been tightly screwed together, the interstitial spaces are filled

Fig. 926.

with melted selenium. All the odd numbers of brass discs arc in metallic
connection with each other and with one pole of the circuit, and all the even
ones are also in metallic connection with each other and with the other
pole. In this way two conditions are realised — namely, that the surface of
selenium exposed to the action of light is as large, and its resistance as
small, as possible.

This being premised, when light falls on the plane mirror at rest, its rays
are reflected parallel against the parabolic mirror by which they are con-
centrated on the cell, the cylindrical shape being well adapted for this. But
if, by being spoken against, the transmitting mirror vi is put in vibration,
it bulges in and out — that is, becomes convex and concave— and the rays no
longer fall parallel on the parabolic mirror ; tlicy diverge or converge — in
other words, the whole of the light is no longer concentrated on the selenium
cell ; its intensity changes at every instant, and these variations in the action
of the light produce corresponding variations in the resistance of the sele-
nium, which again produce corresponding variations in the strength of the
current, and these are revealed by the articulate sounds of the telephone.

Mr. Bell has found that a great number of substances are thrown into
vibration by the intermittent action of light, as we have seen (446(/). Lord
Raylcigh's calculations show that there is no reason for discarding the ex-

-937 J Kerrs Electro-optical Experiments. 947

planation that the sounds in question arc due to the bendiny of the plates in
consequence of unequal heating'.

937. Kerr's electro-optical experiments. — Dr. Kerr has discovered a
remarkable relationship between electricity and light. He finds that when
certain dielectrics are subjected to a state of electrical strain, they develop
doubly refringent properties (639). The general arrangement of the experi-
ments is as follows : a cell, P (fig. 927), is suitably constructed of stout glass
plates, in which is placed the liquid under examination ; its dimensions are
4 inches in length by i inch in width, and about J, of an inch in thickness.

i-F- -^■- l«-""-i -~-—W-

Fig. 927.

Two copper plates placed horizontally, and kept at a distance of about ^r, of
an inch, can be connected with the poles of a Holtz machine (fig. 687), or
what is more convenient, with the opposite coatings of a Leyden jar, which
in turn is worked by such a machine. B is the mirror of a heliostat,
by which a beam of light may be sent in any direction. M and N are
two Nicol's prisms (660) ; C is a compensator, while D is a condensing
lens.

Of the two Nicol's prisms, M serves as polariser, and N as analyser
(656) ; at the outset they are arranged so that their principal sections are at
right angles to each other, and make an angle of 45° with the vertical.
Thus the light polarised by the prism M is extinguished by the analyser N,
so that the field between them is quite dark, and remains so even when
the cell is filled with liquid ; the cell is so arranged that the observer
looks through the slit of dielectric which is between the conductors in the
cell.

If now the plates are placed in opposite electrical conditions, the field at
once becomes clear. Of all dielectrics hitherto examined, carbon bisulphide
IS that which best exhibits the phenomenon. A fraction of a turn of a Holtz
machine is at once sufficient to produce light in the field, which disappears
immediately the plates are discharged. As the machine is worked and the
potential rises, the light between the conductors gradually increases in bright-
ness until a pure and brilliant white is obtained ; with increase of potential
a fine progression of chromatic effects is obtained ; the luminous band
between the conductors changes first from white to a straw colour, which
deepens gradually to a rich yellow ; it then passes through orange to a deep
brown, next to a pure and dense red, through purple and violet to a rich
and full blue, and then to green. All the colours are beautifully dense and
pure, and as fine as anything seen in experiments with crystals in the polari-
scope. The phenomenon generally ceases at the green of the second order
with a discharge of electric spark?. The action of bisulphide of carbon
under electrical strain is similar to that of glass stretched in a direction

3 p 2

948 Dynmiiical Electricity. [937-

parallel to the lines of force ; it is an action of the same kind as that of
a uniaxial birefringent ctystal (640) ; in this respect carbon bisulphide oc-
cupies a place among dielectrics similar to that of Iceland spar among
crystals.

In order to measure the effect produced, a compensator, C, is placed
behind the cell ; the plates are connected with a Thomson's electrometer
in such a manner that the potential can be directly measured, and then
compared simultaneously with the difference of the path of the extraordinarj'
and ordinary ray in the dielectric. Kerr arrived thus at the law : ' the
strength of the electro-optical action of a given dielectric, that is, the
difference in the path of the ordinary and extraordinary rays, for unit
thickness of the dielectric, varies directly as the square of the resultant
electrical force.' Kerr also found that when a pencil of plane polarised
light is reflected from the polished surface of either pole of an electromagnet
of iron, it undergoes a rotation in a direction contrary to that of the mag-
netising current. This result is also obtained when it is reflected from the
sides of the electromagnet, if the magnet is excited.

938. Diamag-netism. — Coulomb observed, in 1802, that magnets act upon
all bodies in a more or less marked degree ; this action was at first attributed
to the presence of ferruginous particles. Brugmann also found that certain
bodies — for instance, bars of bismuth — when suspended between the poles of
a powerful magnet, do not set axially between the poles, that is, in the line
joining the poles, but egtiatorially^ or at right angles to that line. In other
words, while a magnetic substance such as iron sets along the lines of force
of the magnetic field, a bar of bismuth sets at right angles to the field.
This phenomenon was explained by the assumption that the bodies were
transversely magnetic. Faraday made the important discovery in 1845 that
all solids and liquids which he examined are cither attracted or repelled by
a powerful electromagnet. The bodies which are attracted are called mag-
netic or parainagnetic, or also ferromagnetic, substances, and those which
are repelled or take a magnetisation opposite that of the lines of force are
diamagnctic bodies. Among the metals, iron, nickel, cobalt, manganese,
platinum, cerium, osmium, and palladium are magnetic ; while bismuth,
antimony, zinc, tin, mercury, lead, silver, copper, gold, and arsenic are
diamagnetic, bismuth being the most so and arsenic the least. Diamagnetic
effects were first observed by Faraday in a particular kind of glass called
heavy glass ; they can only be produced by means of veiy powerful mag-
nets, and it is by means of Faraday's apparatus that they have been dis-
covered and studied. In experimenting on the diamagnetic effects — solids,
liquids, and gases— armatures of soft iron, S and Q (tigs. 928-930), of dif-
ferent shapes, are screwed on the magnets.

i. Diamagnetisin of solids. If a small cube of copper, suspended by a
fine silk thread between the poles of the magnet (fig. 929), be in rapid rota-
tion between the poles of an electromagnet, it stops the moment the current
passes through the coils. If the movable piece have the form of a small
rectangular bar it sets cquatorially, or at right angles to the axis of the bob-
bins, if it is a diamagnctic substance, such as bismuth, antimony, or copper-,'
but axially, or in the direction of the axis, if it is a magnetic substance, such
as iron, nickel, or cobalt. Besides the substances enumerated above, the

-938]

Diainai^-nctisiii.

949

following- are diamaynetic : rock crystal, alum, glass, phosphorus, iodine,
sulphur, sugar, bread ; and the following- are magnetic : many kinds of
paper and sealing-wax, fluorspar, graphite, charcoal, O^cc.

ii. DiiDiuignctism of liquids. To experiment with liquids, very thin glass
tubes tilled with the substance are suspended between the poles instead of

Fig. 928.

Fig. 929

Fig. 930.

the cube in in the figure 929. If the liquids are magnetic, such as solutions
of iron or cobalt, the tubes set axially ; if diamagnetic, like water, blood,
milk, alcohol, ether, oil of turpentine, and most saline solutions, the tubes set
equatorially. Very remarkable changes take place in the direction of mag-
netic and diamagnetic substances when they are suspended in liquids. A
magnetic substance is indifferent in an equally strong magnetic liquid ; it
sets equatorially in a stronger magnetic substance, and axially in a sub-
stance which is less strongly magnetic ; it sets axially in all diamagnetic
liquids.

A diamagnetic substance surrounded by a magnetic or diamagnetic sub-
stance sets equatorially. According to its composition glass is sometimes
magnetic and sometimes diamagnetic, and as glass tubes are used for con-
taining the liquids in these investigations its deportment must first be deter-
mined, and then taken into account in the experiment.

The action of powerful magnets on liquids may also be observed in the
following experiment devised by Pliicker. A solution of a magnetic liquid
is placed on a watch-glass between the two poles, S and Q, of a powerful
electromagnet. When the current passes, the solution forms the enlarge-
ment represented in fig. 930 ; this continues as long as the current passes,
and is produced to different extents with all magnetic liquids. The changes
in the aspects of the liquids are, however, so small as to require careful
scrutiny to detect their existence. A method of magnifying these changes
so as to render them visible to larger audiences was devised by Prof.
Barrett. A source of light is placed above the watch-glass containing a drop
of the solution to be tried. Below the watch-glass, and between the legs of
the magnet, is placed a mirror at an angle of 45°. By this means the beam
of light passing through the watch-glass is reflected at right angdes on to a
screen, where an image of the drop is focussed by the lens. If now a drop of
diamagnetic liquid, such as water, or, better, sulphuric acid, be placed on the
watch-glass, as soon as the current passes, the flattened drop retreats from

950 Dynamical Electricity. [938-

the two poles, and gathers itself up into a little heap, as at A (fig. 930). So
doing, it forms a double convex lens, by which the light is brought to a short
focus below the drop, an effect instantly seen on the screen. When the current
is interrupted the drop falls, and the light returns to its former appearance.
A magnetic liquid, such as a solution of perchloride of iron, has exactly the
opposite effect. The drop attracted to the two poles becomes flattened, and
instead of a plano-convex shape, at which it rests, it becomes nearly^concavo-
convex, as at B. The light is dispersed, and the effect manifest on the screen.
Instead of a mirror and lens, a sheet of white paper may be placed in an in-
clined position under the watch-glass, and the effects are somewhat varied,
but equally well-pronounced.

iii. Diai)iag7ietisin of gases. Bancalari observed that the flame of a candle
placed between the two poles in Faraday's apparatus was strongly repelled
(fig. 9?8). All flames present the same phenomenon to different extents,
resinous flames or smoke being most powerfully affected.

The magnetic deportment of gases maybe e.xhibited for lecture purposes
by inflating soap bubbles with them between the poles of the electromagnet,
and projecting on them either the lime or the electric light.

Faraday experimented on the magnetic or diamagnetic nature of gases.
He allowed gas mixed with a small quantity of a visible gas or vapour, so
as to render it perceptible, to ascend between the two poles of a magnet,
and observed their deflections from the vertical line in the axial or equatorial
direction ; in this way he found that oxygen was least, nitrogen more, and
hydrogen most diamagnetic. With iodine vapour, produced by placing a
little iodme on a hot plate between the two poles, the repulsion is strongly
marked. Becquerel found that oxygen is the most strongly magnetic of all
gases, and that a cubic yard of this gas condensed would act on a magnetic
needle like 5-5 grains of iron. This magnetism of gases may be shown by
suspending a glass globe to the pan of a balance, above the pole of a
powerful magnet ; this globe being exhausted it is exactly counterpoised,
and having been filled with a given gas the weight is ascertained which is
required to detach them. With oxygen the attraction is appreciable, and
is five times as much as air under the same pressure. Faraday found that
oxygen, although magnetic under ordinary circumstances, became diamag-
netic when the temperature was much raised, and that the magnetism or
diamagnctism of a substance depends on the medium in which it is placed.
A suljstance, for instance, which is magnetic in \'acuo may be diamag'netic
in air.

In the crystallised bodies which do not belong to the regular system, the
directions in which the magnetism or diamagnetism of a body is most easily
excited are generally related to the crystallographic axis of the substance.
The optic axis of the uniaxial crystals sets either axially or equatorially when
a crystal is suspended between the poles of an electromagnet. Faraday has
assumed from this the existence of a inag>ietfl-crystalli?ic force, but it appears
probable from Knoblauch's researches that the action arises from an unequal
density in different directions, inasmuch as unequal pressure in different
directions produces the same result.

According to Pliicker, for a given unit of magnetising force, the specific
magnetisms developed in equal weights of the undermentioned substances

-938] Diaiiiagnctisiii. 95 1

are represented by the following numbers, those bodies with the minus signs
prefixed being diamagnetic : —

Iron

. 1 ,000,000

Nickel oxide

. 287

Cobalt .

. 1,009,000

Water .

• -25

Nickel .

465,800

Bismuth

. -23-6

Iron oxide

759

Phosphorus .

. -13-1

iv. Detonation produced by the rupture of a current under the influence
of a pozuerful electromagnet. The following experiment by Ruhmkorfif is a
remarkable effect of Faraday's apparatus. When the two ends of a stout wire
in which the current of the electromagnet passes are placed between the two
poles S and Q of fig. 928 — that is to say, when the current is closed between
S and Q — this closing takes place without a spark and without noise, or
merely a feeble noise and a spark. But when the two ends are separated,
and the current is hence broken, a violent noise is heard, almost as strong as
the report of a pistol. This appears to be the extra current, the intensity of
which is greatly increased by the influence of two poles.

The repulsion produced in a diamagnetic body under the influence ot a
powerful magnet is due to the fact that the magnet develops in the end
nearest to it like polarity, and in the end furthest away unlike polarity ; a
phenomenon the exact opposite of that of iron.

The following experiment, which is due to Weber, is considered to prove
that diamagnetism is a polar force. A coil was placed near the end of an
electromagnet, its axis being in the prolongation of the axis of the magnet,
and its ends being connected with a sensitive galvanometer. When a bar
of bismuth was suddenly introduced and removed from the coil, induction
currents were produced in the circuit, the direction of which, as shown by
the galvanometer, was the exact opposite of that which iron would ha\e
produced under the same circumstances.

95-

Dynaviical Electricity.

[939-

CHAPTER VIII.

THERMO-ELECTRIC CURRENT.

Fig. 931.

939. Thermo-electricity. — In 1821, Professor Seebeck, of Berlin, found
that by heating one of the junctions of a metallic circuit, consisting of two
metals soldered together, an electric current was produced. This pheno-
menon may be shown by means of the apparatus represented in fig. 931,

which consists of a plate
of copper, inn, the ends
of which are bent and
soldered to a plate of bis-
muth, op. Inside the cir-
cuit is a magnetic needle,
a, moving on a pivot.
When the apparatus is
placed in the magnetic
meridian, and one of the
solderings gently heated,
as shown in the figure,
the needle is deflected in
a manner which indicates
the passage of a current
from n to in, that is, from the heated to the cool junction in the copper. If,
instead of heating the junction n, it is cooled by ice, or by placing upon it
cotton-wool moistened with ether, the other junction remaining at the ordi-
nary temperature, a current is produced, but in the opposite direction, that
is to say, from in to n ; in both cases the current is in general stronger in
proportion as the difference in temperature of the solderings is greater.

Seebeck gave the name thermo-electric to this current, and to the couple
\\ liich produces it, to distinguish it from the hydro-electric or ordinary voltaic
current and couple.

940. Thermo-electric series. — If small bars of two dififerent metals are
soldered together at one end while the free ends are connected with the
wires of a galvanometer, and if now the point of junction of the two metals
lie heated, a current is produced, the direction of which is indicated by the
deflection of the needle of the galvanometer. Moreover, the strength of the
current, calculated from the deflection of the gahanometer, is proportional
to the electromotive force of the therino-elcinent. By experimenting in this
way with different metals, they may be formed in a list such that each metal
gives rise to positive electricity when associated with one of the following, -
and negative electricity with one of those that precede : — that is, that, in
heating the soldering, the positive current goes from the positive to the ncga-

940]

ThcDiw-electric Series.

953

Gas coke .

-o-i

Zinc .

0-2

5-5

Cadmium .

0-3

Strontium .

2-0

Arsenic

3-8

1-03

Iron .

5-2

Red Phosphorus

9-6

Antimony .

9-8

i-o

Tellurium .

179-9

Selenium .

— 290-0

tive metal across the soldering, just as if the soldering represented the liquid
in a hydro-electrical element ; hence out of the element — in the connecting
wire and the galvanometer, for instance — the current goes from the negative
to the positive metal.

Thus a couple, bismuth-antimony, heated at the junction would corre-
spond to a couple, zinc-copper, immersed in sulphuric acid. The following
is a list drawn up from Matthiessen's researches, which also gives compara-
tive numeVical values for the electromotive force : —

Bismuth

Cobalt .

Potassium .

Nickel.

Sodium

Lead .

Tin . . .

Copper

Silver .

Platinum

Such a list represents what is called a thermo-electric series, and the
meaning of the numbers in this series is that, taking the electromotive force
of the copper-silver couple as unity, the electromotive force of any pair of
metals is expressed by the difference of the numbers where the signs are the
same and by the sum where the signs are different. Thus the electromotive
force of a bismuth-nickel couple would be 25 — 5 = 20; of a cobalt-iron
9-( — 5-2) = 14-2, and of an iron-antimony — 5-2-9-8 = —4-6, Where the
positive sign is affixed, the current is from the other metal to silver across
the soldering ; and where the negative, from silver to that metal.

It will be observed how great is the electromotive force of the highly
crystalline metals. Alloys are not always intermediate to the metals of which
they are composed, and, therefore, the position of the metals is greatly
affected by slight admixtures. The thermo-electric behaviour of substances
is greatly affected by hardness, direction of crystallisation, and so forth, and
to this is no doubt due many of the discrepancies in the lists given by different
observers.

Of all the bodies mentioned in the above series, bismuth and selenium
produce the greatest electromotive force ; but from the expense of this
latter element, and on account of its low conducting power and the difficulty
of making good joints, antimony is generally substituted. The antimony is
the negative metal but the positive pole, and the bismuth the positive metal
but the negative pole, and the current goes from bismuth to antimony across
the junction.

If copper wires connected with the ends of a galvanometer are soldered
together to the ends of an antimony rod, and if one of the junctions is heated
to 50°, the other being maintained at 0°, a certain deflection is observed in
the galvanometer. If, similarly, a compoundbar, consisting of antimony and
tin soldered together, be connected with the ends of the galvanometer, and if
the junction copper-tin as well as the junction tin-antimony be heated to 50°,
while the junction antimony-copper is kept at 0°, the deflection is the same

954 Dynamical Electricity. [940-

as in the previous case. Hence the electromotive force produced by heating
the two junctions, copper-tin and tin-antimony, is equal to the electromotive
force produced by heating the copper-antimony ; and, generally, if a metal, b,
is associated with a metal, a, which is above it in the list, and in like manner
if b is associated with c, which is below it in the list, then the electromotive
force produced by heating the combination ac is equal to the sum of the
electromotive forces produced by heating ab and be separately.

If the two junctions of a given couple be heated to the temperatures t
and 6, and then to 6 and f, respectively, the electromotive force produced by
heating the junctions to the temperatures, / and /', is equal to the sum of the
electromotive forces produced in the other two cases ; that is, that for small
intervals the electromotive force is directly proportional to the temperature.

With greater ranges this, no longer holds ; as the temperature increases
the differences of potential gradually diminish, and at a certain temperature
of the hot junction no current is produced ; this temperature is called the
neutral temperature. In the case of a silver-iron couple this is when one
junction is at o°, the other is at 223° ; in the case of copper-iron, it is when
the hot junction is at 276°.

When the couple is heated beyond the neutral temperature, the pheno-
menon of inversion now takes place — that is, the direction of the current
changes. Thus, with iron-copper, whereas below 276° copper is positive to
iron, above that temperature iron is positive to copper.

There is another general case in which no current is produced by heating
the two junctions, and that is whenever the arithmetical mean of the tempe-
ratures of the junction is equal to this neutral temperature. Thus, for silver
and iron this temperature is 228-5°, ^^id "o current is produced when the
temperature, /, of the one is 186, 145, and 1 18, the corresponding one of the
other being 260, 302, and 328. If the mean temperature in one case is above
and in another below, the current has different directions in the two cases ;
hence the electromotive force cannot always be increased by raising the
temperature of one or lowering the temperature of another.

As compared with ordinary hydro-electric currents, the electromotive
force of thermo currents is very small ; thus the electromotive force of a
bismuth-copper element with a difference of 100° C. in the temperatures of
their junctions is, according to Neumann, ,,!,, that of a Daniell's element : the
electromotive force of an iron-argentan couple with 10° to IS"^ difterence of
temperature at their junctions is ,.j,^^- that of a Daniell's, according to Kohl-
rausch that of a copper-argentan couple by ,^,'„-, of a Daniell for 100° C.
The E.M.F. of a bismuth-antimony couple is 0000057 volt for a degree
Centigrade.

941. Causes of ttaermo-electrlc currents.— Thermo-electric currents
are probably to be attributed to an electromoU\ e force produced by the con-
tact of heterogeneous substances, a force which \ aries with the temperature.
When all the parts of a circuit are homogeneous, no current is produced on
heating, because the heat is equally propagated in all directions. This is
the case if the wires of the galvanometer are connected by a second copper
wire. But if the uniformity of this is destroyed by coiling it in a spiral, or
]by knotting it, the needle indicates by its deflection a current going from \\\(:
heated part to that in which the homogeneity has been destroyeil. If the

-942J

Thernw-electric Battery.

955

ends of the galvanometer wires be coiled in a spiral, and one end heated and
touched with the other, the current goes from the heated to the cooled end.

When two plates of the same metal, but at different temperatures, are
placed in a fused salt such as borax, which conducts electricity but exerts
no chemical action, a current passes from the hotter metal through the fused
salt to the colder one. Hot and cold water
in contact produce a current which goes
from the warm water to the cold.

Svanberg has found that the thermo-
electromotive force is influenced by the
crystallisation ; for instance, if the cleavage
of bismuth is parallel to the face of contact,
it is greater than if both are at right angles,
and that the reverse is the case with anti-
mony. Thermo-electric elements may be
constructed of either two pieces of bismuth
or two pieces of antimony, if in the one the
principal cleavage is parallel to the place of
contact, and in the other is at right angles.
Hence the position of metals in thermo-
electric series is. influenced by their crystalline structure.

Many crystallised minerals have great electromotive force when heated
with metals or with each other. Thus the combination copper pyrites —
copper when heated in a spirit lamp has an electromotive force of o-i2, and
copper pyrites — iron pyrites of o-i8 of a volt.

942. Ttaermo-electric battery. — From what has been said it will be
understood that a thermo-electric couple consists of two metals soldered

Fig. 932.

Fig. 93 S.

together, the two ends of which can be joined by a conductor. Fig. 932
represents a bismuth-copper couple ; fig. 933 represents a series of couples
used by Pouillet. The former consists of a bar of bismuth bent twice at
right angles, at the ends of which are soldered two copper strips, f, d^ which
terminate in two binding screws fixed on some insulating material.

When several of these couples are joined so that the second copper of
the first is soldered to the bismuth of the second, then the second copper of

956

• D) ma VI ical Elect ricit) '

[942-

this to the bismuth of the third, and so on, this arrangement constitutes a
thermo-electric battery, which is worked by keeping the odd solderings, for
instance, in ice, and the even ones in water, which is heated to ioo°.

943. Nobili's thermo-electric pile. — NobiH devised a form of thermo-
electric batteiy, or pile^ as it is usually termed, in which there are a large
number of elements in a very small space. For this purpose he joined the
couples of bismuth and antimony in such a manner that, after having formed
a series of five couples, as represented in fig. 935, the bismuth from b was
soldered to the antimony of a second series arranged similarly ; the last
bismuth of this to the antimony of a third, and so on for four vertical series,
containing together 20 couples, commencing by antimony, finishing by
bismuth.

Thus arranged, the couples are insulated from one another by means
of small paper bands covered with varnish, and are then enclosed in a
copper frame, P (fig. 934), so that only the solderings appear at the two
ends of the pile. Two small copper binding screws, ni and «, insulated

in an ivory ring, communicate in the
interior, one with the first antimony,
representing the positive pole, and
the other with the last bismuth, repre-
senting the negative pole. These
binding screws communicate with the
extremities of a galvanometer wire
when the thermo-electric current is to
be observed.

944. Becquerel's thermo-electric
battery. — Becquerel found that arti-
ficial sulphuret of copper heated from 200^ to 300° is powerfully positive,
and that a couple of this substance and copper hasan electromotive force
nearly ten times as great as that of the bismuth and copper couple in fig. 932.

Fig- 934-

Fig- 935-

Native sulphuret, on the contrary, is powerfully negative. As the artificial
sulphuret only melts at aljout 1,035°, it may be "^^^d at very high tempera-
tures. The metal joined with it is Cierman silver (qo of copper and 10 of
nickel). Fig. 936 represents the arrangement of a battery of 50 couples

-945]

CliiuioicVs ThcrDW-clcctric Battery.

957

arranged in two series of 25. Fig". 937 gives on a larger scale the view of a
single couple, and fig. 93S that of 6 couples in two series of 3. The sulphuret
is cut in the form of rectangular prisms, 10 centimetres in length, by 18 mm.
in breadth, and 1 2 mm. thick. In front is a plate of Cierman silver, w, intended
to protect the sulphuret from roasting when it is placed in a gas flame.
Below there is a plate of (German silver MM, which is bent several times so

F'g- 937-

Fig. 938.

as to be joined to the sulphuret of the next, and so on. The couples, thus
arranged in two series of 25, are fixed to a wooden frame supported by two
brass colums, A, B, on which it can be more or less raised. Below the couples
is a brass trough, through which water is constantly flowing, arriving by
the tube b and emerging by the stopcock r. The plates of German silver
are thus kept at a constant temperature. On each side of the trough are two
long burners on the Argand principle, fed by gas from a caoutchouc tube, a.
The frame being sufficiently lowered, the ends are kept at a temperature of
200° or 300°. For utilising the current, two binding screws are placed on
the left of the frame, one communicating with the first sulphuret, that is, the
positive pole, and the other with the last German silver, or the negative pole.
At the other end of the frame are two binding screws, which facilitate the
arrangement of the couples in different ways.

945. Clamond's thermo-electric battery. — Of the attempts which have
been made to apply thermo-electric currents to directly practical purposes
perhaps the most successful has been Clamond's, which has been used
for telegraphic purposes and also for electroplating. Its characteristic
features are the construction and arrangement of the elements, and the
manner in which the heating is effected.

The negative element consists of an alloy of two parts of antimony and
one of zinc, forming a flat spindle-shaped bar from 2 to 3 inches in length, by
I inch in thickness (fig. 940). The positive metal is a thin strip or lug of tin-
plate, stamped as represented at a a' in fig. 939 ; this s then bent in as shown
at r, and being held in a mould, the alloy, which melts at 260° C, is poured
in. The individual elements have then the appearance represented in fig.
940, and to connect them together the tin lugs are bent into shape, and joined
in a circle of elements (fig. 941), being kept in their position by a paste of
asbestos and soluble glass ; flat rings of this composition are also made,
and are placed between each series of rings piled over each other ; the con-
nection between the individual elements and between the sets of rings is

958

Dynamical Electricity.

[945-

lo.

made by soldering together the projecting ends of the tin lugs. Thin plates

of mica are placed between the alloy and the tin plate, excepting at the

place of soldering. Looked at from the inside

the faces of the battery present the appearance

of a perfect cylinder.

The heating is effected by means of coal
gas, admitted through an earthenware tube,
A B, fig. 942, perforated by numerous small
holes ; this is surrounded by a somewhat larger
iron tube, C D, reaching nearly to the top of the
cylinder, which is closed by a lid, E F. Air
enters at the bottom of this tube, and the heated gases, passing up the tube,
curl over the top, descend on the outside, and escape by a chimney, G H. This.

Fig. 939.

Fig. 940.

Fig. 941. Fig. 942.

arrangement economises gas and prevents danger from overheating, as the
gas-jets do not impinge directly on the element. The supply of gas is
regulated by an automatic arrangement, so that the temperature is not
higher than about 200°.

Although sometimes convenient, thermo-electric batteries are not an
economical source of electricity. Thus a Clamond's battery of 120 elements
has an E.M.F. of 8 volts, and a resistance of 3-2 ohms; its maximum
available work can be shown to be 5 watts per second ; and the consump-
tion of gas per hour is 180 litres. The heat of combustion of a litre of gas
gives 5,200 gramme calories ; the heat expended per second is, therefore,
260 calorics, which would correspond to 1,084 watts. The yield is, there-
fore, about ..,',„ of the heat supplied.

946. Mellonl's thermomultlplier. — We have already noticed the use
which IMelloni made of N<)l)ili's pile, in conjuiution with the galvano-
meter, for measuring the n\ost feeble alterations of temperature. Th6
.irrangcmcnt he used for his experiment is represented in fig. 943.

On a wooden base, provided with levelling screws, a graduatcil copper

946]

Melloni 's Thermoimiltiplier.

959

rule, about a metre long, is fixed edgeways. On this rule the various parts
composing the apparatus are placed, and their distance can be fixed by
means of binding screws. <? is a support for a Locatelli's lamp, or other source
of heat ; F and E are screens ; C is a support for the bodies under experi-
A

Fig. 943-

ment, and ni is a thermo-electrical battery. Near the apparatus is a gal-
vanometer, D ; this has only a comparatively few turns of a tolerably thick
(I mm.) copper wire ; for the electromotive force of the thermo-currents is
small, and as the internal resistance is small too, for it only consists of metal,
it is clear that no great resistance can be introduced into the circuit if the
current is not to be completely stopped. Such galvanometers are called
thermomultiplie7-s. The delicacy of this apparatus is so great that the heat
of the hand is enough, at a distance of a yard from the pile, to deflect the
needle of the galvanometer.

In using it for measuring temperature, the relation of the deflection of the
needle, and therefore of the strength of the current, to the difference of the
temperatures of the two ends must be determined. That known, the tem-
peratures of the ends not exposed to the source of heat being known, the
obser\'ed deflection gives the temperature of the other, and therewith the
intensity of the source of heat.

The most sensitive arrangement of this class is the radiojuicrotiicter
invented by Mr. Boys. It consists of a light thermojunction suspended by
a thin quartz thread between the poles of a strong horse-shoe magnet ; it
resembles in fact D'Arsonval's galvanometer (fig. 761). With the slightest
difference in the temperature of the two ends of the bars of the thermo pair
a current is produced in its circuit, and this being in a magnetic field is
deflected like any current under the influence of a field. And as the force
tending to deflect it is the product of the current with the strength of the
field, it follows that with a strong field only an extremely feeble current is
necessary to produce a considerable deflection. By its means Mr. Boys can
detect differences of less than one millionth of a degree Centigrade. It
will clearly respond to a quantity of heat not greater than that which would be
received on a halfpenny by the flame of a candle at a distance of 1,530 feet.

960

Dynamical Electricity.

[947-

947. Properties and uses of tbermo-electric currents. — Thermo-elec-
tric currents are of extremely low potential, but of great constancy : for their
opposite junctions, by means of melting ice and boiling water, can easily be
kept at 0° and 100^ C. On this account. Ohm used them in the experimental
establishment of his law. They can produce all the actions of the ordinary
battery in kind, though in less degree. By means of a thermo-electrical pile
consisting of 769 elements of iron and German silver, the ends of which
differed in temperature by about 10° to 15°, Kohlrausch proved the presence
of free positive and negative electricity at the two ends of the open pile
respectively. He found that the potential of the free electricity was nearly
proportional to the number of elements, and also that the electromotive force
of a single element under the above circumstances was about ^-.^-^ that of a
single Daniell's element. On account of their low potential, thermo-electric
piles produce only feeble chemical actions. Botto, however, with 120 platinum
and iron wires, decomposed water.

948. Thermo-electric diag-ram. — Thermo-electric relations may be very
conveniently illustrated by means of what is called the thermo-electric dia-
gram. In fig. 944 the abscissae represent the temperatures of the junctions
on the centigrade scale. If, now, the thermo-electric deportment of any
metal with another, taken as standard, be determined for any given tempe-

laUuc, the corrcsixjnding differences of potential arc reprcscntcil by an
ordinate according to a definite scale. In the diagram the ordinates repre-
sent microvolts (964), and lead is taken as standard. A line which connects
the ordinates thus determined is called a thermo-ctectric tine ; the lines arc
here represented as straight, though some, such as iron and nickel, present
distinct sinuosities, and may thus cross the straight line belonging to
another metal more than once, indicating therefore more than one neutral
temperature.

-949]

Becquerel's Electric Pyrometer.

961

It will be seen that, if we know the dififerences of potential of any two
metals in respect of lead, the thermo-electrical lines give us the differences
of potential of these two metals directly. If, for example, for the metals
copper and iron the junctions are heated to 0° and 100° respectively, the
mean temperature is 50°, and the difference of the two ordinates_yjj/' gives
the thermo-electric force of the combination for this mean temperature, the
metal at the top, copper, being electropositive ; the area xo— iS^i represents
the total tRermo-electric force in the circuit. If the temperatures of the two
junctions were 300° and 500°, the mean temperature will now be 400°, and
the difference, _y J/', would represent the thermo-electric force, which in this
case would be from iron to copper ; that is, iron is now electropositive to
copper.

The point n where two lines cross one another, and where, therefore, there
is no electromotive force, represents the neutral temperature, or temperature
of inversion (940) ; for copper-iron this is at 276°, for iron-cadmium it is at 140°.

949. Becquerel's electric pyrometer. — This apparatus is an improved
form of one originally devised by Pouillet. It consists (fig. 945) of two wires,

I*"ig. 945.

one of platinum and the other of palladium, both two metres in length and
a square millimetre in section. They are not soldered at the ends, but firmly

962 Dynavncal Electricity. [949-

tied for a distance of a centimetre with fine platinum wire. The palladium
wire is enclosed in a thin porcelain tube ; the platinum wire is on the outside,
and the whole is enclosed in a larger porcelain tube, P. At the end of this
is the junction, which is adjusted in the place the temperature of which is to
be investigated. At the other end project the platinum and palladium wires
in and «, which are soldered to two copper wires that lead the current to a
inagneto7neter, G. These wires at the junction are placed in a glass tube
immersed in ice, so that, being both at the same temperature, they give rise
to no current.

The magnetometer, which was devised by Weber, is in effect a large
galvanometer. It consists of a magnetised bar, ab, placed in the centre of
a copper frame, which deadens the oscillations (904) and rests on a stirrup,
H, which in turn is suspended to a long and very fine platinum wire. On
the stirrup is fixed a mirror, M, which moves with the magnet, and gives
by reflection the image of divisions traced on a horizontal scale, E, at a
distance. These divisions are observed by a telescope. With this view,
before the current passes the image of the zero of the scale is made to coin-
cide with the micrometer wire of the telescope : then the slightest deflection
of the mirror gives the image of another division, and therefore the angular
deflection of the bar (522). This angle is always small, and should not
exceed 3 or 4 degrees : this is effected by placing, if necessary, a rheostat or
any resistance coil in the circuit. The angular deflection being known, the
intensity of the current and the temperature of the junction are deduced
from pyrometric tables. These are constructed by interpolation when the
strengths are known which correspond to two temperatures near those to be
observed. The indications of the pyrometer extend to the fusing point of
palladium.

950. Peltier's experiment. — When on a bar of bismuth, BB', cut half-
way through at its centre (fig. 946), is soldered a bar of antimony with a
similar cut, and when the ends A and B are connected with a gahanometer,
the needle of the galvanometer is deflected in one direction when the junction
is heated, and in the other when it is cooled.

Peltier found by means of this apparatus, which is known as Peltier's
cross, that when the end A' was connected with one pole, and B' \\ith the
other pole of a voltaic element, so that a current passed from A' through the
junction to B', the needle was deflected in such a direction as to show that
the junction was heated when the positive current passed from A' to B',
while it was cooled when the current passed in the opposite direction.
This is culled the Peltier effect. In order to show the cooling eftect, this
experiment may be made by hermetically fixing in two tubulures in an air
thermometer a compound bar consisting of bismuth
and antimony soldered together, in such a manner
that the ends project on each side. The projecting
parts are provided with binding screws, so as to allow
a current to be passed through. When the positive
current passes from the antimony to the bisniutii, tlie
air in the bulb is heated, it expands, and the liquid iji
the stem sinks ; Ijut if it passes in the opposite direc-
tion the air is cooled, it contracts, and the liquid rises in the stem. The

-950]

Peltier s Experiment.

963

current must not be too strong ; that of a single Bunscn's cell is usually
sufilicient ; it is best regulated by a rheostat (949).

By making a small hole at the junction of a bismuth and antimony bar, in
which was placed a drop of water and a small thermometer, the whole being-
cooled to zero, Lenz found that when a current was passed from bismuth
to antimony the water was frozen and the thermometer sank to -3'5°C.

The Peltier experiment may also be illustrated by interposing an iron
wire between two copper wires, and surrounding the first with water at 0°,
and the second with ice at 0°. On passing a feeble current, it is found that
as much ice melts at one junction as is produced at the other.

The Peltier effect is independent of the heating effect produced when a
current traverses any conductor, and which may be called the frictional
heating or Joule effect. The heat due to this cause is proportional to the
square of the current, C, to the resistance, R, and to the time, /, and is
independent of the direction of the current (830) ; while the Peltier effect is
proportional to the strength of the current and to the time, and is reversible
with its direction. This suggests a method of determining the effect in ques-
tion. If this be called /;>, the heat due to it will be /;>€/, and that due to
the frictional heating will be C'-R/. Hence if the current be passed so that
in one case the Peltier effect coincides with the Joule effect, while in the
other it is opposed to that effect, we shall have for the total heat H and H'
in the two cases ; H = C'^R^+ ^>C/, and H' = C-R/- ^feC/, from which

^~ 2Ct •

That the Peltier effect is independent of the Joule heating has been in-
vestigated by Edlund, by a method the principle of which is represented in
fig. 947. M and N are two bulbs,
and are connected by a narrow glass
tube, in which is a drop of liquid
serving as index. The rods of metal
A and B are fixed airtight in the bulbs,
and are soldered at 7n and ?t, while
the free ends can be connected
with a battery. If the pieces in
and n inside the glass vessels
offer the same resistance, and these
vessels are of the same size, when the
current passes the Joule effect is the
same in each case, and consequently
the index is equally pressed in opposite directions, and therefore does not move-
But the Peltier effect is opposite in the two vessels, and produces a displace-
ment of the index, from which the change of temperature can be deduced.

The Peltier effect, as will be seen, is greater as the term C'-R, or the
strength of the current, is less, and hence it can only be shown with feeble
currents.

These experiments form an interesting illustration of the principle, that
whenever the effects of heat are reversed heat is produced ; and whenever
the effects ordinarily produced by heat are otherwise produced, cold is the

3Q 2

Fig. 947.

964

Dynamical Electricity

[950-

result ; for cooling takes place when the current is in the same direction
as the thermo-current which would be produced by heating the junctions,
and heating when the current is in the opposite direction.

950(7. Thomson effect. — If we take two bars of the same metal A B and
A' B', which are connected at the ends A A' , by a wire, while a current can be

passed through the other,
then the temperature of each
part of the bar due to the
Joule effect would be the
same when the stationary
condition is attained. If the
two ends B B' are kept at a
constant temperature of 100°
by being immersed in boiling
water, while the others A A,
are placed in melting ice,
and are thus at 0°, and if
now a thermopile be placed
with its two opposite faces in contact with symmetrical positions of the two
bars, it will be found that when a current passes through the system at A A',
the galvanometer of the thermopile is deflected, showing that there is a dif-
ference of temperature at the two ends of the pile, that is, that the corre-
sponding parts of the bars are not at the same temperature. In the case of
copper, silver, zinc, and antimony the point would be hotter on that bar
along which the positive current passes from cold to hot ; in the case of
tin, aluminum, platinum, bizmuth, and iron it is when the negative current
passes.

This phenomenon, which is known as the Thomson effect from its dis-
coverer. Sir W. Thomson, is most marked in antimony among positive
metals, and in iron ; it is a sort of electrical convection of heat ; in copper
the positive current carries electricity along with it more readily than iron ;
it has, in short, a greater specific lieat of electficity.

'^iiiiiii!iiiiiiiriiiiiiiiiiiiiiiii!niiiiiiii]iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiniiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiMiiiiiii^
Fig. 948.

-962] Determination, of the Resistance of a Conductor.

965

CHAPTER IX.

DETERMINATION OF ELECTRICAL CONSTANTS.

Fig. 949.

951. Rbeostat. — A Rheostat is an instrument by which the resistance
of any given circuit can be increased or diminished without opening the
circuit. The original form invented

by Wheatstone consists of two parallel
cylinders, one, A, of brass, the other,
B, of wood (fig. 949). In the latter
there is a spiral groove, which termi-
nates at « in a brass ring, to which is
fi.xed the end of a fine brass wire. This
wire, which is about 40 yards long, is
partially coiled on the groove ; it passes
to the cylinder A, and, after a great
number of turns on this cylinder, is
fixed at the extremity e. Two binding
screws, n and o, connected with the
battery, communicate by two steel
plates ; one with the cylinder A, the
other with the ring a.

When a current enters at <?, it
simply traverses that portion of the wire rolled on the cylinder B, where the
windings are insulated by the grooves ; passing thence to the cyHnder A,
which is of metal, and in contact with the wire, the current passes directly
to in, and thence to n. Hence, if the length of the current is to be in-
creased, the handle d must be turned from right to left. If, on the contraiy,
it is to be diminished, the handle is to be fixed on the axis c, and turning
then from left to right, the wire is coiled on the cylinder A. The length of
the circuit is indicated in feet and inches, by two needles, at the end of
the apparatus not seen in the figure, which are moved by the cylinders A
and B.

952. Determination of tbe resistance of a conductor. Reduced
lengrtb — If in the circuit of a constant element a tangent galvanometer be
interposed, a certain deflection of the needle will be produced. If, then, dif-
ferent lengths of copper wire of the same diameter be successively interposed,
corresponding deflections will in each case be produced. Let us suppose
that in a particular case the tangent of the angle of deflection (823) observed
with the element and tangent galvanometer alone was rSS, and that when
5, 40, 70, and 100 yards of copper wire were successively placed in the
circuit, the tangents of the corresponding deflections were 0-849, 0*172,

966

D) 'iia HI ical Electricity.

[952-

0-105, ^"d 0-074. Now, in this experiment, the total resistance consists of two
components — the resistance ofifered by the element and the tangent gal-
vanometer, and the resistance offered by the wire in each case. The former
resistance may be supposed to be equal to the resistance of x yards of copper
wire of the same diameter as that used, and then we have the following
relations : —

Lefigt/i of wire. TangeiJt of angle of deflection.

X yards '. . '. 1-88

A- + 5 „ 0-849

;i-+4o- 0-172

.t-+7o „ . ■ 0-105

A-+ 100 „ 0-074 ■

If the intensities of the currents are inversely as the resistances — that is,
as the lengths of the circuits — the proportion must prevail,

X : .r+ 5 =0-849 : i'88 ;
from which .t-= 4-1 1. Combining, in like manner, the other observations, we
get a series of numbers, the mean of which is 4-08. That is, the resistance
offered by the element and galvanometer is equal to the resistance of 4-08
yards of such copper wire, and this is said to be the reduced length of the
element and galvanometer in terms of the copper wire.

It is of great scientific and practical importance tohave a ttm't or standard
of comparison of resistance, and numerous such have been proposed. Jacobi
proposed the resistance of a metre of a special copper wire a millimetre in
diameter. Copper is, however, ill adapted for this purpose, as it is difficult
to obtain pure. Matthiessen proposed an alloy of gold and silver, contain-
ing two parts of gold and one of silver ; its conducting power is very little
affected by impurities in the metals, by annealing, or by moderate changes
of temperature.

Siemens' unit is a metre of pure mercury, having a section of a square
millimetre. Its actual material reproduction for ordinary use is a German
silver wire 3-8 metres in length and 0-9 mm. in diameter. It is 0-9534 of

an ohm (963). A
„„Tm _ mile of No. 16 pure

copper wire repre-
sents a resistance
of 13-67 ohms.

953. Resistance
colls.— The actual
material ])roduction
of a standard resist-
ance is ordinarily a
given length of wire
of a certain defi-
nite material, and is
known as a 7-csist-
ancc coil. An alloy^
of silver with about \ of platinum is'best, as it is very permanent, and its re-
sistance varies little with increase of temperature. Such resistance coils are

-954] Resistance Coils. 967

usually employed in what are called resistance boxes (fig. 950). Fig. 951
represents the way in which resistance coils are affixed inside the box. On
the top of the box, which is of slate or ebonite, are a number of solid pris-
matic pieces of brass fixed a little
distance apart ; at their ends are
conical perforations in which fit brass
plugs. Inside the box are fitted to
'these brass pieces the various lengths
of wires which represent very accu-
rately the resistances ; they are
covered with insulated wire, and are
wound double, so as to neutralise any
extraneous inductive action. If the

1 r • • 1 ''''g- 951-

termmals of a circuit are connected

with T T', fig. 951, and all the plugs are inserted, the resistance box offers no
appreciable resistance, for the current passes by the plugs and the massive
metal ; but by taking out any of the plugs the current has to pass through the
wire coil between the two brass pieces, and thus its resistance is introduced.
In figure 950 this represents the use of a resistance of 74 ohms.

The coils are in multiples and submultiples of ohms, and are so arranged
that their combination may be as greatly varied with as few resistances as
possible. Thus a set of eleven coils of o-i, 0-2, 0-2, 0-5, 2, 2, 5, 10, 10, 20, and
50 enables us to introduce any resistance from 0"i to 100 into the circuit.

Resistance boxes have almost entirely superseded the rheostat and
similar instruments. They are more accurate, and not nearly so likely to
suffer from use.

954. Absolute measure of electrical resistance. — When the resistance
of any conductor has been measured and expressed by reference to any of
the standards of resistance mentioned in the preceding paragraph, the num-
ber denoting the result of the measurement still does not tell us what the
resistance of the conductor in question really is ; it only tells us what mul-
tiple it is of the resistance of the particular conductor with which the com-
parison has been made. It gives us merely a relative and not an absolute
measure. Just in the same way, if we are told that the pressure of the steam
in a boiler is equal to (say) 8 atmospheres (157), this statement does not in
itself enable us to form any estimate of what the actual pressure of the steam
is ; it only tells us that, whatever the pressure of an atmosphere may be,
that of the steam is 8 times as great. In order that we may be able to cal-
culate what effects the pressure of the steam is capable of producing, we
require to have it stated in absolute measure— that is, not how much greater
or less it is than some other pressure — but what actual force is exerted by it
on each unit of surface. So, for very many purposes, we require absolute
measures of electrical resistance, instead of mere comparisons of the resist-
ance of one conductor with that of another.

To see how it is possible to get an absolute measure of resistance, we
must go back to the fundamental meaning expressed by the term. If, by
any means whatever, a definite electromotive force or difference of potential is
maintained between any two given cross-sections of a conductor, a constant
electric current flows from one cross-section to the other, and, for the same

968 Dynamical Electricity. [954-

conductor, the ratio of the electromotive force to the strength of the resulting
current is consta7it. That is, if Ej, E,,, E.., ... be various values succes-
sively given to the electromotive force, and Cj, C.„ C3, . . . be the corre-
sponding strengths of the current, then

E,^E,^E3^ ... = R (a constant).

Uj U2 1-3

This constant ratio of electromotive force to strength of current is charac-.
teristic of the individual conductor employed, and is called its electrical
resistance. And, when the resistance of a conductor is stated as the value
of the ratio in question, the statement gives us the absolute measure of the
resistance : that is, it gives us definite information about the electrical pro-
perties of that particular conductor without implying a comparison of it with
any other conductor.

Hence it appears that the absolute resistance of a given conductor is
determined if we can ascertain the ratio of any electromotive force to the
strength of the current which it is capable of producing in the conductor in
question. It is not, hoAvever, needful to make an independent measurement
of this ratio in the case of every conductor whose resistance we require to
know ; it is sufficient to determine it once for all for some one conductor, and
then, taking this conductor as a standard, to compare the resistance of other
conductors with that of this one, by means of Wheatstone's Bridge (948),
or any other convenient method.

The methods available for determining the ratio between electromotive
force and resistance, required for an absolute measurement of resistance,
depend on the electromagnetic phenomena presented by electric conductors
and currents ; it will be sufficient here to indicate the general principles
upon which such methods can be founded. From what has been said it will
be seen that any method for this purpose involves a measurement of electro-
motive force and a measurement of the strength of a current. It will be
convenient to treat these two parts of the process separately.

A. Absolute measurement of electromotive force. — When any electric
conductor is moved in a magnetic field (707), that is to say, in any region
where there is magnetic force, an electromotive force is in general developed
in the conductor during its motion. The magnitude of this electromotive
force depends upon the strength of the magnetic field, on the length and
form of the conductor, and on the velocity and direction of its motion. The
simplest case is presented by a straight conductor, with its length perpen-
dicular to the direction of the force in a uniform magnetic field, and moving
at right angles to its length and to the direction of the force. If T be the
strength of the field, / the length of the conductor, and v the velocity, the
electromotive force E is

E=/T77',

where /' is a constant, dcjicnding on the unit ado])lcd for the measurement
of electromotive force. If we define the unit of electromotive force as that
which is developed in a conductor of unit length mor'ing {in the way specified
above) with unit velocity in a magnetic yield of unit intensity the constant I:
becomes = i, and the value of E is

E = T/7'.

-954] Absolute Measure of Electrical Resistance. 969

If the length and the direction of motion of the conductor are not at right
angles to the direction of magnetic force, we must project both on a plane
perpendicular to the direction of the force ; thus, if the conductor is inclined
at an angle a, and moves in a direction making an angle |3, both being
measured from the direction of magnetic force, the electromotive force
becomes

E = T/ sin a. V sin /3.

If the conductor is bent in any way, so that a has different values for different
parts, and if the direction or velocity of its motion varies from one part to
another, we may conceive of it as divided into a great number of equal parts,
each so small that no sensible variation of o, /3, or v can occur within it, we
may calculate the electromotive force due to each of these small parts taken
separately by the last formula, and then, adding all the results together, we
obtain the electromotive force developed in the whole conductor. A little
consideration will show that the following statement is equivalent to that just
given : namely, the electromotive force generated in a conductor moving
in any manner in a magnetic tield is proportional at each instant to the
rate of variation of the area swept over by its projection on a plane perpen-
dicular to the direction of the magtietic force ; and the average electromotive
force acting in the conductor during any interval of time is proportional
directly to the total area swept over by its projection during the interval,
and inversely to the length of the interval.

In order to apply practically the principles that have been pointed out,
it is most convenient to take advantage of the magnetic field due to the
magnetism of the earth. Throughout any moderate space at a distance
from magnets or masses of iron, the magnetic force due to the earth is
uniform in intensity and direction. Suppose, then, a circular conducting
ring, placed so that its plane is perpendicular to the direction of the earth's
magnetic force — that is, to the direction of the dipping needle — to be turned
through half a revolution about one of its diameters ; we may regard its pro-
jection on a plane perpendicular to the direction of the earth's force to be
made up of the projections of the two semicircles into which it is divided by
the axis of rotation. During the half-turn made by the ring, the projection
of each semicircle sweeps through an area equal to that of the whole ring ;
but one projection passes over this area in one direction, and the other in
the opposite direction. Consequently, equal electromotive forces are gene-
rated in the two halves of the ring, in opposite directions as regarded from
outside, but both in the same direction if considered as tending to produce a
current round the ring : the total electromotive force is therefore the sum of
the forces in the two halves, and if r be the radius of the ring, and therefore
7rr^ its area, and n the number of revolutions per second, so that the time

occupied by each half-revolution is , the average electromotive force act-
ing in the ring as it rotates uniformly about a diameter is
2T . 7rr-'-f- -T7rr^»,

271

where T stands for the whole intensity of the earth's magnetic force. If
instead of a single ring, we have a circular coil of wire of u convolutions,

970 Dynamical Electricity. [954-

and if the axis of rotation makes any angle a with the line of clip, the elec-
tromotive force due to the rotation of the coil is
E = 4T7Tr-HU sin a.
Consecjucntly, the rotation of a coil of wire under the circumstances named
furnishes the means of obtaining an electromotive force, the absolute value
of which is given by the intensity of the magnetic field, the dimensions and
speed of the coil, and the position of its axes of rotation. If we can deter-
mine the strength of current which this electromotive force is capable of
producing in a given conductor, the absolute resistance of the conductor is
at once known.

B. Absolute measureiiieiit of the strength of currents. — The method ot
measuring the strength of electric currents is founded on the fact that a
force is exerted between a conductor carrying a current and any magnetic
pole in its neighbourhood. In general, both the distance and the direction,
as seen from a given magnetic pole, vary from point to point of the con-
ductor, so that it is generally impossible to give any simple statement of
the law according" to which a given current acts upon a magnetic pole in a
given position. But, if we consider only a very small length of a current,
neither the distance of its various points from a given magnetic pole, nor
their directions, can vary to a sensible extent ; and when these two condi-
tions are constant, the law of the force between the current and the pole
may be stated as follows : As to direction the force is perpendicular to a
plane containing the current and the pole, and acts upon a north pole, to-
wards the left hand of an observer looking at the pole from the line of the
current, and so placed that the nominal direction of the current is from his
feet to his head, or, upon a south pole, towards the right hand of an ob-
server similarly placed ; as to magnitude, the force is proportional directly
to the length (/) and to the strength (C) erf the current, to the strength of the
magnetic pole (;;/), and to the sine of the angle {6) made by the direction of
the current with a straight line drawn from it to the pole, and inversely to
the square of the distance {r') from the current to the pole. Hence, if the
force be denoted by/, we have

f=/&J^ sine,

r''-

where /' is a constant, depending on the units in which the numerical values
of the various c]uantities are expressed. If we define the unit strength of
cuirent as the strength of a current of loJiich unit length placed at unit dis-
taiice from a magnetic pole of unit strength., and nuiking evcryiohere a right
angle with a line drawti from it to the pole, everts unit force on the pole., k
becomes unity, and wo have

,- C;/// . n r^ fr'-
I = ,. sin 6, or C= -; . ^.
;- - ;/// sin 6

The most convenient way of founding upon these principles a practical

measurement of the strength of a current is to cause the current to go one

or more times round a vertical circle of kno\vn radius placed in the plane _

of the magnetic meridian, with a very short magnet suspended at the centre.

This is the arrangement of the tangent galvanometer already described

(823). If H is the intensity of the horizontal component of the earth's mag-

-954] Absolute Measure of Electrical Resistance. 971

netic force, the force which must be exerted upon each pole of a magnet
whose poles are of the strength + in and — ;;;, in a direction perpendicular
to the magnetic meridian, in order to deflect the magnet through an angle
7, is

/= Wm tan y.

Putting this value of/into the expression given above for the strength of
a current, we have

,, _ Hw tan 7 r'-
inl sin 6
But in the case supposed, that of a tangent-galvanometer with the current
going u' times round the circle, we have l = u'2na, if a is the radius of the
circle ; moreover, the distance r' of each part of the current from the magnet
is constant and equal to the radius, or r' = a, and the angle 6 is also constant,
being everywhere a right angle, so that sin 6=1; consequently we get for
the strength of the current in absolute measure,

C = - , -- tan y = ^ tan y.

fnu 2Tta 2nu

We have thus shown how both electromotive force and strength of cur-
rent can be measured in absolute units, and if these two measurements be
combined, the ratio of the numerical value of the electromotive force, acting
in a conductor, to that of the strength of the resulting current, is the measure
of the resistance of the conductor in question. Using the notation employed
above, this leads to the following expression for the absolute measure of re-
sistance.

J, _ E _4 Tirr^tm sin a . 2-nu'
~ C H r' tan 7

Various practical methods of measurement founded upon this principle have
been devised, and when any of them is employed the value of the resistance
under investigation is obtained by putting in this formula the values of elec-
tromotive force and strength of current that result from the particular
arrangement adopted.

It may be observed with regard to the above expression, that the factors
TT, u, u', sin a and tan 3, are all of them simple numbers, that T and H are
quantities of the same kind, so that their ratio is also a pure number. The
only factors which involve reference to physical units are therefore r'-, r' and
;/, and the two former being both distances, the ratio r^-^r' is the first power
of a distance, while «, the number of revolutions per unit of time, is the re-
ciprocal of the time occupied by a single revolution. Hence the expression
for the absolute resistance of a conductor is in all cases reducible to

a distance 1 r *

. X a numerical factor ;

a time

that is to say, electrical resistance may be expressed in terms of the units of
length (or distance) and time in the same manner as a velocity, and the
natural unit of resistance, like the natural unit of velocity, would be repre-
sented byaunit of length per unit of time. Adopting' the C.G.S. system, the ab-
solute unit of resistance becomes one centimetre per second ; such a resistance,
however, is so small that resistances commonly occurring in practice would
have to be represented by inconveniently great multiples of it. As a

9/2 Dynmnkal Electricity. [954-

practical standard of resistance, it is, therefore, more usual to employ the
ohjn (963), which is a resistance of one thousand million centimetres per
second, or,

lo" centimetres
I second

955. ■Wheatstone's brldgre. — The various methods of determining the
electrical conductivity of a body consist essentially in ascertaining the ratio
between the resistance of a certain length of the conductor in question,
having a given section, to that of a known length of a known section of some
substance taken as standard. The most convenient method of ascertaining
experimentally the ratio between the resistance of two conductors is by a
method known as that of W heat stone' s bridge, xhe general principle of which
may be thus stated : —

The conductors, which may be denoted by AB and BC, are connected end
to end, as shown in fig. 952, and one end of each is also connected with a
battery, say the end A of AB with the positive pole, and the end C of BC
with the negative pole ; the ends that are ni connection with the battery are
likewise connected together by another conductor, AB'C. A current will
thus pass from A to C by each of the two paths ABC and AB'C, and there

Fig. 952.

will be a gradual fall of potential in passing from A to C along either path,
so that for every point in the conductors AB and BC there is a point in the
wire AB'C which has the same potential. If one end of a galvanometer
wire BGB' be connected with the point of junction B, the point of AB'C
which has the same potential as the point B can be found by applying the
other end of the galvanometer wire to AB'C, and shifting the point of con-
tact towards A or C until the galvanometer shows no deflection. Let B' be
the point so found ; the fact that when it is connected with B by the bridge
BGB' no current passes from one to the other proves that the potential
at B' is the same as the potential at B. From this it follows that if r and r'
are the resistances of AB and BC respectively, and s and s' the resistances
of AB'and B'C,

r : r' = s : s'.

If the conductor AB'C is a wire of uniform material and diameter, the
ratio of the resistances j- and s' will be the ratio of the lengths of the corre-
sponding portions of wire, and can therefore be at once really ascertained.

To prove this, let MN, NO, MN' and N'O' (fig. 953) be taken in the
same straight line, proportional respectively to the several resistances
r, r', s, s' ; and let MP Ijc drawn at right angles to O'MO of a length
])rop()rtional to the difference of potential between the points A and C. Then
if the straight lines PO and PO' be drawn, the potential at N (the point of
junction of the conductors whose resistances r and r' are to be compared —

-955]

WJieatstone's Brids:e.

973

i.e. the point corresponding to B in the previous figure) will be given by the
length of the line NO, drawn from N at right angles to NO ; and the point

P
S' S -r I yp'

Fig- 953.

N' (corresponding to B' in the previous figure), Avhere the potential is the
same as at N, will be found by drawing QQ' parallel to OO', and letting fall
from Q' the perpendicular Q'N' upon O'M. The geometry of the figure
gives obviously,

-^=^:2and-^=-^-S
r-^r' MP s + s' MP'

and therefore since NQ = NjQ,

A convenient form of Wheatstone's bridge, and one well adapted for
purposes of instruction, is that represented in fig. 954. It consists of a long
mahogany board, on which is fixed a thick copper band, which practically
offers no resistance. To the ends of this band is fixed a straight platinum

fig- 954-

wire, near which is a scale divided into 100 parts. At c and ^are breaks
in the copper band, provided with binding screws, in which are introduced
the resistances to be compared, O and x. The wires, from an element
which gives only a weak current, so as not to introduce heating effects, are
connected with the binding screws b and b'. Another wire connects the
binding screw g and one end of a sensitive galvanometer, the other end
of which is connected with a sliding spring contact-key g\ which is so
constructed that when the knob is depressed a knife-edge makes contact
with any part of the wire. The resistances to be compared having been
introduced at c and d., the position on the platinum wire is found by trial,
at which, when the key is depressed, the needle of the galvanometer is not
deflected. When this is found, for instance, at 34, the resistance of O : the
resistance of x = 34 : 66.

974 Dynamical Electricity. [955-

The principle of Wheatstone's bridge is of constant use in the measure-
ments required in telegraphy, and many other applications of electricity.
In practice the variations of the resistance are effected by means of resist-
ance coils (953) suitably arranged.

The resistance of a galvanometer may be determined by making it one
of the four conductors of a Wheatstone's bridge arrangement, replacing it
in the bridge by an ordinary contact-key. The resistances of the other con-
ductors are then varied until, on making contact, the deflection of the galva-
nometer is constant.

956. Equivalent conductors. — The resistance of a conductor depends,
as we have seen (825), on its length, section, and conductivity. Two con-
ductors, C and C, whose length, conductivity, and section are respectively
X,X', /c,(c', co,co', would offer the same resistance, and might be substituted for
each other in any voltaic circuit, without altering its strength, provided that

= —^— ; and such conductors are said to be equivalent to each other. An

KM K Ui

example will best illustrate the application of this principle.

It is required to know what length of a cylindrical copper wire 4 mm.
in diameter would be equivalent to 12 metres of copper wire i mm. in
diameter.

Let X = 12 the length of the copper wire i mm. in diameter, and X' the
length of the other wire ; then since in this case the material is the same, the

conductivity is also the same, and the equation becomes— =--. Now the

sections of the wires are directly as the squares of the diameters, and hence

we have " = — , or X' = 12 x 16 = 192. That is, 192 metres of copper wire 4
I- 4-

mm. in thickness would only offer the same resistance as 12 metres of copper

wire I mm. in thickness.

How thick must an iron wire be \\hich for the same length shall offer the
same resistance as a copper wire 2*5 mm. in diameter?

Here, the length being the same, the expression becomes /cw = k'o)', or since
the sections are as the squares of the diameter, Kif- = K'd''. The conductivity
of copper is unity, and that of iron 0-138. Hence we have 2 5^ = ^'- x 0-138
or ^'- = 6-25^0-138 = 45-3 mm, or d' = 6-7 mm. That is, any length of a
copper wire 2-5 mm. in diameter might be replaced by iron wire of the same
length, provided its diameter were 6-7 mm.

957. Determination of tbe Internal resistance of an element. — The
following is the method of determining tlie internal resistance of an clement.
A circuit is formed consisting of one element, a rheostat, and a gahanomcter,
and the strength C is noted on the galvanometer. A second element is then
joined with the first, so as to form one of double the size, and therefore halt
the resistance, and then by adding a length, /, of the rheostat wire, the
strength is brought to what it originally was. Then if E is the electromotive
force, and R the resistance of the element, r the resistance of the galvano-
meter and the other parts of the circuit ; the current strength C in the one

F E

case is C = ^ — , and in the other = —- — — ,,
R + r AR + ;'+/

cases is the same, R = 2/.

-958] Electrical Conductivity. 975

Another method is that due to Mance. The element whose internal
resistance is to be determined is placed in one of the arms of a Wheatstone
bridge, as at fig. 954, a resistance box being placed in the other. The gal-
\anometer is connected with the ends of the wire, and a simple contact-key is
interposed in the ordinary position of the galvanometer, and by trial its posi-
tion is found for the sliding contact such that when the key is depressed no
alteration is produced in the deflection of the galvanometer. When this
is found, the ordinary conditions of the bridge hold, that is, that the cross
products of the resistances are equal.

958. Electrical conductivity. — We may regard conductors in two
aspects, and consider them as endowed with a greater or less facility for
allowing electricity to traverse them, a property which is termed cotidiictivity.,
or we may consider conductors interposed in a circuit as offering an obstacle
to the passage of electricity — that is, a resistance which it must overcome.
A good conductor offers a feeble resistance, and a bad conductor a great
resistance. Conductivity and resistance are the inverse of each other.

The conductivity of metals has been investigated by many physicists by
methods analogous in general to that described in the preceding paragraph,
and very different results have been obtained. This arises mainly from the
various degrees of purity of the specimens investigated, but their molecular
condition has also great influence. Matthiessen found the difference in con-
ductivity between hard-drawn and annealed silver wire to amount to 8-5,
for copper 2-2, and for gold 1-9 per cent. The following are results of a
series of careful experiments by Matthiessen oft the electrical conductivity
of metals at 0° C. compared with silver as a standard : —

Silver .

loo-o

Platinum

. i8-o

Copper .

• 99-9

Iron

. i6-8

Gold .

. 8o-o

Tin . . .

• 13-1

Sodium

• 37-4

Lead .

• 8-3

Aluminum .

• 34-0

German silver

• 77

Zinc

. 29-0

Antimony

. 4-6

Cadmium

■ 237

Mercury

. 1-6

Brass .

. 22-0

Bismuth

. 1-2

Potassium

. 20-8

Graphite

. 0-07

Silver and copper have the smallest resistance for a given volume^ while
aluminum has the smallest for a given weight. ■

The conductivity of metals is diminished by an increase in temperature.
The law of this diminution is expressed hy the formula

Kt = K„{.^- at + bt'-) ;
where k, and k,j are the conductivities at / and 0° respectively, and a and b
are constants, which are probably the same for all pure metals. f"or ten
metals investigated by Matthiessen he found that the conductivity is ex-
pressed by the formula

k' — k" ( I - 0-0037647/ + 0-00000834/-).

It seems that this value is about 0-00368 for each degree C. This co-
efficient agrees in a surprising manner with the coefficient of expansion of
gases, which is ^■^.

Liquids are far worse conductors than metals. The conductivity of

976 Dynamical Electricity. [958-

a solution of one part of chloride of sodium in 100 parts of water is
__J_.._^ that of copper. In general, acids have the highest and solutions of
alkalies and neutral salts the lowest conductivity. The conducting power
of a solution increases with the number of molecules, but not in direct pro-
portion. For each solution, there is a certain strength, which is short of
saturation, which represents the maximum of conductivity (845). For
copper sulphate this is 18 per cent., and for sodium chloride 26-4 per cent.
If two badly conducting liquids be mixed the conductivity of the mixture is
greater than that of either of the constituents.

The following is a list of the conductivity of a few liquids as compared
with that of pure silver : —

Pure silver ....... 100,000,000,000

Nitrate of copper, saturated solution .... 8990

Sulphate of copper ditto 5420

Chloride of sodium ditto 31520

Sulphate of zinc ditto 5770

Sulphuric acid, I -ID sp. gr. 99070

„ „ 1-24sp.gr 132750

„ „ 1-40sp.gr 90750

Nitric acid, commercial .^8680

Distilled water 7

The last number was that found by Kohlrausch for distilled water, which
had been specially purified. Accordingly, a disc of water a millimetre in
thickness offers the same resistance as a column of silver of the same dia-
meter, but of a length equal to that of the moon's orbit. The least trace of
impurity in water markedly raises its conductivity : thus standing in the air
for 5 hours doubles it ; the addition of a millionth part of sulphuric acid—
that is, a drop in about 17 gallons — increases the conductivity tenfold. Ac-
cordingly we may say in effect that perfectly pure water is not a conductor,
and therefore is not appreciably decomposed.

Liquids and fused conductors increase in conductivity by an increase of
temperature (845). This increase is expressed by the formula

/f, = K, (! + «■/),

and the values of a are considerable. Thus for a saturated solution of sul-
phate of copper it is 0-0286.

The influence oi light \\\iov\. electrical conductivity in the case of selenium
has been already alluded to (930), and is directly proved by the following
cx])erimcnt. A thin strip of this metalloid, about 38 mm. in length by 13
in breadth, was provided at the ends with conducting wires and placed in a
box with a draw-lid. The selenium, having been carefully balanced in a
Wheatstone's bridge, was exposed to diffused light by withdrawing the lid,
when the resistance at once fell in the ratio of 1 1 to 9. On exposure to the
various spectral colours, after having been in the dark it was found to be most
affected by the red ; but the maximum action was just outside the red, where
the resistance fell in the ratio of 3 to 2. Momentary cxposiu-e to the light'of
a gas lamp or even to that of a candle caused a diminution of resistance.'
Exposure to full sunlight diminished the resistance to one half.

-959] Determination of Electromotive Force. 977

The effect produced on exposure to light is immediate, while recurrence
to the normal state takes place more slowly. A vessel of hot water placed
near the strip produced no effect, and hence the phenomenon cannot be
due to heat, but there appear to be certain rays which have the power of
producing a molecular change in the selenium by which its conductivity is
increased.

If the two electrodes of a Ruhmkorff's coil are connected with a Geissler's
tube, suitably e.\hausted, so that a discharge just does not pass when the
apparatus is in the dark, it is at once formed when the path is exposed to
the ultra violet rays of light.

When a large and small induction coil are inserted in the same circuit
so that they spark simultaneously, it is found that by interposing a screen
between the two the smaller spark is shorter than when it is exposed to the
light of the other. The action diminishes as the distance between the two
sets of sparks increases. By varying the nature of the screen and other
experiments, it has clearly been established that this alteration is not due
to any electrical effect, but is to be ascribed solely to the ultra violet rays.

959. Setermination of electromotive force. — IVheatstone's metbod.
In the circuit of the element whose electromotive force is to be determined
a tangent galvanometer and a rheostat are inserted, the latter being so
arranged that the strength, C, of the current is a definite amount ; for
example, the galvanometer indicates 45°. By increasing the amount of the
rheostat wire by the length, /, a diminished strength, c (for instance, 40°), is
obtained.

A second standard element is then substituted for that under trial, and
by arranging the rheostat, the strength of the current is first made equal to
C, and then, by addition of /, length of the rheostat, is made = c.

Then if E and E, are the two electromotive forces, R and Ri their resist-
ances when they have the intensity I, and / and l^ the lengths added, we
have

Trial Element. Standard Element.

c=iL c=E,

R Ri

.= E - E.

RW Rj+//

from which we have

E = E,^.

Hence the electromotive forces of the elements compared are directly as the
lengths of the wire interposed.

Another method is that of Wiedemann. The two elements are con-
nected in the same circuit with a tangent galvanometer, or other apparatus
for measuring strength, first, in such a manner that their currents go in
the same direction, and secondly, that they are opposed. Then if the elec-
tromotive forces are E and E', their resistances are R and R', the other
resistances in the circuits r, while C, is the intensity when the elements are
in the same direction, and C, the intensity when they go in opposite direc-
tions, then

978

whence

Dynamical Electricity.

[959-

E;E'_andC„-
R + R' + r

E-E'
R + R' +

^, E(C,-Cd)

The difference of potentials or E.M.F. between any two points of a
circuit conveying a current, such as that of a magneto machine, may be
determined by charging a condenser from the terminals at the points in
question, and discharging it through a galvanometer with a high resistance,
and then repeating the operation with a standard cell, such as that of Latimer
Clarke, the E.M.F. of which is 1-433 volts (964). If ^is the deflection of the
galvanometer when the standard cell is used, and D the deflection after the

discharge of the current, and if a shunt be used so that only of the current

nV>

passes througli the galvanometer, then E.M.F. = _— - x i'433.

959(^«. Measurement of capacity. — In order to compare the capacities
of two condensers, the two armatures are severally connected with the two
poles of a battery, and are then discharged through a ballistic galvanometer ;
the amount of charge, and therefore the capacities, are proportioned to the
angles of throw of the needle.

If we have a condenser of known capacity this method may be used to
measure the E.M.F. of a battery, or rather to compare the E.M.F. of two
couples. Two capacities, C and C, may also be compared, by an arrange-
ment (fig. 955) resembling that of Wheatstone's bridge, by connecting the

Fi^. 955.

inner coaluigs at c and d respectively (fig. 954), their outer coatings being put
to earth. The two resistances « and <j' are adjusted, so that by raising or
lowering the key K, which puts the battery E in connection with A, no
current is shown in the galvanometer.

The condition of equilibrium is that tlie two points of the bridge B and
B' arc at the same potential, that is to say, that at a given lime the charges
(,) and ()^ arc jiroportional to the capacities C and C, ; as these charges are
proportional to the currents which produce them, and as these latter again
are inversely as the resistances, we have the proportion
(Z:Z, = a' : a.

</>o. Siemens' electrical resistance thermometer. — Supposing in a
\\ htalstonc ;> bridge arrangement, after the ratio r : r^ s : s^ has been esta-

-961] Divided or Branch Currents. 979

blished, the temperature of one of the coils, r, for instance, be increased, the
above ratio will no longer prevail, for the resistance of r will have been
altered by the temperature (958), and the ratio oi s and s^ must be altered so
as to produce equivalence. On this idea Siemens has based a mode of ob-
serving the temperature of places which arc difficult of direct access. He
places a coiipf known resistance in the particular locality whose temperature
is to be observed : it is connected by means of long good conducting wires
with the place of observation, where it forms part of a Wheatstone's bridge
arrangement. The resistance of the coil is known in terms of the rheostat,
and by preliminary trials it has been ascertained how much additional wire
must be introduced to balance a given increase in the temperature of the re-
sistance coil. This being known, and the apparatus adjusted at the ordinary
temperature, when the temperature of the resistance coils varies, this variation
in either direction is at once known by observing the quantity which must
be brought in or out of the rheostat to produce equivalence.

This apparatus has been of essential service in watching the tempera-
ture of large coils of telegraph wire, which, stowed away in the hold of vessels,
are very liable to become heated. It might also be used for the continuous
and convenient observation of underground and submarine temperatures.
If a coil of platinum wire were substituted for the copper, the apparatus could
be used for watching the temperature of the interior of a furnace. It has
been found that the magnetism of ships (715) excited so perturbing an
influence on the needle of the galvanometer as to make its indications
untrustworthy. Hence for use in such cases Siemens replaces the galvano-
meter, as an indicator, by a voltameter specially constructed for the purpose.
The same principle has Ipeen applied by Professor Langley to the inven-
tion of an instrument called the Bolometer, or actinic balance, for measuring
radiant heat. In the two arms of a Wheatstone's bridge are introduced
resistances which have very small mass, each consisting of a band of iron
half a millimetre in breadth, and 0-004 mr"- i" thickness, folded on itself 14
times so as to form a rectangle 07 cm. in length by 12 cm. in breadth.
The sensitiveness is far greater than that of the most sensitive thermopile,
and makes it possible to measure a difference of temperature of the ,„J„j of
a degree between the two resistances. It has been used by the inventor to
measure the distribution of heat in the solar spectrum. By its means he
has been able to map the dark heat of the spectrum, and to extend it far
beyond the limits which were previously known.

961. Blvided or brancb currents. — In fig". 956 the current from Bunsen's
element traverses the wire rqpiun. Let us take the case in which any two
points of this circuit, // and q, are joined by a second wire, nxq. The current
will then divide at the point q into two others, one of which goes in the
direction qpnni, while another takes the direction qxntn. The two points q
and // from which the second conductor starts, and at which it ends, are called
the points of derivation, the wire qpm and the wire qxn are derived wires.
The currents which traverse these wires are called the derived or partial
currents ; the current which traverses the circuit rqpnin before it branches
is the primitive current ; and the name principal current is given to the
whole of the current which traverses the circuit when the derived wire

3 R2

980 Dynamical Electricity. [961-

has been added. The principal current is stronger than the primitive one,
because the interposition of the wire qxn lessens the total resistance of the
circuit.

If the two derived wires are of the same length and the same section,

their action

would be the

same as if they

werejuxtaposed,

and they might

be replaced by

;i single wire of

the same length

but of twice

^'S- 956. the section, and

therefore with half the resistance. Hence the current would divide into

two equal parts along the two conductors.

When the two wires are of the same length but of different sections, the
current would divide unequally, and the quantity which traversed each wire
would be proportional to its section, just as when a river divides into two
branches, the quantity of water which passes in each branch is proportional
to its dimensions. Hence the resistance of the two conductors joined would
be the same as that of a single wire of the same length, the section of which
would be the sum of the two sections.

If the two conductors qpn and qx7i are different, both in kind, length,
and section, they could always be replaced by two wires of the same kind
and length, with such sections that their resistances would be equal to the
two conductors ; in short, they might be replaced by equivalent conductors.
These two wires would produce in the circuit the same effect as a single
wire, which had this common length, and whose section would be the sum
of the sections thus calculated. The current divides at the junction into two
parts proportional to these sections, or inversely as the resistances of the two
wires. Suppose, for instance, qpn is an iron wire 5 metres in length and
3 mm. square in section, and qxn a copper wire.

The first might be replaced by a copper wire a metre in length, whose
section would be f x i (taking the conductivity of copper at 7 times that of
iron) or if^^ square mm. The second wire might be replaced by a copper
wire a metre in length with a section of | square mm. These two wires
would present the same resistance as a copper wire a metre in length, and
with a section of ~ + \ = 3Y5 square millimetres.

The principal current would divide along the wires into two portions,
which would be as ,\ : \.

The most important laws of divided circuits are as follows : —
i. The sum of the strcnt^tJis in the divided parts of a ciycidt is equal to
the strength of the principal current.

ii. The strengths of the currents in the divided parts of a circuit are
inversely as their resistances ; or, what is the same, the division of a current
into partial currents which lie between two points is directly as the respective
conductivities of these branches.

And as problems on divided or shunt circuits frequently occur in tele-

962]

Electrical Mcasiiritisr Instninicnts.

981

graphy, the following foimuhu, which include these laws, are given for a
simple case.

If C be the strength of the current in the undivided part of the circuit
rqp/nn, and if c is the strength in one branch (say) in the above figure gpn
and c' in qxn ; if R, r, and r^ are the corresponding resistances, the electro-
motive force being E, then

P _ • E (r + rj Er , Er,

Rr + Rr, + rr, Rr + Rrj + rr.

The resistance R, of the whole circuit is

C':

Rr + R^j + rr^

and therefore the total resistance of the branch currents gpn and qxn is

961a. XTse of shunts. — The principle of divided or branch circuits has
an important application in shutits, by which any given proportion of even a
powerful current may be transmitted through a delicate
galvanometer, and thus their range is greatly extended.

They consist of a set of resistances usually J, g\, and
gig, of that of the galvanometer, arranged as represented
in fig. 957. G and G' are in connection with the ter-
minals of the galvanometer, and P, P' with those of the
battery. The gaps, O, A, B, C can be closed by plugs,
and thus the corresponding resistances introduced. When
they are all open, the entire current would pass through the
galvanometer. By plugging O the current is short-circuited,
and none of it passes through the galvanometer.

If g is the resistance of the galvanometer, s that of
the shunt, C the total current, and c that which passes
through the galvanometer and produces the deflection,
we may deduce from the laws of branch circuits

o^nrv^j^^j

gc = s{C-c) or C^

.J^s

Fig. 957-

The expressions^ — =in is called the inidtiplying poiuer of the shunt ;

it is the value by which the observed current must be multiplied to obtain
the principal currents. In the above cases the multiplying powers are 10,
100, and 1000 respectively,

962. Electrical IVXeasurlng: Instruments. — The numerous and impor-
tant technical applications of electricity have given rise to the invention of
numerous instruments for the simple and direct measurement of powerful
electrical currents. The amperomcter^ or briefly avwieter, for instance, gives
at once the strength of a current in amperes.

As a type of this instrument we may take a recent form of that invented
by Professors Ayrton and Perry ; it depends on the principle that when a
portion of an iron core is partly within and partly without a magnetising

Dynamical Electricity.

[962-

coil, it is drawn inwards when a current is passed through the coil. The
essential feature of the apparatus is a coil of insulated wire, in the axis of
which is a spiral attached at one end to an index moving over a graduated
scale. At the other end of the spiral is a brass cap to which is attached a
thin cylinder of fine sheet iron, which is in fact the core ; it encircles the
spiral and projects outside the coil. The spiral itself is formed of a
ribbon of thin phosphorus bronze coiled so as to form a very narrow cylinder.
This construction gives it the property that, unlike ordinary spirals, when its
length increases the free end rotates through a considerable distance.
Accordingly, when the current passes through the coil, the iron tube is
drawn within the spiral to an extent varying with the strength of the current ;
this thereby elongates the spiral to which it is attached, and the index
attached to the latter moves over the scale, finally taking up a position
which depends on the strength of the current. Such instruments are
graduated empirically and within any desired range by observing the de-
flection caused by passing through them currents of known strength.

The voltmeter^ which is not to be confounded with the voltameter (846),
measures the difference of potential between any two points of a circuit.
It consists essentially of a coil such as the above, but
with a great length of long fine wire. This can be in-
serted as a shunt without appreciably altering the resist-
ance of the circuit. Like the ammeter, this is empirically
graduated.

Cardcw's voltmeter depends on the heating effect pro-
duced when a current tra\crses a wire and consists essen-
tially of a long fine platinum wire, stretched by a spring or
a weight to which is attached a multiplying motion and
an index. This wire, being introduced between the points
of the circuit to be measured, becomes heated to an extent
proportional to the square of the difference of potentials,
and the motion of the index is a measure of this heating.
The principle of the clcctrodyiuDnomctcr is that of
measuring the repulsion between parallel currents moving
in opposite directions, one of them being fixed and the
other movable. Fig. 958 represents the essential features
of a form devised by Siemens for measuring the strength
of the powerful currents used in electric lighting ; w is
a coil of stout copper wire, and li'' a single wire ; nn
are mercury cups, and kk binding screw, by which con-
nection is made with the main circuit LL.

The wire it.'' is surrounde/;! by a stout spiral spring,
which is connected at one end with this wire, and at the other with a screw,
.J- ; this is provided with an index, z^ which mo\es o\er a graduated scale, S.
An index, z'z\ is also fixed to the wire iv'. At the outset both indexes point
to zero ; when the current passes it will be seen from the direction of the
arrows that it traverses the fixed and movable coils in opposite directions,
and the point z' is displaced along the scale. l>y turning the screw s it
is brought back to zero, in doing which the index z is moved through an'
angle which is a measure of the torsion of the spiral spring f, and this

Fig. 958.

-963] Absolute Electrical Units. 983

angle is proportional to the square of the strength of the current by which
the movable coil is deflected.

The electrodynamometer has by no means the sensitiveness which can
be readily obtained with galvanometers ; but it has the advantage that its
indications are independent of tlie strength of the external field, and when
the two coils are traversed by the same current they are also independent of
the direction of the current ; and can accordingly be used with advantage in
measuring alternatnig currents.

963. Absolute electrical units. — The great importance of having a
uniform system of measurements of physical magnitudes which should be
universally adopted is at once obvious, and this has been more especially
felt in the applications of electricity. The first step in this direction was
taken by the British Association, which adopted the system of absolute units
known as the C.("i.S. system, of which mention has already been made
(6i(?, 709), and which this account is intended to supplement.

The essence of an absolute system of physical measurements is that the
various units may be directly expressed in mechanical units {b\a). A system
of absolute electrical units may be based on either the electrostatic, the
electromagnetic, or again on the electrodynamic actions. There is no
theoretical reason why one should be preferred to another of these, but in
practice only the two former are used. Of these the electrostatic system is
perhaps the simpler, but that based on electromagnetism is most convenient,
and best lends itself to the practical determination of the most important
standards, such as those of electromotive force and resistance.

E/ectrostati'c Units.

We shall distinguish the dimensions of these units by small letters placed
in brackets.

Quiuitity of Electricity, q. Coulomb's law given for the repulsive force

between two equal quantities q, of electricity at the distance /, /= 1. (734),

from which q = l ^f. Hence we have for the dimensions of unit quantity of
electricity [^] = I f\ = UM^T-'.

Potefitial. V. The potential of a quantity of electricity at the distance /

is the quotient of the quantity by the distance. Hence [7/] = ^ = L-M^T^'.

Capacity, c. The capacity of a conductor is the quotient of the quantity
of electricity with which it is charged, by the potential which this quantity

produces in it ; [t"]= - from which \c\ = L. Hence the capacity of a con-
ductor is expressed by a length. Unit capacity is thus that of a body which
is raised by unit quantity to unit potential. An insulated conducting sphere
which has a diameter of one centimetre has unit capacity.

Current, i. The strength of a current is the quantity of electricity which

passes in a given time ; [/] = 2 = L? M ^*T-. Accordingly unit current is that

which conveys unit quantity of electricity in a second.

Resistance, r. From Ohm's law (S25), the resistance of a conductor is

984 Dynamical Electricity. [963-

the quotient of difference of potentials at the two ends of a wire by the
strength of a current. Hence [r] = ^ = L-'T, which shows that the dimen-
sions of resistance are the inverse of a velocity.

Electromag)ietic Units.

Quantity of magnetism. From Coulomb's law/ = — - from which [M] =

LIM^T-', that is, the same as that of quantity of electricity on the electro-
static system. Unit magnetic pole is that which repels an equal pole at a
distance of a centimetre with a force of a dyne.

Magnetic Field. H. Unit magnetic field is that field in which unit
quantity magnetism is acted on by unit force. Hence F = HM, from which

[h}=l-'m;t-'.

Current. I. The unit of electrical current in the electromagnetic system
is that which, traversing unit length of an arc of a circle of unit radius, exerts
unit force on unit pole, or unit magnetism at its centre. Its dimensions are

Quantity of electricity. Q. The quantity of electricity conveyed by a con-
ductor is the product of the current by the time that it lasts. Hence unit
quantity is that which passes in a second in a conductor in which unit current
is flowing, [Q] = IT = UMi.

Resistance. R. The resistance of a conductor may be defined by Joule's

law, W = r^RT. Hence [R] = ^, that is, the resistance of a conductor is
expressed by a velocity.

Electromotive force. Dilference of potentials [E]. From Ohm's law,
E = IR = UMiT--.

964. Practical units. — The values of the absolute units in the C.G.S.
system are not convenient for measuring the magnitudes which ordinarily
occur. Thus the absolute unit of resistance is that represented by the
twenty-thousandth part of a millimetre of pure copper wire
a millimetre in diameter. It has therefore iDeen necessary to
choose units better suited for practical uses, and at the Inter-
national Congress of Electricians at I'aris in 1881 an Inter-
national Commission was formed for the purpose of deciding
on such units and determining their value. In 1884 the
Commission agreed to recommend the following, which are
in the main those introduced by the British Association.

The practical unit of resistance is equal to 10^ absolute
electromagnetic C.G.S. units of resistance, and is called the
Ohm. It has been decided to represent it by a column of
'B- 959- pure mercury with a cross section of a square millimetre ;

its exact length has been determined experimentally by the Commission,
and has been taken at ro6 metre. This is known as the legal ox Congress
ohm. Copies of this standard may be made either in mercury (fig. 959), or
in wire (fig. 958), and each copy has the value marked upon it, which is^
correct for a certain temperature. A wire of pure copper, a millimetre in
diameter and 46-25 metres in length, has a resistance of one ohm. Siemens'
unit (952) has a resistance of 0-94339 ohm. The copper conducting wire

-964] Practical Units. 985

of an ordinary submarine cable has a resistance of about 1 1 ohms per
mile.

In order to express multiples and submultiples the prefixes mega or
micro are used, which are respectively a million times as great or as small.
Thus a megohm is 10'' ohms, that is, 10'^' absolute units of resistance. In
like manner a micro/im is lo'" ohm, that is, 10^ = 1000 such units.

The Volt is the practical unit of electromotive force or of difference of
potentials, and is equal to lo"* absolute units. From the difficulty of getting
an element which is perfectly constant, more especially when it is closed, the
standard of E.M.F. is best derived from measurements of resistance and of
strength of current, which are both convenient and very accurate. Com-
pared with the electrostatic unit of potential the volt is very small, being
only -I- of such a unit. The electromotive force of a Daniell's cell is about
a twelfth greater than a volt. According to the latest determinations of Lord
Rayleigh a Latimer Clarke's element has the E.M.F. i'433 volt.

The Ampere is the unit of current, and is the current produced by the
electromotive force of a volt in a circuit having a resistance of an ohm. It
is therefore equal to lO"' C.G.S. units. A millampci'e is the thousandth of
an ampere.

The resistance of a Daniell's element with an external cylinder of zinc,
8 inches high and ^ik '" diameter, surrounding the porous pot, is about 1*3
ohm, and taking its E.M.F. at ro8 volt its current when on short circuit is about
0-8 ampere. In like manner a medium-sized Bunsen has a resistance ot
about o-i ohm, and as its E.M.F. is rS volt, the current on short circuit is
18 amperes. A Brush machine the current of which ignited 16 lamps had an
E.M.F. of 839 volts ; its internal resistance was 10-55, and the external, in-
cluding the lamps, was 73 ohms. Accordingly the current was 10-04 amperes.
A Holtz machine has in electromagnetic measure the E.M.F. of 90,000 volts ;
its internal resistance, when it makes two turns in a second, is calculated at
27 X lo** ohms, and accordingly its current is -^—-^^^ of an ampere, or j^j,- of a
millampere. Such a current is too weak for telegraph work ; the currents
which are used with the ordinary Morse receivers have a strength of 14 to
16 millamperes.

The Coulomb is the unit of quantity of electricity, and is that quantity
which traverses the section of a conductor in a second, when a current of an
ampere is passing through it. A coulomb of elec- rt

tricity in traversing an electrolyte decomposes a |

weight of the body expressed by 0-00001038 times its
electrochemical equivalent.

The Farad is the unit of capacity, and is such that
in a condenser of that capacity the quantity of a
coulomb produces a difference of potential of a volt.
It is IO-' C.G.S. units. The farad is far too large a
unit for practical use, thus the capacity of the globe li - , .j J .j,,!;,!,,
is only 0-000636 of a farad, that of the sun does not
amount to a farad. Accordingly the technical unit of
capacity is the millionth part of this, and is called the
microfarad. This is lO"'"' units. A Leyden jar with a 'S- 9 •

total coated surface of a square metre, and the glass of which is 1 mm.
thick, has a capacity of ^ of a microfarad. The capacity of an ordinary

986 Dynamical Electricity. [964-

siibmarine cable may be taken at about 5 of a microfarad per knot or
nautical mile of 1S52 metres. A sphere nine kilometres in diameter has a
capacity of a microfarad.

The practical standards consist of circular or square sheets of tinfoil with
projecting tongues, a and a' (fig. 960), fastened on thin sheets of mica. Be-
tween each such coated sheet is placed an uncoated one of mica, the two
sets of tongues being severally connected with each other, and thus the
coatings represent the coated surfaces of a condenser. The whole is en-
closed in a box ; a condenser having a capacity of a microfarad will repre-
sent a coated surface of over 6 square yards.

Watt. — The energy, W, of an electrical current in unit time may be

TT-

variously expressed ; thus W = C-R = - = CE. This latter expression is the

most convenient for practical purposes ; if the factors which express the watt

are given in practical units, it represents the work done by unit current

(ampere) when impelled by an E.M.F. of a volt. It is thus a volta7npere.,

and on the proposal of the late Sir W. Siemens has been called a Watt.

If the factors are given in absolute units, \'^ A is equal to lo'' ergs. It

may also be defined as the work done by the quantity of electricity of a

coulomb falling through a difference of potentials equal to a volt, and in this

form the definition io closely analogous to that of a kilogramme metre.

The watt is =4^ of an English horse-power, or one horse-power = 746 watts.
The French cheval vapeiir oi ']^ kilogramme-metres or 543U foot-pounds per
second is equal to 736 watts.

965. Relation of the electrostatic to the electromaernetic unit. — It
we compare the dimensions of the units of quantity and of the other electrical
magnitudes in the electrostatic with those of the corresponding dimensions
as expressed in the electromagnetic system, we find that the ratios are

independent of the unit of mass, and that _, that is, the expression of a

velocity, always enters into the ratio between them. Now the ratio of the
two sets of units may be determined experimentally. Suppose, for in-
stance, that a condenser is charged with electricity. Knowing its dimen-
sions, the quantity, q, of the charge may be determined in electrostatic
measure, by measuring, for instance, the repulsion which a given proportion
of the total charge produces in a torsion balance of known dimensions. The
same condenser, being charged to the same extent, may be discharged
through a galvanometer, and by measuring the deflection produced, and
knowing the constants of the instrument, the quantity may be obtained in
electromagnetic units, and thus the ratio of the quantity expressed in the two
sets of units maybe deduced. Or, again, the E.M.F. of a Daniell's cell may
be measured first by the aid of an absolute electrometer, which will give in
electrostatic units of potential about 0-0036. On the other hand the potential
determined in electromagnetic measure has the value ^•o8SxIO^ Hence
it would thus be found that in round numbers the electromagnetic unit
of quantity is e([ual to 3-io"' electrostatic units of quantity. This is easily
intelligible, since the latter is the quantity of electricity which attracts or.
repels another equal quantity at a distance of I cm. with a force of a dyne,
while the latter is the quantity which traverses the wire in a second when

-965] Relation of Electrostatic to Electromagnetic Unit. 987

the current has unit intensity. Similarly, by makins:^ determinations of the
ratio m all cases in which the same magnitude may be determined in elec-
trostatic as well as in electromagnetic measure, it is found that the agree-
ment in the numbers found is very close, and as the mean of the best
results is 2-9857 x 10"'. As the ratio between the units is always of the
dimensions of a velocity, and holds under the condition that the centimetre
is the unit of length, and the second is the unit of time, this velocity is
298,570 kflometres, or 185,530 miles in a second. Now this number agrees
very closely with that for the velocity of light— 185,420 miles (507).

Faraday, discarding the idea of action at a distance, considered that
electrical forces are transmitted through an elastic medium, and that this
was the luminiferous ether (637). Maxwell, starting from these ideas, was
led to the development of his electromagfutic theory of light; this theory
requires that an electromagnetic wave motion must be transmitted with a
velocity represented by the ratio of the electrostatic to the electromagnetic
unit of quantity of electricity ; this, as we have seen, is equal to the velocity
of light. Now, if luminous and electromagnetic waves are transmitted in
one and the same medium and with the same velocity, it is natural to suppose
that they are identical in kind. The theory also requires the relation be-
tween the refractive index of a body and the dielectric constant which we
have already found to exist (748).

These theoretical previsions of what is known as the Faraday-Maxwell
theory have quite recently received a striking confirmation in a most remark-
able and beautiful series of experiments by Professor Hertz, of which we can
only give a bare outline of some of the principal results.

In order to demonstrate that light is essentially an electromagnetic
phenomenon, it would be necessary to produce, with a vibratory motion of
a purely electromagnetic origin, the same class of phenomena as can be
produced with ordinary light, such, more especially, as interference and re-
fraction. The difficulty is the great length of the waves with which we have
to deal ; for from the laws of wave motion (253), if the frequency of the
electrical oscillations were as great as ten thousand in a second, that would
represent a wave-length of 300 kilometres, and for a wave-length of 3 metres
the duration should not be greater than the hundred-millionth of a second.
Now in the discharge of a Leyden jar, or the still more rapid one which takes
place between the ends of the secondary wire of a Ruhmkorff s coil, the dura-
tion of the oscillation is comprised within the ten-thousandth and the
hundredth-thousandth of a second.

By an ingenious but simple contrivance, Hertz has succeeded in produc-
ing electrical oscillations, or true rays of electrical force, the duration of which
is not greater than one five-hundred-billionth of a second. The means by
which this is effected is called the discharger., and it has this remarkable
property : if a metal wire be bent in a circle so that the ends are at a
fraction of a millimetre apart, and this be held in the vicinity of the dis-
charger, a position is found by trial in which a continual flow of microscopic
sparks passes between the ends ; and this takes place even when the wire is
at a distance of some metres. There is one dimension for which the sparks
are a maximum for a particular form of discharger, and it is clear that this
is the case when the period of oscillation of the wire synchronises with those

988 Dynamical Electricity. [965-

of the discharger. It acts, in fact, for the electromagnetic waves hke a
resoftator (255) for sound waves, and this is the name by which it is called.
Its diameter was usually 35 cm.

By vaiying the position and distance of the resonator in reference to the
discharger. Hertz was able to explore and plot out the exact form of the
wave motion in the space about the discharger, and in such a way as almost
to make the undulations visible. He was able thus to perform with these
rays of electrical force the ordinary elementary experiment made with light
and with radiant heat. He could show that they proceed in straight lines,
and that they are reflected by plane metallic surfaces ; he demonstrated the
phenomenon of interference, and from the distance of the nodes and loops
along with the frequency of the oscillations he made a determination of
the velocity of electricity, which gave yz x 10° cm. per second. The rays
could be concentrated to a focus by means of a parabolic mirror. Using a
large prism of pitch 5 feet in height, with a refracting angle of 30°, and with
a face of over a square yard, he could demonstrate the refraction of the
electrical rays, and his measurements of the refractive index agree suffi-
ciently well with those obtained by purely optical means. By means of a
grating of parallel copper wires he found that the rays are stopped when
the wires are at right angles to the direction of the oscillations, and are
transmitted when the wires are parallel to the electrical rays. The grating
acts in regard to the rays like a tourmaline with respect to plane polarised
light (666). One of the most curious observations in these experiments is
the fact that while a conductor such as a sheet of zinc, or of tinfoil, will cut
off the rays, insulators do not stop them ; they can pass, for instance,
through a wooden door.

These remarkable experiments leave no doubt that light, radiant heat,
and electromagnetic actions are transmitted in the same way ; and it may
be expected that they will lead to important conclusions both for the theory
of light and of electricity.

-967J Currents of Muscle at Rest. 989

CHAPTER X.

ANIMAL ELECTRICITY.

966. Muscular currents. — The existence of electrical currents in living
muscle was first indicated by Galvani, but his researches fell into oblivion
after the discovery of the voltaic pile, which was supposed to explain all the
phenomena. Since then, Nobili, Matteucci, and others, especially, in late
years, Du Bois Reymond, have shown that electric currents do exist in living
muscles and ner\es, and have investigated their laws.

For investigating these currents it is necessary to have a delicate gal-
vanometer, and also electrodes which will not become polarised or give a
current of iheir own, and which will not in any way alter the muscle when
placed in contact with it ; the electrodes which satisfy these conditions best
are those of Du Bois Reymond, as modified by Bonders. Each consists of
a glass tube, one end of which is narrowed and stopped by a plug of paste
made by moistening china-clay with a half per cent, solution of common salt ;
the tube is then partially filled with a saturated solution of sulphate of zinc ;
and into this dips the end of a piece of thoroughly amalgamated zinc wire,
the other end of which is connected by a copper wire with the galvanometer ;
the moistened china-clay is a conducting medium which is perfectly neutral
to the muscle, and amalgamated zinc in solution of sulphate of zinc does not
become polarised.

967. Currents of muscle at rest. — In describing these experiments the
surface of the muscle is called the natural longitudinal section ; the tendon
the natural transverse section ; and the services obtained by cutting the
muscle longitudinally or transversely are respectively the artificial lotigitu-
dinal and artificial transverse sections.

If a living irritable muscle be removed from a recently killed frog, and
the clay of one electrode be placed in contact with its surface, and of the
other with its tendon, the galvanometer will indicate a current from the
former to the latter ; showing, therefore, that the surface of the muscle is
positive with respect to the tendon. By varying the position of the elec-
trodes, and making various artificial sections, it is found —

1. That any longitudinal section is positive to any transverse section.

2. That any point of a longitudinal section nearer the middle of the
muscle is positive to any other point of the same section farther from the
centre.

3. In any artificial transverse section any point nearer the periphery is
positive to one nearer the centre.

990

Dynamical Electricity.

[967-

Fig. 961

4. The current obtained between two points in a longitudinal or in a
transverse section is always much more feeble than that obtained between
two different sections.

5. No current is obtained if two points of the same section equidistant
from its centre be taken.

6. To obtain these currents it is not necessary to employ a whole muscle,
or a considerable part of one, but the smallest fragment that can be experi-
mented with is sufficient.

7. If a muscle be cut straight across, the most powerful current is that
from the centre of the natural longitudinal section to the centre of the arti-
ficial transverse ; but if the muscle be

'^ ^_ _ '' cut across obliquely, as in fig. 961, the

cz — i;^^' most positive point is moved from c

" ~ _--;=_ _^_3) towards b, and the most negative from

~~ ~-^— ^ <■/ towards a {'■ currents of inclination').

To explain the existence and rela-
tions of these muscular currents, it may be supposed that each muscle is
made up of regularly disposed electromotor elements, which may be re-
garded as cylinders whose axes are parallel to that of the muscle, and
whose sides are charged with positive and their ends with negative electri-
city ; and, further, that all are suspended and enveloped in a conducting
medium. In such a case (fig. 961) it is clear that throughout most of the
muscle the positive electricities of the opposed surfaces would neutralise one
another, as would also the negative charges of the ends of the cylinders ; so
that, so long as the muscle was intact, only the charges at its sides and ends
would be left to manifest themselves by the production of electromotive
phenomena ; the whole muscle being enveloped in a conducting stratum, a
current would constantly be passing from the longitudinal to the transverse
section, and, a part of this being led off by the wire circuit, would manifest
itself in the galvanometer.

This theory also explains the currents between two different points on the
same section ; the positive charge at b, for instance (fig. 962), would have more
resistance to overcome in getting to the transverse section than that at </»

tlicrcforc it has a higher tension ; and \i b and d are connected by tlie elec-
trodes,/' will be found positive to r/, and a current will pass from the former
to the latter. What are called currents of inclination are also explicable on
the above hypothesis, for the oljlicjuc section can be represented as a number

-970] Electrical Currents in Nerve. 991

of elements arranged as in fig. 963, so that both the longitudinal surfaces and
the ends of the cylinders are laid bare, and it can thus be regarded as a
sort of oblique pile whose positive pole is towards b and its negative at a,
and whose current adds itself algebraically to the ordinary current and dis-
places its poles as above mentioned.

A perfectly fresh muscle, very carefully removed, with the least possible
contact wittT foreign matters, sometimes gives almost no current between its
different natural sections, and the current always becomes more marked after
the muscle has been exposed a short time ; nevertheless, the phenomena
are vital, for the currents disappear completely with the life of the muscle,
sometimes becoming first irregular or even reversed in direction.

968. Rbeoscoplc frog. Contraction without metals. — The existence
of the muscular currents can be manifested without a galvanometer, by using

Fig. 963.

another muscle as a galvanoscope. Thus, if the nerve of one living muscle
of a frog be dropped suddenly on another living muscle, so as to come in
contact with its longitudinal and transverse sections, a contraction of the
first muscle will occur, due to the stimulation of its nerve by the passage
through it of the electric current derived from the surface of the second.

969. Currents In active muscle. — When a muscle is made to contract
there occurs a sudden diminution of its natural electric current, as indicated
by the galvanometer. This is so instantaneous that, in the case of a single
muscular contraction, it does not overcome the inertia of the needle of the
galvanometer ; but if the contractions be made to succeed one another very
rapidly— that is, if the muscle be tetaitised (827) — then the needle swings
steadily back towards zero from the position in which the current of the
resting muscle had kept it, often gaining such momentum in the swing as to
pass beyond the zero point, but soon reverting to some point between zero
and its original position.

The negative variation in the case of a simple muscular contraction can,
however, be made manifest by using another muscle as a rheoscope ; if the
nerve of this second muscle be laid over the first muscle in such a position
that the muscular current passes through it, and the first muscle be then made
to contract, the sudden alteration in the strength of its current stimulates
the nerve laid on it (827), and so causes a contraction of the muscle to which
the latter belongs.

The same phenomenon can be demonstrated in the muscles of warm-
blooded animals ; but with less case, on account of the difficulty of keeping
them alive after they are laid bare or removed from the body. Experiments
made by placing electrodes outside the skin, or passing them through it, are
inexact and unsatisfactory.

970. Electric currents in nerve. — The same electromotor indications.

992 Dynamical Electricity. [971-

can be obtained from nerves as from muscles — at least, as far as their smaller
size will permit ; the currents are more feeble than the muscular ones, but
can be demonstrated by the galvanometer in a similar way. Negative vari-
ation has been proved to occur in active nerve as in active muscle. The
effect of a constant current passed through one part of a nerve on the amount
of the normal nerve-current, measured at another part, has already been
described (Chap. III., Electrotonus).

971. Electrical fisb. — Electrical fish are those fish which have the re-
markable property of giving, when touched, shocks like those of the Leyden
jar. Of these fish there are several species, the best known of which are the
torpedo, the gymnotus, and the silurus. The torpedo, which is very common
in the Mediterranean, has been carefully studied by Becquerel and Breschet
in France, and by Matteucci in Italy. The gj^mnotus was investigated by
Humboldt and Bonpland in South America, and in England by Faraday,
who had the opportunity of examining live specimens.

The shock which they give serves both as a means of offence and of
defence. It is purely voluntary, and becomes gradually weaker as it is
repeated and as these animals lose their vitality, for the electrical action
soon exhausts them materially. According to Faraday, the shock which the
gymnotus gives is equal to that of a battery of 1 5 jars exposing a coating of
25 square feet, which explains how it is that horses frequently give way under
the repeated attacks of the gymnotus.

Numerous experiments show that these shocks are due to ordinary
electricity. For if, touching with one hand the back of the animal, the
belly is touched with the other, or with a metal rod, a violent shock is felt
in the wrists and arms ; while no shock is felt if the animal is touched with
an insulating body. Further, when the back is connected with one end of a
galvanometer wire and the belly with the other, at each discharge the needle
is deflected, but immediately returns to zero, which shows that there is an
instantaneous current ; and, moreover, the direction of the needle shows that
the current goes from the back to the belly of the fish. Lastly, if the cur-
rent of a torpedo be passed through a helix in the centre of which is a small
steel bar, the latter is magnetised by the passage of a discharge.

By means of the galvanometer, Matteucci established the following
facts : —

I. When a torpedo is lively, it can give a shock in any part of its body,
but as its vitality diminishes, the parts at which it can give a shock are
nearer the organ which is the seat of the development of electricity. 2. .A.ny
point of the back is always positive as compared with the correspond-
ing point of the belly. 3. Of any two points at different distances from
the electrical organ, the nearest always plays the part of a positive pole,
and the farthest that of a negative pole. With the belly the reverse is the
case.

The organ where the electricity is produced in the tori)cdo is double, and
formed of two jjarts symmetrically situated on two sides of the head and
attached to the skull-bone by the internal face. Each part consists of nearly
|iaralicl lamella- of connective tissue inclosing small chambers, in which lie-
ilie so-( ailed electrical plates^ each of which has a final ner\e-ramification
distributed on one of its faces. This face, on which the nerve ends, is

-972] Application of Electricity to Medicine. 993

turned the same way in all the plates, and when the discharj^^e takes place
is always negative to the other.

Matteucci investigated the influence of tlie brain on the discharge. For
this purpose he laid bare the brain of a living torpedo, and found that the
first three lobes could be irritated without the discharge being produced, and
that when they were removed the animal still possessed the faculty of giving
a shock. The fourth lobe, on the contrary, could not be irritated without
an immediate production of the discharge ; but if it was removed, all dis-
engagement of electricity disappeared, even if the other lobes remained
untouched. Hence it would appear that the primary source of the electricity
elaborated is the fourth lobe, whence it is transmitted by means of the nerves
to the two organs described above, which act as multipliers. In the silurus
the head appears also to be the seat of the electricity ; but in the gymnotus
it is found in the tail.

972. Application of electricity to medicine.— The first applications of
electricity to medicine date from the discovery of the Leyden jar. Nollet
and Boze appear to have been the first who thought of the application, and
soon the spark and electrical friction became a universal panacea, but it
must be admitted that the results of subsequent trials did not come up to the
hopes of the early experimentalists.

After the discovery of dynamic electricity Galvani proposed its applica-
tion to medicine; since which time many physicists and physiologists have
been engaged upon this subject, and yet there is still much uncertainty as
to the real effects of electricity, the cases in which it is to be applied, and
the best mode of applying it. Practical men prefer the use of currents to
that of statical electricity, and, except in a few cases, discontinuous to
continuous currents. There is, finally, a choice between the currents of the
battery and induction currents ; further, the effects of the latter differ,
according as induction currents of the first or second order are used. In
fact, since induction currents, although very intense, have a verj' feeble
chemical action, it follows that when they traverse the organs they do not
produce the chemical effects of the current of the battery, and hence do not
tend to produce the same disorganisation. Further, in electrifying the
muscles of the face, induction currents are to be preferred, for these currents
only act feebly on the retina, while the currents of the battery act energeti-
cally on this organ, and may affect it dangerously. There is a difference in
the action of induced currents of different orders ; for while the primary
induced current causes lively muscular actions, but has little action on the
cutaneous sensibility, the secondary induced current, on the contrary, in-
creases the cutaneous sensibility to such a point that its use ought to be
proscribed to persons whose skin is very irritable.

Hence electrical currents should not be applied in therapeutics without
a thorough knowledge of their various properties. They ought to be used
with great prudence, for their continued action may produce serious acci-
dents. Matteucci says : ' In commencing, a feeble current must always be
used. This precaution now seems to me the more important as I did not
think it so before seeing a paralytic person seized with almost tetanic con-
vulsions under the action of a current formed of a single element. Take
care not to continue the application too long, especially if the current is

994 Dynamical Electricity. [972-

encrgetic. Rather apply a frequently interrupted current than a continuous
one, especially if it be strong ; but after twenty or thirty shocks, at most, let
the patient take a few moments' rest.'

Of late years, however, feeble continuous currents have come more into
use. They are frequently of great service when applied skilfully, so as to
throw the nerves of the diseased part into a state of cathelectrotonus or
anelectrotonus (827), according to the object which is wished for in any
g-iven case.

-974] JSIeteorograph. 995

ELEMENTARY OUTLINES

METEOROLOGY AND CLIMATOLOGY

METEOROLOGY.

973. MeteoroIog:y. — The phenomena which are produced in the atmo-
sphere are called meteors ; and mefeoj-ology is that part of physics which is
concerned with the study of these phenomena.

A distinction is made between aerial meteors, such as winds, hurricanes,
and whirlwinds ; aqueous meteors, comprising fogs, clouds, rain, dew, snow,
and hail ; and luminous meteors, as lightning, the rainbow, and the aurora
borcalis.

974. Meteorog-rapli. — The importance of being able to make continuous
observations of \arious meteorological phenomena has led to the construc-
tion of various forms of automatic arrangements for this purpose, of which
that of Osier in England may be specially mentioned. One of the most com-
prehensive and complete is Secchi's meteorograph, of which we \\\\\ gi\e here
a description.

It consists of a base of masonry about 2 feet high (fig. 964) ; on this are
fixed four columns, about 2i yards high, which support a table on which is
a clockwork regulating the whole of the movements. The phenomena are
registered on two sheets which move downwards on two opposite sides, their
motion being regulated by the clockwork. One of them occupies ten days
in so doing, and on it are registered the direction and velocity of the wind,
the temperature of the air, the height of the barometer, and the occurrence
of rain ; on the second, which only takes two days, the barometric height
and the occurrence of rain are repeated, but on a much larger scale ; this
gives, moreover, the moisture of the air.

Direction of the 7i'ind.— The four principal directions of the wind are
registered by means of four pencils fixed at the top of thin brass rods, a, b, c,
d (fig. 964), which are provided at the bottom ends with soft iron keepers
attracted by two electromagnets, E E', for west and north, and by two other
electromagnets lower down for south and east. These four electromagnets,
as well as all the others on the apparatus, are worked by a single sand
batter)' (886) of twenty-four elements. The passage of the current in one or

3S2

996 Meteorology. [974-

the other of these electromagnets is regulated by means of a vane (fig. 965)
consisting of two plates at an angle of thirty degrees with each other, by

/n. /

/T "1*

-^d^-=^^j>

'i''™''''"l!i!!1il!illil!!!Iliil!i;u W ■■'■'^^

Fig. 964.

which greater steadiness is obtained than with a single plate. In the rod of

the vane is a small brass plate, 0 ; this part is in the centre of four metal

Fig. 965

-974] Meteorograph. 997

sectors insulated from each other, and each provided with a binding screw,
by which connection is estabHshed with the binding screw K, and the electro-
magnets EE'. The battery current
reaches the rod of the vane by the wire a,
and thence the sliding contact 0, which
leads it to the electromagnet for the north,
for instancei*

If the current passed constantly in this
electromagnet, the pencil on the rod d
would be stationary ; but from the electro-
magnet E'the current passes into a second
electromagnet, //, over the clockwork, and
is thereby alternately opened and closed,
as will be seen in speaking of the velocity
of the wind. Hence the armature of the
rod d, alternately free and attracted, os-
cillates ; and its pencil, which is always
pressed against the paper AD by the
elasticity of the rod, traces on it a series
of parallel dashes as the paper descends,
and so long as the wind is in the north.
If the wind changes then to west, for
instance, the rod a oscillates, and its
pencil traces a different series of marks.

The rate of displacement of the paper being known, we get the direction of
the prevalent wind at a given moment.

Velocity of the wind. — This is indi-
cated by a Robinson's aftemo?neter, and
is registered in two ways ; by two counters
which mark in decametres and kilometres
the distance travelled by the wind ; and
by a pencil which traces on a table a curve,
the ordinates of which are proportional to
the velocity of the wind.

Robinson, who originally devised this
form of anemometer (fig. 966), proved
that its velocity is proportional to that of
the wind ; in this apparatus the length
of the arms is so calculated that each re-
volution corresponds to a velocity of ten
metres (975). The anemometer is placed
at a considerable distance from the meteor-
ograph, and is connected with it by a
copper wire, d, which passes to the electro-
magnet,», of the counter. On its rod there
is, moreover, an excentric, which at each
turn touches a metal contact in connec-
tion with the wire d. The battery current reaches the anemometer by a wire
a the current is closed once at each rotation, and pr 5ses to the electro-

Fig. 566.

998 Meteorology. [974-

magnet «, which moves the needle of the dial through one division. There
are fifty such divisions, which represent as many turns of the vane, and
therefore so many multiples of ten metres. The lower dial marks the kilo-
metres.

The curve of velocities is traced on the sheet by a pencil, /, fixed to a
horizontal rod. This is joined at its two ends to two guide-rods, <; and _y,
which keep it parallel. The pencil and the rod are moved laterally by a
chain which passes over two pulleys, r' and r, and is then coiled over a pulley
placed on the shaft of the counter, but connected with it merely by a ratchet-
wheel : and moved thus by the counter and the chain, the pencil traces
every hour on the sheet a line the length of which is proportioned to the
velocity of the wind. From hour to hour an excentric moved by clockwork
detaches, from the shaft of the counter, the pulley on which is coiled the
chain, and this pulley becoming out of gear, a weight,/, connected with the
pencil z, restores this to its starting-point. All the lines, V, traced succes-
sively by the pencil, start from the same straight line as ordinates, and their
ends give the curve of velocities.

The counters on the right and left are worked by electromagnets, w ?«',
and are intended to denote the velocity of special winds ; for instance, those
of the north and south, by connecting their electromagnets with the north
and south sectors of the vane (fig. 966).

Teniperatiir-e of the air. — This is indicated by the expansion and con-
traction of a copper wire of 16 metres in length stretched backwards and
forwards on a fir post 8 metres in length. The whole being placed on the
outside — on the roof, for instance — the expansion and contraction are trans-
mitted by a system of levers to a wire, c, which passes to the meteorograph,
where it is jointed to a bent lever, /. This is jointed to a horizontal rod, s,
which supports a pencil, and at the other end is jointed to a guide-rod, x.
Thus the pencil, sharing the oscillations of the whole system, traces the curve
of the temperatures.

Pressure of the ai/ziosphet'e. — This is registered by the oscillations of a
barometer, B, suspended at one end of a bent scale-beam, I F, playing on a
knife-edge (fig. 968). The arm F supports a counterpoise ; to the arm I is
suspended the barometer B, which is wider at the top than at the bottom.
A wooden flange or floater, Q, fixed to the lower part of the tube, plunges in
a bath of mercury, so that the buoyancy of the liquid counterbalances part of
the weight of the barometer. Owing to the large diameter of the barometric
chamber, a very slight variation of level in this chamber makes the tube
oscillate, and with it the scale-beam I F. To the axis of this is a triangle,
gkk, jointed to a horizontal rod, which in turn is connected with a guide-rod,
2. In the middle of this rod is a pencil which, sharing in the oscillations of
the triangle gk/c, traces the cur\e H of pressure. A bent lever at the bottom
of the barometer tube keeps this in a vertical position.

Rainfall. — This is registered between the direction of tlic winds and the
curve II by a pencil at the end of a rod, ?/, which is worked l>y an electro-
magnet, c. On the roof is a funnel which collects tiie rain, and a long tube
leads the water to a small water-balance, with tlic cups placed near the
meteorograph (fig. 967). To the axis of the scale-beam one pole of the battery
is connected ; the left cup being full, tips up, and a contact, a, closes the

Fig. 967.

-974] Measiiniiient of the Rainfall. 999

current, which passes then to one of the binding screws, C, and hence to the
electromagnet, e. Then the right cup, being in turn full, tips in the opposite
direction, and the contact b now transmits the current to the electromagnet.
Thus, at each oscillation this latter attracts its armature, and with it the
rod a^ which makes a mark by means of a pencil at the end. If the rain is
abundant the oscillations of the beam are rapid, and the marks being very
close together give a deep shade ; if, on the contrary, the oscillations are
slow, the marks are at a greater distance and give a light shade. When
the rain ceases the oscillations cease also, and the _
pencil makes no mark.

To complete this description of the first face of
the meteorograph : S is the alarum-bell of the clock-
work, 00 a cord supporting a weight which moves
the works of the hour-hand. LZ is a second cord that
supports the weight which works the alarum ; the
wheel U, placed below the clockwork, winds up the
sheet AD when it is at the bottom of its course.

The second sheet (fig. 968) gives the barometric
height and the rainfall like the first, but on a larger
scale, since the motion of the sheet is five times as
rapid. Its principal function is that of registering the
moisture of the air. This is effected by means of the
psychrometer (fig. 969). T and T' are two thermo-
meters fixed on two plates. The muslin which covers
the second is kept continually moist by water dropping on it. In each of
the bulbs are fused two platinum wires ; the stems of the thermometers are
open at the top, and in them are two platinum wires, m and «, suspended
to a metal frame movable on four pulleys supported by a fixed piece, B.
The frame A, in contact with the current of the battery, is suspended
to a steel wire, L, which passes over a pulley to the meteorograph
(fig. 967). Here is a long triangular lever, W, which supports a small wheel,
to which is fixed the wire L. The lever W, which turns about an axis,/, is
moved by a rod, a, by means of an excentric, which the clock works every
quarter of an hour. At each oscillation the lever \V transmits its motion
to a small chariot, on which is an electromagnet, x, and at the same time to
the steel wire L, which supports the frame A (fig. 969). The chariot, moved
towards the left by the rotation of the excentric, lets the frame sink. The
moment the first platinum wire reaches the mercurial column of the drv
bulb thermometer, which is the highest, the current is closed, and passes into
the electromagnet of the chariot. An armature at once causes a pencil to
mark a point on the sheet which is the beginning of a line representing the
path of the dry bulb thermometer. As the frame continues to descend, the
second platinum wire touches the mercury of the wet bulb, and closes a
current in a relay, M, which opens the circuit of the electromagnet, .t'. The
pencil is then detached ; then, returning upon itself, the chariot reproduces
the closing and opening of the circuit in the opposite direction, the pencil
makes another mark, which is the end of the line. There are thus formed
two series of dots arranged in two curves, one of which represents the path of
the dry, and the other the path of the wet, bulb. The horizontal distance of the

looo Meteorology. [974-

two points of these curves is proportional to the difference / — /j of the tem-
peratures indicated at the same moment by the thermometers (fig. 969).

(2unntiiy of rai'fi. — Tlic (|uantity of rain wliich falls in a given time
is registered on a disc of paper on a pulley, R. On the groove of this is
coiled a chain, to which is suspended a brass tube, P. This is fixed at the

975]

Direction and Velocity of Winds.

lOOI

'fTh'

bottom to a float, which plunges in a reservoir placed in the base of the
meteorograph. On passing out of the water-balance (fig. 964) the water
passes into this reservoir, and as its section is one-fourth that of the funnel,
the height of water which falls is quadrupled ; it is measured on a scale, (],
divided into millimetres.

As the float rises, a weight, Z, moves the pulley in the contrary direction,
and its rotation is proportional to the height of
water which has fallen. A pencil moves at the
same time from the centre to one circumference of
the paper disc with a velocity of 5 mm. in 24
hours : hence the quantity of rain which falls every
day is noted on a different place on the paper
disc.

975. Birection and velocity of winds. —
Winds are currents moving in the atmosphere with
variable directions and velocities. There are eight
principal directions in which they blow — north.,
nort/i-easf, east, south-east., south, soutJi-iuest, ivest,
and north-west. Mariners further divide each of
the distances between these eight directions into
four others, making in all 32 directions, which are
called points or rhutnbs. A figure of 32 rhumbs
on a circle, in the form of a star, is known as the
mariner's card.

\'elocity is determined by means of the
anemometer (fig. 966), a small vane with fans,
which the wind turns ; the velocity is deduced from
the number of turns made in a given time. In our
climate the mean velocity is from 18 to 20 feet in a
second. With a velocity of less than 18 inches in
a second no movement is perceptible, and smoke
ascends straight ; with a velocity between i^ and
2 feet per second the wind is perceptible and moves a pennant ; from 13 to
22 feet it is moderate, it stretches a flag and moves the leaves of trees ;
with from 23 to 36 feet velocity it is fresh and moves the branches of
trees ; with 36 to 56 feet it is strong and moves the larger branches and
the smaller stems ; with a velocity of 56 to 90 feet it is a storm, and entire
trees are moved ; and from 90 to 120 it is a hurricane.

To measure the pressure of the wind a plate is used, which by means of a
vane is always kept in a direction opposite that of the wind. Behind the
plate are one or more springs which are the more pressed the greater is the
pressure of the wind against the plate. Knowing the distance through which
the plate is pressed, we can calculate the pressure which the wind exerts on
the plate in question.

With some degree of appro.ximation, and for low velocities, the pressure
.iirty *uu tat-en as proportional to the square of the velocity. Thus, if the
pressure on the square foot is 0-005 pound, with a velocity of 1-5 foot in
a second, it is 0-02 pound with a velocity of 3 feet, and 0-123 '^^'•th a velocity
of 7-33 feet.

Fig. 969.

1002 Meteorology. [976-

976. Causes of winds. — Winds are produced by a disturbance of the
eciuilibrium in some part of the atmosphere : a disturbance always resultmg
from a difference in temperature between adjacent countries. Thus, if the
temperature of a certain extent of ground becomes higher, the air in contact
with it becomes heated, it expands and rises towards the higher regions of
the atmosphere ; whence it flows, producing winds which blow from hot to
cold countries. But at the same time the equilibrium is destroyed at the
surface of the earth, for the barometric pressure on the colder adjacent parts
is greater than on that which has been heated, and hence a current will be
produced with a velocity dependent on the difference between these pres-
sures ; thus two distinct winds will be produced — an upper one setting out-
luards from the heated region, and a lower one setting inwards towards it.

977. Regrular, periodical, and variable winds. — According to the more
or less constant directions in which winds blow, they may be classed as
regular, periodical, and variable winds.

i. Regular winds are those which blow all the year through in a virtually
constant direction. These winds, which are also known as the trade winds,
are uninterruptedly observed far from the land in equatorial regions, blowing
from the north-east to the south-west in the Northern Hemisphere, and from
the south-east to the north-west in the Southern Hemisphere. They prevail
on the two sides of the equator as far as 30° of latitude, and they blow in
the same direction as the apparent motion of the sun — that is, from east to
west.

The air above the equator being gradually heated, rises as the sun passes
round from east to west, and its place is supplied by the colder air from the
north or south. The direction of the wind, however, is modified by this fact,
that the velocity which this colder air has derived from the rotation of the
earth— namely, the velocity of the surface of the earth at the point from
which it started — is less than the velocity of the surface of the earth at the
point at which it has now arrived : hence the currents acquire, in reference
to the equator, the constant direction which constitutes the trade winds.

ii. Periodical winds are those which blow regularly in the same direction
at the same seasons and at the same hours of the day : the monsoon,
simoom, and the land and sea breeze are e.xamples of this class. The name
tnofisoon is given to winds which blow for six months in one direction and
for six months in another. They are principally observed in the Red Sea
and in the Arabian C.ulf, in the Bay of Bengal and in the Chinese Sea.
These winds blow towards the continents in summer, and in a contrary
direction in winter. The simoom is a hot wind that blows over the deserts
of Asia and Africa, and which is characterised by its high temperature and
l)y the sands which it raises in the atmosphere and carries with it. During
the prevalence of this wind the air is darkened, the skin feels dry, the
respiration is accelerated, and a burning thirst is experienced.

This wind is known under the name oi sirocco in Italy and Algiers, where
it blows from the great desert of Sahara. In Egypt, where it prevails from
the end of April to June, it is called kamsi/i. The natives of Africa, in order ,
to protect themselves from the effects of the too rapid perspiration occasioned
by this wind, cover themselves with fatty substances.

A wind characteristic of Switzerland and known as the Fo/ui originates as

-979] Weather Charts. 1003

follows : a mass of air coming from the south-east being impelled over a
mountain ridge becomes rarefied as it ascends ; the temperature rises and it
deposits its moisture on the other side as rain or snow. Being driven still
forward into the valleys, the superincumbent pressure being greater the air
is condensed and its temperature rises, and having parted with its moisture
it appears as a wind which is at once hot and dry. One observation gave
the temperature at 31-4 C, while it only contained 20 per cent, of moisture.

The tajid and sea breeze is a wind which blows on the sea-coast, during
the day from the sea towards the land, and during the night from the land to
the sea. For during the day the land becomes more heated than the sea, in
consequence of its lower specific heat and greater conductivity, and hence, as
the superincumbent air becomes more heated than that upon the sea, it as-
cends and is replaced by a current of colder and denser air flowing from the
sea towards the land. During the night the land cools more rapidly than the
sea, and hence the same phenomenon is produced, but in a contrary direction.
The sea breeze commences after sunrise, increases up to three o'clock in the
afternoon, decreases towards evening, and is changed into a land breeze
after sunset. These winds are only perceived at a slight distance from the
shores. They are regular in the tropics, but less so in our climates ; and
traces of them are seen as far as the coasts of Greenland. The proximity of
mountains, and also of forests, likewise gives rise to periodical daily breezes.

iii. Vat table luinds are those which blow sometimes in one direction and
sometimes in another, alternately, without being subject to any law. In mean
latitudes the direction of the winds is very variable ; towards the poles this
irregularity increases, and under the arctic zone the winds frequently blow
from several points of the horizon at once. On the other hand, in approach-
ing the torrid zone, they become more regular. The south-west wind prevails
in England, in the north of France, and in Germany ; in the south of France
the direction inclines towards the north, and in Spain and Italy the north
wind predominates.

978. law of the rotation of winds. — Spite of the great irregularity
which characterises the direction of the winds in our latitude, it has been as-
certained that the wind has a preponderating tendency to veer round accord-
ing to the sun's motion — that is, to pass from north, through north-east, east-
south-east to south, and so on round in the same direction from west to
north ; that it often makes a complete circuit in that direction, or more
than one in succession, occupying many days in doing so, but that it rarely
veers, and very rarely or never makes a complete circuit in the opposite
direction. This course of the winds is most regularly observed in winter.
According to Leverrier, the displacement of the north-east by the south-
west wind arises from the occurrence of a whirlwind formed upon the Gulf
Stream. For a station in south latitude a contrary law of rotation prevails.

This law, though more or less suspected for a long time, was first formally
enunciated and explained by Dove, and is known as Dove's laiv of rotation
ofwifids.

979. "Weatber charts. — A considerable advance has been made in
weather forecasts by the frequent and systematic publication of lueather
cJtarts ; that is to say, maps in which the barometric pressure, the tempe-
rature, the force of the wind, &c., are expressed for considerable areas in an

T004 Meteorology. [979-

exact and comprehensive manner. A careful study of such maps renders
possible a forecast of the weather for a day or more in advance. We can
here do little more than explain the meaning of the principal terms in use.

If lines are drawn through those places on the earth's surface where the
corrected barometric height at a given time is the same, such lines are
called isobarometric lines, or more briefly, isobaric lines, or isobars. Between
any two points on the same isobar there is no difference of pressure.
Isobars are usually drawn either for a difference of 5 mm., or of y^ of an inch.

If we take a horizontal line between two isobars, and at that point at
which the pressure is greatest draw a perpendicular line on any suitable
scale, which shall represent the difference in pressure between the two places,
the line drawn from the top of this perpendicular to the lower isobar will
form an angle with the horizontal, and the steepness of this angle is a
measure of the fall in pressure between the two stations, and is called the
barometric gradient. Gradients are usually expressed in England and
America in hundredths of an inch of mercury for one degree of sixty nautical
miles, and on the Continent in millimetres for the same distance. The
closer are the isobars the steeper is the gradient, and the more powerful
the wind ; and though no exact numerical relationship can be proved to exist
between the steepness of the gradient and the force of the wind, it may be
mentioned that a gradient of about 6 represents a strong breeze ; and a
gradient of 10, or a difference in pressure of j', of an inch for 60 miles,
is a stiff gale.

The direction of the wind is from the place of higher pressure to that of
lower, and in this respect the law of Buys Ballot may be mentioned, which
has been foursd to hold in all cases of the Northern Hemisphere, where
local configuration does not come into play. // ice stand with our back to
the wind the li?ie of lower pressure is on the left hand. For places in the
Southern Hemisphere exactly the opposite law holds.

If within any area the pressure is lower, the wind blows round that area,
the place of lowest pressure being on the left. The direction of the wind is,
in short, opposite that of the hands of a watch. Such a circulation is called
cyclonic ; it is that which is characteristic of the West Indian hurricanes,
which are known as cyclones. Conversely the wind blows round an area of
higher pressure in the same direction as the hands of a watch ; and this cir-
culation is called a?iti-cyclonic.

Cyclonic systems arc by far the most frequent, and arc characterised by
steep gradients ; the air in them tends to move in towards the centre, and
thence to the upper regions of the atmosphere. They bring with them o\-er
the greater part of the region which they cover, much moisture, an abundance
of cloud, and heavy rain. An anti-cyclonic system has the opposite charac-
teristics ; the gradients are slight, the wind light, and moves with the hands
of a watch. The air is dry, so that there is but little cloud, and no rain.
Cyclonic systems, from the dampness of the air, produce warm weather in
winter, and cold, wet weather in summer. Anti-cyclonic systems bring our
hardest frosts in winter and greatest heat in summer, as there is but little ,
moisture in the air to temper the extremes of climalr. Both systems travel
over the earth's surface — the cyclones rapidly, but the anti-cyclones more
slowly.

-981] Clouds. 1005

980. Pogs and Mists. — When aqueous vapour rising from a vessel of
boiling water diffuses in the colder air, it is condensed ; a sort of cloud is
formed which consists of a number of small hollow vesicles of water, which
remain suspended in the air. These are usually spoken of as vapour, yet
they are not so— at any rate not in the physical sense of the word, for in
reality they are partially condensed vapour.

When this condensation of aqueous vapour is not occasioned by contact
with cold solid bodies,, but takes place throughout large spaces of the atmo-
sphere, it constitutes /(T^j- or niists^ which, in fact, are nothing more than the
appearance seen over a vessel of hot water.

A chief cause of fogs consists in the moist soil being at a higher tem-
perature than the air. The vapours which then ascend condense and become
visible. In all cases, however, the air must have reached its point of satura-
tion before condensation takes place. Fogs may also be produced when a
current of hot and moist air passes over a river at a lower temperature than
its own, for then, the air being cooled, as soon as it is saturated, the excess
of vapour present is condensed. The distinction between mists and fogs is
one of degree rather than of kind. A fog is a very thick mist.

By observations based on diffraction phenomena (650), the diameter 01
fog vesicles has been found to vary from 0-0154 to 0-0521 mm. ; the longer
the continuance of fine weather, the smaller are the vesicles ; before rains
they increase rapidly.

Dines, by direct microscopic measurement, found that the diameter of
fog particles varied with the same fog from 0-015 to 0-127 irirn. ; the larger
occur in dense fogs, in lighter fogs they sink to 0-0033. Kamtz found from
0-014 to 0-035 mm.

When water is coated with a layer of coal-tar, it is prevented from
evaporating. Frankland ascribes the d7y fog met with in London to the
large quantities of coal-tar and paraffine vapour which are sent into the
atmosphere, and which, condensing on the vesicles of fog, prevent their
evaporation.

Aitkin has shown that aqueous vapour never condenses unless some
liquid or solid is present on which it is deposited. Particles of dust in the
air are the nuclei for clouds and fogs. This he showed by passing steam
into filtered air ; it remained quite clear, while a turbidity was produced
under the same circumstances in unfiltered air. The density of the cloud
was found to depend on the number of particles of dust in the air. A most
abundant source of dust is the combustion of coal. The sulphur in the coal
in burning also forms sulphurous acid, which, though a g'as, is found to act
as a nucleus.

981. Clouds. — Clouds are masses of vapour, condensed into little drops
or vesicles of extreme minuteness, like fogs. There is no difference of kind
between fogs and clouds. Fogs are clouds resting on the ground. To a
person enveloped in it, a cloud on a mountain appears like a fog. They
always result from the condensation of vapour which rises from the earth.
According to their appearance, they have been divided by Howard into four
principal kinds : the nimbus^ the stratus, the cumulus^ and the cirrus. These
four kinds are represented in fig. 970, and are designated respectively by one
two, three, and four birds on the wing.

ioo6 Meteorology. [981-

The cirrus consists of small whitish clouds, w hich have a fibrous or wispy-
appearance, and occupy the highest regions of the atmosphere. The name
of marei tails, by which they are generally known, well describes their
appearance. From the low temperature of the spaces which they occupy^
it is more than probable that cirrus clouds consist of frozen particles ; and
hence it is that halos, coronas, and other optical appearances, produced by
refraction and reflection from ice-crystals, appear almost always in these
clouds and their derivatives. Their appearance often precedes a change of
weather.

The cumulus are rounded spherical forms which look like mountains
piled one on the other. They are more frequent in summer than in winter,
and after being formed in the morning they generally disappear towards
evening. If, on the contrary, they become more numerous, and especially
if surmounted by cirrus clouds, rain or storms may be expected.

Stratus clouds consist of very large and continuous horizontal sheets,
which form chiefly at sunset and disappear at sunrise. They are frequent
in autumn and unusual in spring-time, and arc lower than the preceding.

The nimbus, or ram clouds, which are sometimes classed as one of the
fundamental varieties, are properly a combination of the three preceding
kinds. They affect no particular form, and are solely distinguished by a
uniform grey tint and l)y fringed edges. They are indicated on the right of
the figure by the presence of one bird.

The fundamental forms pass into one another in ilic most varied manner; -
Howard has classed these transitional forms as cirro-cumulus, cirro-stratus,
and cumulo-stratus, and it is often very diflicult to tell, from the appearance

For mat ion of Clouds. 1007

of a cloud, wliich type it most resembles. The cirro-cumulus is most cha-
racteristically known as a 'mackerel sky;' it consists of small roundish
masses, disposed with more or less irregularity and connection. It is fre-
quent in summer, and attendant on warm and dry weather. Cirro-strattis
appears to result from the subsidence of the fibres of cirrus to a horizontal
position which at the same time approach laterally. The form and relative
position wjien seen in the distance frequently give the idea of shoals of fish.
The tendency of ciunulo-stratus is to spread, settle down into the nimbus.,
and finally fall as rain.

The height of clouds varies greatly; in the mean it is from 1,300 to 1,500
yards in winter, and from 3,300 to 4,300 yards in summer. But they often
exist at greater heights ; Gay-Lussac, in his balloon ascent, at a height of
7,630 yards, observed cirrus clouds above him, which appeared to be at a
considerable height. In Ethiopia, D'Abbadie observed storm-clouds whose
height was only 230 yards above the ground.

In order to explain the suspension of clouds in the atmosphere, Halley
first proposed the hypothesis of vesicular vapours. He supposed that clouds
are formed of an infinity of extremely minute vesicles, hollow, like soap-
bubbles filled with air, which are hotter than the surrounding air ; so that
these vesicles float in the air like so many small balloons. Others assume
that clouds and fogs consist of extremely minute droplets of water which are
retained in the atmosphere by the ascensional force of currents of hot air,
just as light powders are raised by the wind. Ordinarily, clouds do not
appear to descend, but this absence of downward motion is only apparent.
In fact, clouds do usually fall slowly, but then the lower part is continually
dissipated on coming in contact with the lower and more heated layers ; at
the same time the upper part is always increasing from the condensation of
new vapours, so that from these two actions clouds appear to retain the
same height.

982. Formation of clouds. — Many causes may concur in the formation
of clouds. The usual cause of the formation of a cloud is the ascent, into
higher regions of the atmosphere, of air laden with aqueous vapour ; it
thereby expands, being under diminished pressure ; and in consequence
of this expansion it is cooled, and this cooling produces a condensation of
vapour. Hence it is that high mountains, stopping the currents of air and
forcing them to rise, are an abundant source of rain. If the air is quite dry
its temperature would be one degree lower for every 300 metres. The case
is different with moist air ; for when the air has ascended so high that its
temperature has fallen to the dew-point, aqueous vapour is condensed, and
in consequence of this heat is liberated ; when the dew-point is thus attained,
and the air is saturated, the cooling due to the ascent and expansion of air
is counteracted by this liberation of latent heat, so that the diminution of
temperature with the height is considerably slower in the case of moist than
of diy air. About one half of the entire quantity of moisture in the air is
contained in the first six or seven thousand feet upon the ground.

The following calculation will give us the quantity of water separated in
a given case : Suppose air at a temperature of 20° to be saturated with
acjueous vapour at that temperature ; the pressure of the vapour will be 17-4
mm., and the weight contained in one cubic metre of air 17-1 grammes.

ioo8 Meteorology. [982-

If the air has risen to a height of 3,500 metres, it has come under a
pressure which is only \ of what it was ; its temperature is 4°, and its
volume about li times what it originally was. As it remains saturated the
pressure will be 6"i mm., and the quantity of vapour will be 6*4 grammes
in a cubic metre, that is to say, 6-4 x 1^ = 9-6 grammes in the whole mass of
what was originally a cubic metre. The pressure of aqueous vapour has
sunk during the ascent from 17-4 mm. to 6-i mm., and its weight 17-1
grammes to 9-6 grammes ; that is, a weight of 7-5 grammes has been deposited
for that mass of air which at the sea-level occupied a space of one cubic
metre. These 7-5 grammes are in the form of the small droplets which
constitute fogs or clouds.

If the mass of air had risen to a height of 8,500 metres, where the pres-
sure is only one-third that on the sea-level, the temperature is —28°, and
the space it occupies three times as great as at first. The pressure of
aqueous vapour is 0-5 mm., and its weight o-6 gramme in a cubic metre.
Hence there is now only i'8 gramme left of the entire quantity of aque-
ous vapour originally present, and the remaining 15 -3 grammes would be
separated as water or ice. A similar calculation will show that at a height
of 4,200 metres, where the temperature is zero and the pressure |, the quan-
tity of water present in the original cubic metre is only 0-82 gramme, the
rest being deposited.

Thus, a mass of air which, at the sea-level, occupies a space of a cubic
metre, and is saturated with aqueous vapour at 20°, and then contains 17-1
grammes, will only contain 9-6 grammes at a height of 3,500 metres, 8-2
grammes at 4,200 metres, and i-8 gramme at 8,500 metres. Hence, while
a mass of air rises from the sea-level to a height of 4,200 feet, 8-9 grammes of
aqueous vapour are separated as cloud-vesicles ; at 8,500 metres, or about
double the height, 6-4 grammes are separated in the form of ice.

A hot moist current of air mixing with a colder current undergoes a
cooling, which brings about a condensation of the vapour. Thus the hot
and moist winds of the south and south-west, mixing with the colder air of
our latitudes, give rain. The winds of the north and north-east tend also,
in mixing with our atmosphere, to condense the vapours ; but as these winds,
owing to their low temperature, are veiy dry, the mixture rarely attains
saturation, and generally gives no rain.

The formation of clouds in this way is thus explained by Hutton. The
tension of aqueous vapour, and therewith the quantity present in a given
space when saturated, diminishes according to a geometric progression,
while the temperature falls in arithmetical progression, and therefore the
elasticity of the vapour present at any time is reduced by a fall of temperature
more rapidly than in direct proportion to the fall. Hence, if a current of
warm air, saturated with aqueous vapour, meets a current of cold air also
saturated, the air acquires the mean temperature of the two, but can only
retain a portion of the vapour in the invisible condition, and a cloud or mist
is formed. Thus, suppose a cubic metre of air at io° C. mixes with a cubic
metre of air at 20° C, and that they are respccti\cly saturated with aqueous
vapour. By formula (401) it is easily calculated that the weight of water-'
contained in the cubic metre of air at 10° C. is 9*397 grammes, and in that
at 20° C. is 17-632 grammes, or 27-029 grammes in all. When mixed they

-983] Rain. 1009

produce two cubic metres of air at 15° C. ; but as the weight of water
required to saturate this is only 2 x 12-8 = 25-6 grammes, the excess, 1-429
gramme, will be deposited in the form of mist or clouds.

983. Rain. — When the individual vapour-vesicles become larger and
heavier by the condensation of aqueous vapour, and when finally individual
vesicles unite, they form regular drops, which fall as rain.

The quantity of rain which falls annually in any given place, or the annual
rainfall, is measured by means of a rain-gauge^ ox pluviotneter. Ordinarily it

consists of a cylindrical vessel
M (figs. 971 and 972), closed at
the top by a funnel-shaped lid,
in which there is a very small
hole, through which the rain
falls. At the bottom of the
vessel is a glass tube. A, in
which the water rises to the
same height as inside the rain-
gauge, and is measured by a
scale on the side, as shown in
the figures.

Fig. 971. Fig. 972. The apparatus being placed

in an exposed situation, if at
the end of a month the height of water in the tube is two inches, for example,
it shows that the water has attained this height in the vessel, and, conse-
quently, that a layer of two inches in depth expresses the quantity of rain
which this extent of surface has received.

It has been noticed that the quantity of rain indicated by the rain-gauge
is greater as this instrument is nearer the ground. This has been ascribed
to the fact that the raindrops, which are generally colder than the layers of
air which they traverse, condense the vapour in these layers, and therefore
constantly increase in volume. Hence more rain falls on the surface of the
ground than at a certain height. But it has been objected that the excess
of the quantity of rain which falls, over that at a certain height, is six or
seven times that which could arise from condensation, even during the whole
course of the raindrops from the clouds to the earth. The difterence must
therefore be ascribed to purely local causes, and it is now assumed that the
difference arises from eddies produced in the air about the rain-gauge, which
are more perceptible as it is higher above the ground ; as these eddies dis-
perse the drops which would otherwise fall into the instrument, they diminish
the quantity of water which it receives.

In any case it is clear that if raindrops traverse moist air, they will, from
their temperature, condense aqueous vapour and increase in volume. If, on
the contrary, they traverse dry air, the drops tend to vaporise, and less rain
falls than at a certain height ; it might even happen that the rain did not
reach the earth.

From measurements of the coron^e (981) Delezenne determined the
diameter of the globules in the case of rain-clouds just about to fall, and in
the case of the cloud from a low-pressure steam-engine (471). The former
was found to vary from 0-0565 to 0'0226 mm., and the latter from 0'005i to

1 010 Meteorology. [983-

0-0042 mm. With the former 5,500 droplets would be needed to make a
drop of water a millimetre in diameter, and with the latter 50,000.

According to the same author there would be about 1 5 mgr. of globules in
a cubic metre of a cloud which produced a rainfall of 10 mm. of water in an
hour. With this number the mean distances of the vesicles with the above
magnitudes are respectively r845, 0706, 0-167, and 0-148 mm.

The rainfall varies with the height of a station above the sea-level at the
rate of 3 or 4 per cent, for each 100 feet of altitude above the sea.

Many local circumstances may affect the quantity of rain which falls in
different countries ; but, other things being equal, most rain falls in hot cli-
mates, for there the vaporisation is most abundant. The rainfall decreases,
in fact, from the equator to the poles. At London it is 23-5 inches ; at
Bordeaux it is 25-8 ; at Madeira it is 27-7 ; at Havannah it is 91-2 ; and at
St. Domingo it is 107-6. The quantity varies with the season : in Paris, in
winter, it is 4-2 inches ; in spring, 6-9 ; in summer, 6*3 ; and in autumn, 4-8
inches. The heaviest annual rainfall at any place on the globe is on the
Khasi Hills in Bengal, where it is 600 inches ; of which 500 inches fall in
seven months. On July i, 1851, a rainfall of 25^ inches on one day was
observed at Cherrapoonjee. At Kurrachec, in the north-west of India, the
rainfall is only 7 inches.

The driest recorded place in England is Lincoln, where the mean rainfall
is 20 inches ; and the wettest is Stye, at the head of Borrowdale in Cumber-
land, where it amounts to 165 inches. The greatest average amount of rain-
fall in any one day, taking' the means of all stations, is i^ inch ; though
individual stations far exceed this amount, sometimes reaching 4 inches.

An inch of rain on a square yard of surface expresses a fall of 46-74
pounds, or 4-67 gallons. On an acre it corresponds to 22,622 gallons, or
100-9935 tons. 100 ions per i?ich per acre is a ready way of remembering
this.

984. 'Waterspouts.— On hot summer days, and when the weather is-
otherwise calm, we often notice sand and dust carried forward in a column
with a whirling motion. As storms come on, larger whirlwinds of this kind
are formed, which carry with them leaves, straw, and even small branches.
When they are of larger dimensions they form real whirlwinds. They are
probably due to the contest of two winds blowing in the upper regions of the
atmosphere. When they pass over land they form large conical-shaped
masses of dust which makes them visible at a distance ; when they pass
over rivers or the sea they present a curious phenomenon. The water is
disturbed, and rises in the form of a cone, while the clouds are depressed
in the form of an inverted cone ; the two cones then unite and form a
continuous column from the sea to the clouds (fig. 973). Even, however^
on the high seas the water of these waterspouts is never salt, proving
that they are formed of condensed vapour, and not of sea- water raised by
aspiration.

985. Influence of aqueous vapour on oliniate. — Tyndall applied the
property possessed by aqueous vapour of powerfully absorbing and radiating
lieat to the explanation of some obscure points in nieteorologj'. He estalj-
lishcd the fact that in a tube 4 feet long the atmospheric vapour on a day of
average dryness absorbs 10 per cent, of obscure heat. With the earth warmed

-985]

bifincncc of Aqueous Vapour on Climate.

ion

by the sun as a source, at the very least lo per cent, of its heat is intercepted
within lo feet of the surface. The absorption and radiation of aqueous
vapour is more than 16,000 times that possessed by dry air.

The 7-adiati7<e power of acjueous vapour may be the main cause of the
torrent-hke rains that occur in the tropics, and also of the formation of
cumulus clouds in our own latitudes. The same property probably causes
the descent of very fine rain, called serein^ which has more the characteristics
of falling dew, as it appears a short time after sunset, when the sky is clear ;
its production has therefore been attributed to the cold resulting from the

Fig. 973.

radiation of the air. It is not the air, however, but the aqueous vapour in
the air, which by its own radiation chills itself, so that it condenses into
serehi.

The absorbent power of aqueous vapour is of even greater importance.
Whenever the air is dry, terrestrial radiation at night is so rapid as to cause
intense cold. Thus, in the central parts of Asia, Africa, and Australia, the
daily range of the thermometer is enormous ; in the interior of the last-
named continent a difference in temperature of no less than 40° C. has been
recorded within 24 hours. In India, and even in the Sahara, ice has been
formed at night, owing to the copious radiation. But the heat which aqueous
vapour absorbs most largely is of the kind emitted from sources of low
temperature ; it is to a large extent transparent to the heat emitted from the
sun, whilst it is almost opaque to the heat radiated from the earth. Con-
sequently, the solar rays penetrate our atmosphere with a loss, as estimated
by Pouillet, of only 25 per cent., when directed vertically downwards, but
after warming the earth they cannot re-traverse the atmosphere. Through

3T 2

IOI2 Meteorology. [985-

thus preventing the escape of terrestrial heat, the aqueous vapour in the air
moderates the extreme chilhng which is due to the unchecked radiation from
the earth, and raises the temperature of that region over which it is spread.
In Tyndall's words, 'aqueous vapour is a blanket more necessary to the
vegetable life of England than clothing is to man. Remove for a single
summer night the aqueous vapour from the air which overspreads this
country, and every plant capable of being destroyed by a freezing tempera-
ture would perish. The warmth of our fields and gardens would pour itself
unrequited into space, and the sun would rise upon an island held fast in the
iron grip of frost.'

986. Tyndall's researches. — Tyndall found that by the action of the
sun and the electric light on vapours under a great degree of attenuation,
they are decomposed. He used a glass tube with glass ends, which could
be exhausted and then filled with air charged with the vapours of volatile
liquids, by allowing the air to bubble through small Wolff bottles containing
them. By mixing the air charged with vapour with different proportions of
pure air, and by varying the degree of exhaustion, it was possible to have a
vapour under any degree of attenuation. The tube could also be filled with
the vapour of a liquid alone. The tube having been filled with air charged
with vapour of nitrite of amyle, a somewhat convergent beam from the elec-
tric lamp was passed into the tube. For a moment the tube appeared
optically empty, but suddenly a shower of liquid spherules was precipitated
on the path of the beam, forming a luminous white cloud. The nature of
the substance thus precipitated was not specially investigated. This effect
was not due to any chemical action between the vapour and the air, for
when either dry oxygen or dry hydrogen was used instead of air, or when
the vapour was admitted alone, the effect was substantially the same. Nor
was it due to any heating effect, for the beam had been previously sifted by
passing through a solution of alum, and through the thick glass of the lens.
The unsifted beam produced the same effect ; the obscure calorific rays did
not seem to affect the result. The sun's light also effects the decomposition
of nitrite of amyle vapour ; and this decomposition was found to be mainly
due to the more refrangible rays. When the electric light, before entering
the experimental tube, was made to pass through a layer of liquid nitrite of
amyle an eighth of an inch in thickness, the luminous effect was not appre-
ciably diminished, but the chemical action was almost entirely stopped.
Thus that special constituent of the luminous radiation which effects the
decomposition of the vapour is absorbed by the liquid. The decomposition
of liquid nitrite of amyle by light, if it take place at all, is far less rapid and
distinct than that of the vapour. The circumstance that the absorption is
the same whether the nitre is in the liquid or in the vaporous state, is con-
sidered by Tyndall as a proof that the absorption is not the act of the
molecule as a whole, but that it is atomic ; that is, that it is to the atoms
that the peculiar rate of vibration is transferred which brings about the
decomposition of the body, liy vaiying the nature of the vapour the shape
of a cloud could be greatly varied, and in many cases presented the most
fantastic and beautiful forms.

It was also found that a vapour which when alone resists the action of
light may, by being associated with another gas or vapour, exhibit a vigor-

-986J TyndaWs Researches. 1013

ous action. Thus when the tube was filled with atmospheric air, mixed with
nitrite of butyle vapour, the electric light produced very little efifect ; but with
half an atmosphere of this mixture, and half an atmosphere of air which had
passed through hydrochloric acid, the action of the light was almost instan-
taneous. In another case mixed air and nitrite of butyle vapour were passed
into the tube so that the mixture was under a pressure of 2*5 mm. Air
passed through aqueous hydrochloric acid was introduced until the pressure
was 3 inches. The condensed beam passed through at first without change,
but afterwards a superb blue cloud was formed.

In cases where the vapours are under a sufficient degree of attenuation,
whatever otherwise be their nature, the visible action commences with the
formation of a blue cloud. The term cloud, however, must not be understood
in its ordinary' sense ; the blue cloud is invisible in ordinary daylight, and
to be seen must be surrounded by darkness, it alone being illuminated by a
powerful beam of light. The blue cloud differs in many important particulars
from the finest ordinary clouds, and may be considered to occupy an inter-
mediate position between these clouds and true cloudless vapour.

By graduating the quantity of vapour, the precipitation may be obtained
of any required degree of fineness ; forming either particles distinguishable
by the naked eye, or particles beyond the reach of the highest microscopic
power. The case is similar to that of carbonic acid gas, which, diffused
in the atmosphere, resists the decomposing^ action of solar light, but is
decomposed when in contact with the chlorophyle in the leaves of plants.

When the blue cloud produced in these experiments was examined by
any polarising arrangement, the light emitted laterally from the beam — that
is, in a direction at right angles to its axis— was found to be perfectly polar-
ised. This phenomenon was observed in its greatest perfection the more
perfect the blue of the sky. It is produced by any particles, provided they
are sufficiently fine. This is quite analogous to the light of the blue sky.
When this is examined by a Nicol's prism, or any other analyser, it is found
that the light emitted at right angles to the path of the sun's rays is polarised.

The phenomena of the firmamental blue, and the polarisation of the
sky light, thus find definite explanations in these experiments. We need only
assume the existence, in the higher regions of the atmosphere, of excessively
fine particles of water ; for particles of any kind produce this effect. It
is easy to conceive the existence of such particles in the higher regions,
even on a hot summer's day. For the vapour must there be in a state of
extreme attenuation ; and inasmuch as the oxygen and nitrogen of the atmo-
sphere behave like a vacuum to radiant heat, the extremely attenuated particles
of aqueous vapour are practically in contact with the absolute cold of
space.

' Suppose the atmosphere surrounded by an envelope impervious to
light, but with an aperture on the sunward side, through which a parallel
beam of solar light could enter and traverse the atmosphere. Surrounded
on all sides by air not directly illuminated, the track of such a beam would
resemble that of the parallel beam of the electric light through an incipient
cloud. The sunbeam would be blue, and it would discharge light laterally in
the same condition as that discharged by the incipient cloud. The azure re-
vealed by such a beam would be to all intents and purposes a blue cloud.'

1014 Meteorology. [987-

987. Bew. Hoarfrost. — Deiu is aqueous vapour which has condensed
on bodies during the night in the form of minute globules. It is occasioned
by the chilling which bodies near the surface of the earth experience in
consequence of nocturnal radiation. Their temperature having then sunk
several degrees below that of the air, it frequently happens, especially in hot
seasons, that this temperature is below that at which the atmosphere is
saturated. The layer of air which is immediately in contact with the chilled
bodies, and which has virtually the same temperature, then deposits a por-
tion of the vapour which it contains (396) ; just as when a bottle of cold water
is brought into a warm room it becomes covered with moisture, owing' to the
condensation of aqueous vapour upon it.

According to this theory, which was first propounded by Dr. Wells, all
causes which promote the cooling of bodies increase the quantity of dew.
These causes are the emissive power of bodies, the state of the sky, and the
agitation of the air. Bodies which have a great radiating power more readily
become cool, and therefore ought to condense more vapour. In fact there
is generally no deposit of dew on metals, whose radiating power is very
small, especially when they are polished ; while the ground, sand, glass and
plants, which have a great radiating power, become abundantly covered
with dew.

The state of the sky also exercises a great influence on the formation of
dew. If the sky is cloudless, the planetary spaces send to the earth an in-
appreciable quantity of heat, while the earth radiates very considerably, and
therefore becoming very much chilled, there is an abundant deposit of dew.
But if there are clouds, as their temperature is far higher than that of the
planetary spaces, they radiate in turn towards the earth, and as bodies on the
surface of the earth only experience a feeble chilling, no deposit of dew takes
place.

Wind also influences the quantity of vapour deposited. If it is feeble, it
increases it, inasmuch as it renews the air ; if it is strong, it dmiinishes it,
as it heats the body by contact, and thus does not allow the air time to
become cooled. Finally, the deposit of dew is more abundant according as
the air is moister, for then it is nearer its point of saturation.

Hoarfrost and rime are dew which has been deposited on bodies cooled
below zero, and has become frozen. The flocculent form which the small
crystals present, of which rime is formed, shows that the vapour solidifies
directly without passing through the liquid state. Hoarfrost, like dew, is
formed on bodies which radiate most, such as the stalks and leaves of vege-
tables, and is chiefly deposited on the parts turned towards the sky.

We must distinguish between the dew formed in consequence of lowering
of temperature by radiation, and the deposit formed by warm moist air
passing over a cold wall ; in mild weather this deposit forms a liquid,
and in severe weather a snow or icy coating. Unlike dew, a deposit of
this kind is most abundantly found on good conductors, for they are the
coldest.

988. Snow. Sleet. — Snow is water solidified in stellate ciystals, vari-.
ously modified, and floating in the atmosphere. These crystals arise frorrr'
the congelation of the minute vesicles which constitute the clouds, when the
temperature of the latter is below zero. They are more regular when formed

-989] Hail. 1015

in ;i calm atmosphere. Their form may 1)C investigated by collecting them
on a black surface, and viewing them through a strong lens. The regularity,
and at the same time variety, of their forms are truly beautiful. Fig. 974
shows some of these forms as seen through a microscope. Very roughly a
fall of one foot of snow may be taken as equal to an inch of rain.

It snows most in countries near the poles, or which are high above the
sea-level. By the limit of perpetual snow — or, briefly snow-line — is meant that
height above the sea-level at which the snow does not melt, even in the
hottest summers. It is lower nearer the poles than the equator : it does not
depend solely on the latitude, but is influenced by many local circumstances.

Fis. 974.

Sleet is also solidified water, and consists ot small icy needles pressed
together in a confused manner. Its formation is ascribed to the sudden
congelation of the minute globules of the clouds in an agitated atmo-
sphere.

When the ground is cooled below zero after severe frost and a thaw sets
in, the moist air passing over the ground deposits its moisture, which is
converted into a continuous sheet of ice ; this is known as glazed frost (the
French verglas) ; it may also occur when raindrops which have been cooled
below zero in the higher regions of the air, and are accordingly in a state of
snperfusion (345), fall on the ground, which may even be above the freezing
point.

989. Hall. — Hail is a mass of compact globules of ice of different sizes,
which fall in the atmosphere. In our climate hail falls principally during
spring and summer, and at the hottest times of the day ; it rarely falls at
night. The fall of hail is always preceded by a peculiar noise.

Hail is generally the precursor of storms, it rarely accompanies them,
and follows them more rarely still. Hail falls from the size of small peas to
that of an ^g'g or an orange, with a core of compressed snow which is sur-
rounded by concentric layers of ice. While snowstorms may last for days,
hailstorms do not last for more than a quarter of an hour. The formation
of hailstones has never been altogether satisfactorily accounted for ; nor
more especially their great size.

ioi6 Meteorology. [990-

990. Ice. Regrelation. — Ice is an aggregate of sno\v-cr>'stals, such as
are shown in fig. 974. The transparency of ice is due to the close contact
of these crystals, which causes the individual particles to blend into an un-
broken mass, and renders the substance optically., as well as mechanically,
continuous. When large masses of ice slowly melt away, a crystalline form
is sometimes seen by the gradual disintegration into rude hexagonal prisms ;
a similar structure is frequently met with, but in greater perfection, in the
ice-caves or glaciers of cold regions.

An experiment of Tyndall shows the beautiful structure of ice. When a
piece of ice is cut parallel to its planes of freezing, and the radiation from
any source of light is permitted to pass through it, the disintegration of
the substance proceeds in a remarkable way. By observing the plate of
ice through a lens, numerous small crystals will be seen studding the interior
of the block ; as the heat continues these crystals expand, and finally assume
the shape of six-rayed stars of exquisite beauty.

This is a kind of negative crystallisation, the crystals produced being
composed of water : they owe their formation to the molecular disturbance
caused by the absorption of heat from the source. Nothing is easier than to
reproduce this phenomenon, if care be taken in cutting the ice. The planes
of freezing can be found by noting the direction of the bubbles in ice, which
are either sparsely arranged in striae at right angles to the surface, or thickly
collected in beds parallel to the surface of the water. A warm and smooth
metal plate should be used to level and reduce the ice to a slab not exceeding
half an inch in thickness.

A still more important property of ice remains to be noticed. Faraday
discovered that when two pieces of melting ice are pressed together they
freeze into one at their points of contact. This curious phenomenon is now
known under the name of Regelation. The cause of it has been the subject
of much controversy, but the simplest explanation seems to be that given
by its discoverer. The particles on the exterior of a block of ice are held by
cohesion on one side only ; when the temperature is at 0° C, these exterior
particles being partly free are the first to pass into the liquid state, and a film
of water covers the solid. But the particles in the interior of the block are
bounded on all sides by the solid ice, the force of cohesion is here a maximum,
and hence the interior ice has no tendency to pass into a liquid, even when
the whole mass is at 0°. If the block be now split in halves, a liquid film
instantly covers the fractured surfaces, for the force of cohesion on the
fractured surfaces has been lessened by the act. By placing the halves
together, so that their original position shall be regained, the liquid films
on the two fractured surfaces again become liounded by ice on both sides.
The film being excessively thin, the force of cohesion is able to act across
it ; the consequence of this is, the liquid particles pass back into the solid
state, and the block is reunited by regelation. Not only do ice and ice thus
freeze together, but regelation also takes place between moist ice and any
non-conducting solid body, as flannel or sawdust ; a similar explanation to
tliat just given has been applied here, substituting another solid for the ice,
(in one side. It must be remarked, however, that many eminent philosophers
dissent from the explanation here given.

Whatever may be the true cause of regelation, there can be no doubt that

-992] Atmospheric Electricity. Franklin's Experiment. 1017

this interesting observation of Faraday's explains many natural phenomena
For example, the formation of a snowball depends on the regelation of the
snow-granules composing it ; and as regelation cannot take place at tem-
peratures below 0° C, for then both snow and ice are dry, it is only possible
to make a coherent snowball when the snow is melting.

The snow-bridges, also, which span wide chasms in the Alps and else-
where, and over which men can walk in safety, owe their existence to the
regelation of gradually accumulating particles of snow.

Bottomley has made a very instructive experiment which illustrates rege-
lation. A block of ice is suspended on two supports, and a fine piano wire
with heavy weights at each end is laid across it. After some time the wire
has slowly cut its way through, but the cut surfaces have reunited, and, except-
ing a few bubbles, show no trace of the operation ; the wire is below zero, as
is proved by placing it in cold water, upon which some ice forms round it.

991. Glaciers. — Tyndall has applied this regelating property of ice to
an explanation of the formation and motion of glaciers, of which the follow-
ing is a brief description : In elevated regions, the sttow-line (988) marks the
boundary' of eternal snow, for above this the heat of summer is unable to
melt the winter's snow. By the heat of the sun and the consequent percola-
tion of water melted from the surface, the lower portions of the snow-field
are raised to 0° C. ; at the same time this part is closely pressed together by
the weight of the snow above ; regelation therefore sets in, converting the
loose snow into a coherent mass.

By increasing pressure the intermingled air which renders snow opaque
becomes ejected and the snow becomes transparent ; ice then results. Its
own gravity, and the pressure from behind, urge downwards the glacier
which has thus been formed. In its descent from the mountain the glacier
behaves in all respects like a river, passing through narrow gorges with
comparative velocity, and then spreading out and moving slowly as its bed
widens. Further, just as the central portions of a river move faster than
the sides, so Forbes ascertained that the centre of a glacier moves quicker
than its margin, and from the same reason (the difference in the friction
encountered) the surface moves more rapidly than the bottom. To explain
these facts Forbes assumed ice to be a viscous body capable of flexure, and
flowing like lava ; but as ice has not the properties of a viscous substance,
the now generally accepted explanation of glacier motion is that supplied by
the theory of regelation. According to this theory, the brittle ice of the
glacier is crushed and broken in its passage through narrow channels, such
as that of Trelaporte on Mont Blanc ; and then, as it emerges from the gorge
which confined it, becomes reunited by virtue of regelation ; in this instance
forming the well-known Mer de Glace. By numerous experiments Tyndall
has established that regelation is adequate to furnish this explanation, and
has artificially imitated, on a small scale, the moulding of glaciers by the
crushing and subsequent regelation of ice.

We see an example of this formation of ice from pressure from the glazed
appearance of the tracks in snow in roads over which heavy carts have
passed.

992. Atmospberlc electricity. Franklin's experiment. — The most
frequent luminous phenomena, and the most remarkable for their effects,

ioi8

Meteorology.

[992-

are those produced by the free electricity in the atmosphere. The first
physicists who observed the electric spark compared it to the gleam of
lightning, and its crackling to the sound of thunder. But Franklin, by the
aid of powerful electrical batteries, first established a complete parallel
between lightning and electricity ; and he indicated, in a memoir published
in 1749, the experiments necessary to attract electricity from the clouds by
means of pointed rods. The experiment was tried by
Dalibard in France ; and Franklin, pending the erec-
tion of a pointed rod on a spire in Philadelphia, had the
happy idea of flying a kite, provided with a metal
point, which could reach the higher regions of the
atmosphere. In June 1752, during stormy weather,
he flew the kite in a field near Philadelphia. The
kite was flown with ordinary pack-thread, at the end
of which Franklin attached a key, and to the key a
silk cord, in order to insulate the apparatus : he then
fixed the silk cord to a tree, and having presented
his hand to the key, at first he obtained no spark.
He was beginning to despair of success, when, rain
having fallen, the cord became a good conductor, and
a spark passed. Franklin, in his letters, describes his
emotion on witnessing the success of the experiment as
being so great that he could not refrain from tears.

Franklin imagined that the kite drew from the
cloud its electricity ; it is, in fact, a simple case of
induction, and depends on the inductive action which
the thunder-cloud exerts upon the kite and the cord.

993. Apparatus to investigate the electricity of
the atmosphere. — To observe the electricity in fine
weather, when the quantity is generally small, an ap-
paratus may be used, as devised by Saussure for this
kind of investigation. It is an electroscope similar to
that already described (751), but the rod to which the
gold leaves are fixed is surmounted by a conductor
2 feet in length, and terminates either in a knob or
a point (fig. 975). To protect the apparatus against
rain, it is covered with a metal shield 4 inches in
diameter. The glass case is square instead of being round, and a divided
scale on its inside face indicates the divergence of the gold leaves. This
electrometer only gives signs of atmospheric electricity as long as it is
raised in the atmosphere so that it is in layers of air of higher electrical
potential than its own.

To ascertain the electricity of the atmosphere, Saussure also used a
copper ball, which he projected vertically with his hand. This ball was
fixed to one end of a metal wire, the other end of which was attached to a
ring, which could glide along the conductor of the electrometer. From the^
divergence of the gold leaves, the electrical condition of the air at the
height which the ball attained could be determined. Becquerel, in experi-
ments made on the St. Bernard, improved Saussure's apparatus by substi-

Fig. 975.

-993] Apparatus to Investigate Atmospheric Electricity. 1019

tuting for the knob an arrow, which was projected into the atmosphere by-
means of a bow. A gilt silk thread, 88 yards long, was fixed with one end
to the arrow, while the other end was attached to the stem of an electro-
scope. Peltier used a gold-leaf electroscope, at the top of which was a
somewhat large copper globe. Provided with this instrument, the observer
places himself in a prominent position ; it is then quite sufficient to raise the
electroscope even a foot or so to obtain signs of electricity.

To observe the electricity of clouds, where the potential is very con-
siderable, use is made of a long bar terminating in a point. This bar,
which is insulated with care, is fixed to the summit of a building, and its
lower end is connected with an electrometer, or even with electric chimes
(fig. 695), which announce the presence of thunder-clouds. As, however, the

Fig. 976.

bar can then give dangerous shocks, a metal ball must be placed near it,
which is well connected with the ground, and which is nearer the bar than
the observer himself; so that if a discharge should ensue, it will strike
the ball and not the observer. Richmann, of St. Petersburg, was killed in an
experiment of this kind, by a discharge which struck him on the forehead.

Sometimes also captive balloons or kites have been used, provided with
a point, and connected by means of a gilt cord with an electrometer.

\ good collector of atmospheric electricity consists of a fishing-rod with
an insulated handle which projects from an upper window. At the top is
a bit of lighted tinder held in a metallic forceps, the smoke of which, being
an excellent conductor, conveys the electricity of the air down a wire attached
to the rod. A sponge moistened with alcohol, and set on fire, is also an
excellent conductor.

A convenient instrument for investigating atmospheric electricity has
been introduced by Sir W. Thomson ; one form of which, used in the

I020 Meteorology. [993-

Meteorological Observatory of Montsouris, is represented in fig. 976. It
consists of a large metal vessel A resting on three insulating glass legs fixed
to the top of a tall column of cast iron. A sheet metal mantle B protects the
supports from the rain. The apparatus is arranged in the open, and can be
filled with water from a pipe C. The Avater issues through a long lateral
jet in A, in a stream so fine that the volume of the water is not appreciably
altered. An insulated wire z, passing through the column, connects the vessel
A with an electrometer placed indoors. This plan of collecting the atmo-
spheric electricity is adopted in balloons, where a flame, for instance, is out of
the question.

The manner in which the electricity of the atmosphere is registered is seen
from fig. 977, which represents the form in use at the above observatory.

In a light tight box is a band of sensitised photographic paper, stretched on
the surface of a cylinder and moved by clockwork.

In one side of the box is a long cyhndrical glass lens, in front of which
at E are two quadrant electrometers (780). Both of these are connected with
the same collector of electricity, placed outside, and their sectors are charged
by the same source of electricity, but one of them is ten times as sensitive
as the other. Near one side of the box is a gas burner with an opaque
chimney A, in two opposite sides of which arc longitudinal slits, through-
which the light passes to two total-reflection prisms (545) //', which are
arranged so as to send two pencils of light on the mirrors ;// w' of the
electrometer. This is shown on a larger scale on the left of the figure : the

-994] Ordinary Electricity of the Atmosphere. 1021

two pencils fall upon the lens L, which concentrates in a point the slices of
light issuing from the chimney and reflected from the mirror. These follow
the motion of the mirror, and thus impress on the sensitive paper the curves
which measure the electrical potential of the air. There is also an arrange-
ment by which an electromagnet puts the electrometers to earth for a i&w
minutes at every hour, and thus discharges them. The mirrors revert then
to their original position and commence a new trace.

If we replace the electrometer with its mirror attached, by a magneto-
meter, we can easily see how the variations in the magnetic declination may
be recorded (702).

994. Ordinary electricity of the atmospbere. — By means of the dif-
ferent apparatus which have been described, it has been found that the
presence of electricity in the atmosphere is not confined to stormy weather,
but that the atmosphere always contains free electricity, in the vast majority
of cases positive, but occasionally negative. When the sky is unclouded,
the electricity is always positive, and it increases with the height above the
ground. The amount is greatest in the highest and most isolated places.
No trace of positive electricity is found in houses, streets, and under trees :
in towns positive electricity is most perceptible in large open spaces, on quays,
or on bridges. Sir W. Thomson found in the Isle of Arran at a height of

9 feet above the ground a difference of potential equal to 200 to 400 Daniell's
elements, or from 216 to 432 volts. This represents a rise of potential of
from 24 to 48 volts for each foot of ascent. This is subject to great varia-
tion ; with winds from the north and north-east the potential was often 6 to

10 times as much as the higher of these amounts. The charge of potential
is most rapid in cold dry weather, when the quantity of moisture in the air
is at its lowest. Thus, at a temperature of - 8° to - 12° C, Exner found a
charge of 600 Daniells per metre in the direction of the vertical. With a
vapour pressure of 2-3 mm. the charge was 325, with 6-8 it was 116, and
with 12-5 it was 68.

Between 5 and 7.30 a.m. the positive electricity in the air is at a mini-
mum ; it increases from 7 to 9.30 .A.-M., according to the season, and then
attains its first maximum. It then decreases rapidly until from 2.30 to
4.30 P.M., and again increases till it reaches its second maximum, from 6.30
to 9.30 P.M. ; the remainder of the night the electricity decreases until sun-
rise. Thus the greatest amount of electricity is observed when the baro-
metric pressure is highest. These increasing and decreasing periods, which
are observed all the year, are more perceptible when the sky is clearer, and
the weather more settled. The positive electricity of fine weather is much
stronger in winter than in summer. It may, in short, be said that electricity
of the air follows the opposite course to that of temperature and moisture. ■

When the sky is clouded, the electricity is sometimes positive and some-
times negative. According to Palmieri the occurrence of negative electricity
is a certain indication that within a distance of 40 miles it either rains,
snows, or hails. It often happens that the electricity changes its sign
several times in the course of the day, owing to the passage of an electrified
cloud. During storms, and when it rains or snows, the atmosphere may be
positively electrified one day, and negatively the next, and the number of the
two sets of days are virtually equal.

I022 Meteorology. [994-

During a thunderstorm the changes in potential and sign of electricity-
are so rapid that the photographic method of registration fails.

From a long series of observations on the electricity of the atmosphere
made in the early morning, Dellman found that the electricity increased
with the density of the fog, but in a far more rapid ratio.

The electricity of the ground has been found by Peltier to be always
negative, and this is the cardinal fact in reference to atmospheric electricity ;
it is so, however, to different extents, according to the hygrometric state
and temperature of the air. The density is, however, exceedingly small,
being calculated at 0-00036 dynes per square centimetre, from which it
follows that the electrical pressure {lyj) is 0-00000082 dynes per square
centimetre, or less than the millionth of a milligramme in weight. Even if
the pressure were ten times as great it would be insufficient to raise even
the lightest bodies.

995. Causes of atmospheric electricity. — Although many hypotheses
have been propounded to explain the origin of atmospheric electricity, it
must be confessed that our knowledge is in an unsatisfactory state.

Volta first showed that the evaporation of water produced electricity.
Pouillet subsequently showed that no electricity is produced by the evapo-
ration of distilled water ; but that if an alkali or a salt is dissolved, even
in small quantity, the vapour is positively and the solution is negatively
electrified. The reverse is the case if the water contains acid. Hence it
has been assumed that as the waters which exist on the surface of the earth
and on the sea always contain salt dissolved, the vapours disengaged ought
to be positively and the earth negatively electrified. The development of
electricity by evaporation may be observed by heating strongly a platinum
dish, adding to it a small quantity of liquid, and placing it on the upper
plate of the condensing electroscope (fig. 716), taking care to connect the
lower plate with the ground. When the water of the capsule is evaporated,
the connection with the ground is broken, and the upper plate raised. The
gold leaves then diverge if the water contained salts, but remain quiescent
if the water was pure.

Reasoning from such experiments, Pouillet ascribed the development
of electricity by evaporation to the separation of particles of water from
the substances dissolved ; but Reich and Ricss showed that the electricity
disengaged during evaporation could be attributed to the friction which
the particles of water carried away in the current of vapour exert
against the sides of the vessel, just as in Armstrong's electrical machine
(758). By a recent scries of experiments, Gaugain has arrived at the same
result.

Sohnckc recalls an experiment of Faraday which he has repeated — that
the friction of minute vesicles of water against dry ice is an abundant source
of electricity ; he ascribes atmospheric electricity to this origin, showing that
in the upper regions both particles of water and of ice may coexist. The ice
particles become positively electrified, while tliose of water arc negative.
When these fall in rain, they carry with them their negative electricity. A
similar theory has been propounded by Luvini.

996, Electricity of clouds. — Clouds are in general electrified usually
positively but sometimes negatively, and only differ in their higher or

-997J Lightning. 1023

lower potential. The formation of positive clouds is by some ascribed to
the vapour disengaged from the ground and condensed in the higher
regions. Negative clouds are supposed to result from fogs, which, by their
contact with the ground, become charged with negative electricity, which
they retain on rising into the atmosphere ; or that, separated from the
ground by layers of moist air, they have been negatively electrified by
induction from the positive clouds, which have repelled into the ground
positive electricity.

Whatever be the origin of atmospheric electricity, there can be no doubt
that the invisible aqueous vapour is the carrier of it, and it is easy to
explain the high potential of clouds from the condensation of this vapour.
For suppose 1,000 vapour-particles, each possessing the same charge of
electricity, coalesce to form a single droplet, the diameter of such a droplet
will be ten times that of the individual particles, that is, its capacity is ten
times as great, since the capacity is equal to the radius (739) ; but the
quantity of electricity will be 1,000 times as great as on the small one, and
therefore the potential will be 100 times as great. Now the number of
vapour-particles which go to form a single droplet is rather to be counted
by billions ; hence, however small be the finite value which we assign to
the potential of the electricity of the vapour-particles, that of the drops will
be infinitely greater, and sufficient to account for the high potential of clouds.
Thunder-clouds are sometimes as low as 700 to 1,000 feet ; but their usual
height appears to be 3,000 to 6,000 feet.

997. liig-htnlng-.— This, as is well known, is the dazzling light emitted by
the electric spark when it shoots from clouds charged with electricity. In
the lower regions of the atmosphere the light is white, but in the higher
regions, where the air is more rarefied, it takes a violet tint ; as does the
spark of the electrical machine in a rarefied medium (787).

The flashes of lightning are often more than a mile, and sometimes,
extend to four or five miles, in length ; they generally pass through the
atmosphere in a zigzag direction — a phenomenon ascribed to the resistance
offered by the air condensed by the passage of a strong discharge. The
spark then diverges from a right line, and takes the direction of least resist-
ance. In a vacuum, electricity passes in a straight line.

De la Rue and Miiller have calculated that the potential required
to produce a flash a mile in length, would be that of 3,516,480 of their
cells (812).

We cannot, however, regard the length of a lightning flash as the direct
striking distance between two conductors. Owing to the number of droplets
met on its path the discharge is rather to be compared with that of the
luminous tubes and panes (789). The experiments of Alascart on the rela-
tion between the striking distance ijT]) and the potential required to pro-
duce it show that the striking distance increases far more rapidly than the
potential. Thus while the potential required for a striking distance of i cm.
is represented by 8-3 ; for 4 cm. it is 15-9 ; for 8 cm. 20-5 ; and for 15 cm.
23-3. From this it is possible that a lightning discharge is produced by a
difference of potentials between two clouds which is not out of proportion
w-ith those obtained by our electrical machines.

Several kinds of lightning flashes may be distinguished — i, the zigzag

I024 Meteorology. [997-

flashes, which move with extreme velocity in the form of a Hne of fire with
sharp outHnes, and which closely resemble the spark of an electrical machine.
The recent investigation of the shape of lightning discharges by means of
extra rapid photographic dry plates (6io) has shown that the path of a dis-
charge is not so sharply zigzag as is usually represented, but has more the
shape of the course of a river as shown on a map, and with frequent branch-
ings ; 2, the sheet flashes, which, instead of being linear, like the preceding,
fill the entire horizon without having any distinct shape. This kind, which
is most frequent, appears to be produced in the cloud itself, and to illuminate
the mass. According to Kundt, the number of sheet discharges are to the
zigzag discharged as 1 1 : 6 ; and from spectrum observations it would appear
that the former are brush discharges between clouds, while the latter are
true electrical discharges between the clouds and the earth. Another kind,
called heat lightni?ig, is ascribed to distant lightning flashes which are below
the horizon, but illuminate the higher strata of clouds so that their bright-
ness is visible at great distances ; they produce no sound, probably in con-
sequence of the fact of their being so far off that the rolling of thunder
cannot reach the ear of the observer. There is further the very unusual
phenomenon of globe lightning., or the flashes which appear in the form
of globes of fire. These, which are sometimes visible for as much as ten
seconds, descend from the clouds to the earth with such slowness that the
eye can follow them. They often rebound on reaching the ground ; at
other times they burst and explode with a noise like that of the report of
many cannon. No adequate explanation has been given of these, though
Plante with a large battery of his cells has imitated the phenomena.

The duration of the light of the first three kinds does not amount to the
millionth of a second, as was determined by Wheatstone by means of his
rotating wheel, which was turned so rapidly that the spokes were invisible ;
on illuminating it by the lightning flash, its duration was so short that
whatever the velocity of rotation of the wheel, it appeared quite stationary ;
that is, its displacement is not perceptible during the time the lightning exists.
The light produced by a lightning flash must be comparable to the sun
in brightness, though it does not appear to us brighter than ordinary moon-
light. Tkit considering its excessively brief duration, and that the full effect
of any light on the eye is only produced when its duration is at least the
tenth of a second, it follows that a landscape continuously illuminated by the
lightning flash would appear 100,000 times as bright as it actually appears
to us during the flash.

Here also may be mentioned the phenomenon known as St. Elmds fire.,
which occurs in a highly electrical state of the atmosphere when the clouds
arc low. It is a sort of brush discharge (787), appearing like small flames
issuing from prominent point-objects such as masts, tops of trees, lightning-
conductors ; it has also been observed on the points of helmets or lances,
alpenstocks ; it is of course most easily seen in the dark, and is accompanied
by a slight rustling noise. On the sea it is not uncommon in thunderstorms
on mastheads and yard-arms.

99S. Thunder. — Thunder is the violent report which succeeds liglUning in
stormy weather. The lightning and the thunder are practically simultaneous,
but an interval of several seconds is always observctl between these two

-999 j Ejfccts of Lightning. 1025

phenomena, which arises from the fact that sound only travels at the rate of
about 1,100 feet in a second (232), while the passage of light is almost instan-
taneous. Hence an observer will only hear the noise of thunder five or six
seconds, for instance, after the lightning, according as the distance of the
thunder-cloud is live or six times 1,100 feet. The noise of thunder arises
from the disturbance which the electric discharge produces in the air, and
which may_^be witnessed in Kinnersley's thermometer (fig. 729). Near the
place where the lightning strikes, the sound is sharp and of short duration.
At a greater distance a series of reports are heard in rapid succession. At a
still greater distance the noise, feeble at first, changes into a prolonged rolling
sound of varying intensity. If the lightning is at a greater distance than 14
or 15 miles it is no longer heard, for sound is more imperfectly propagated
through air than through solid bodies : hence there are lightning discharges
without thunder ; these occur at times when the sky is cloudless.

Some attribute the noise of the rolling of thunder to the reflection of
sound from the ground and from the clouds. Others have considered the
lightning not as a single discharge, but as a series of discharges, each of
which gives rise to a particular sound. But as these partial discharges
proceed from points at different distances, and from zones of unequal density,
it follows not only that they reach the ear of the observer successively, but
that they bring sounds of unequal density, which occasion the duration and
inequality of the rolling. The phenomenon has finally been ascribed to
the zigzags of lightning themselves, assuming that the air at each salient
angle is at its greatest compression, which would produce the unequal in-
tensity of the sound. The distance between the nearest point of a hghtning
flash IS obtained in kilometres if we multiply the time in seconds between
the lightning flash and the beginning of the thunder by 3.

999. Effects of lightning.— The lightning discharge is the electric
discliarge which strikes between a thunder-cloud and the ground. The latter,
by the induction from the electricity of the cloud, becomes charged with
contrary electricity ; and when the tendency of the two electricities to com-
bine exceeds the resistance of the air, the spark passes which is often ex-
pressed by saying that ' a thunderbolt has fallen.' Lightning in general
strikes from above, but ascending lightning is also sometimes observed ;
probably this is the case when the clouds being negatively the earth is posi-
tively electrified, for experiments show that at the ordinary pressure the
positive fluid passes through the atmosphere more easily than negative elec-
tricity.

From the first law of electrical attraction the discharge ought to fall first
on the nearest and best conducting objects, and, in fact, trees, elevated
buildings, metals, are particularly struck by the discharge. Hence it is im-
prudent to stand under trees during a thunderstorm.

The effects of lightning are very varied, and of the same kind as those
of batteries (783), but of far greater power. The lightning'' discharge kills
men and animals, ignites combustililes, melts metals, breaks bad con-
ductors in pieces. When it penetrates the ground it melts the silicious
substances on its path, and thus produces in the direction of the discharge
those remarkable vitrified tubes caWtid fulgurites, some of which are as much
as 12 yards in length ; in most cases there are found to be accumulations of

I026 Meteorology. [999-

water below such fuls,''urites. When it strikes bars of iron, it magnetises
them, and often inverts the poles of compass needles.

After the passage of lightning a highly peculiar odour is frequently
produced, like that perceived in a room in which an electrical machine
is being worked. This is due to the formation of ozone, a peculiar allotro-
pic modification of oxygen (793). An electrified cloud forms with the earth
below a condenser, the intervening mass of air being the dielectric. This
mass of air is therefore in a state of strain like the dielectric in a Leyden
jar, and it is to this state of strain which precedes the actual discharge, rather
than to the discharge itself, that is due the production of ozone.

Heated air conducts better than cold air, probably only owing to its
lesser density. Hence it is that large numbers of animals are often killed
by a single discharge, as they crowd together in a storm, and a column of
warm air rises from the gloom.

1000. Return shock. — This is a violent and sometimes fatal shock which
men and animals experience, even when at a great distance from the place
where the lightning discharge passes. It is caused by the inductive action
which the thunder-cloud exerts on bodies placed within the sphere of its
activity. These bodies are then, like the ground, charged with the opposite
electricity to that of the cloud ; but when the latter is discharged by the
recombination of its electricity with that of the ground, the induction ceases,
and the bodies reverting rapidly from the electrical state to the neutral state,
the concussion in question is produced— the return shock. A gradual de-
composition and reunion of the electricity produces no visible effects ; yet it
is alleged that such disturbances of the electrical equilibrium are perceived
by nervous persons.

The return shock is always less violent than the direct one ; there is no
instance of its having produced any inflammation, yet plenty of cases in
which it has killed both men and animals ; in such cases no broken limbs,
wounds, or burns are observed.

The return shock may be imitated by placing a gold-leaf electroscope
connected by a wire with the ground near an electrical machine ; when the
machine is worked, at each spark taken from the prime conductor the gold
leaves of the electroscope suddenly diverge.

It is stated that persons struck by lightning often lose their lives only
by a temporary injury to the nerves which control the act of respiration ; so
that under favourable circumstances such persons might probably be saved
by producing artificial respiration.

TOOL l,ig-litnIng--conductor.— This was invented by Franklin in 1755.

There are two principal parts in a lightning-conductor, the rod and the
conductor. The rod (fig. Q78) is a pointed bar of iron, preferably galvanised,
or of copper, P, fixed vertically to a tube or rod of iron, which, by moans of
a collar, a a, and tube .^r, is fitted on the roof of the edifice to be protected ;
it is from 6 to 10 feet in height, and its basal section is about 2 or 3 inches
in diameter. The conductor is best formed of a wire rope, C, such as are
used for rigging or for telegraph wires, attached to the rod by a metal collar,
b. The use of copper instead of iron wire in these conductors is recom-'
mended, inasmuch as copper is a better conductor than iron. The metallic
section of the conductor ought to be about half a square inch, and the

-1001] Liglitning-Conductor. 1027

individual wires 0-04 to o-o6 inch in diameter ; they ought to be twisted

in strands, hke an ordinary cord. The conductor is usually led into

a well, and to connect it better with the soil it ends in

two or three branches. If there is no well near, a hole

is dug in the soil to the depth of 6 or 7 yards, and the

foot of the conductor having been introduced, the hole

is filled with powdered coke, which conducts very well.

The best earth contact is obtained when it is possible to

connect the wire conductors with large iron gas or water cl

pipes.

The action of a lightning-conductor is an illustration of
the action of induction and of the property of points (731) ;
when a storm cloud positively electrified, for instance, forms
in the atmosphere, it acts inductively on the earth, repels
the positive and attracts the negative electricity, which accu-
mulates on bodies placed on the surface of the soil, the
more abundantly as these bodies are at a greater height.
The density is then greatest on the highest bodies, which
are therefore most exposed to the electric discharge ; but if
these bodies are provided with metal points, like the rods of
conductors, the negative electricity, withdrawn from the soil
by the influence of the cloud, flows into the atmosphere, and
neutralises the positive electricity of the cloud. Hence, not
only does a lightning-conductor tend to prevent the accumu-
lation of electricity on the surface of the earth, but it also
tends to restore the clouds to their natural state, both which
concur in preventing lightning discharges. This mode of
action of lightning-conductors is often overlooked ; it is stated in reference
to Pietermaritzburg that until lightning-conductors became common in that
town it was constantly visited by thunderstorms at certain seasons. They
come as frequently as ever, but cease to give flashes on reaching the town ;
they do so, however, when they have passed over it. The disengagement
of electricity is, however, sometimes so abundant that the lightning-conductor
is inadequate to discharge the electricity accumulated, and the lightning
strikes ; but the conductor receives the discharge, in consequence of its
greater conductivity, and the edifice is preserved.

A conductor, to be efficient, ought to satisfy the following conditions : —
(i.) the rod ought to be so large as not to be melted if the discharge passes ;
(ii.) it ought to terminate in a point, or in several points, to give readier issue to
the electricity disengaged by induction from the ground ; (iii.) the conductor
must be continuous from the point to the ground, and the connection between
the rod and the ground must be as intimate as possible ; this is the most
important of all, and the one point most frequently neglected in the older
arrangements. A lightning-conductor with load earth contact is not only
useless but dangerous. The continuity of the conductor may be tested by
means of a voltaic cell and a portable form of galvanometer, (iv.) If the
building which is provided with a lightning-conductor contains metallic
surfaces of any extent, such as zinc roofs, metal gutters, or ironwork, these
ought to be connected with the conductor, or, still better, have each a sepa-

3 u 2

:028

Meteofology.

[1001-

rate earth connection. If the last two conditions are not fulfilled, there is a
great danger of lateral discharges — that is to say, that the discharge takes
place between the conductor and the edifice, and then it increases the
danger.

Colladon concludes, from the observation of a series of lightning dis-
charges, that a tall tree, such qs a poplar, whose roots are in dry ground,
may act as a good lightning-conductor, if on the other side of the house
there does not happen to be a well or pool, towards which the electricity can
spring through the house.

I002. Rainbow. — The rainbow is a luminous phenomenon which appears
in the clouds opposite the sun when they are resolved into rain. It consists
of seven concentric arcs, presenting successively the colours of the solar
spectrum. Sometimes only a single bow is perceived, but there are usually
two : a lower one, the colours of which are very bright ; and an external or
seco?idary one, which is paler, and in which the order of the colours is re-
versed. In the interior rainbow the red is the highest colour ; in the other
rainbow the violet is. It is seldom that three bows are seen ; theoretically
a greater number may exist, but their colours become so faint that they cannot
be perceived.

The phenomenon of the rainbow is produced by decomposition of the
white light of the sun when it passes into the drops, and by its reflection
from their inside face. In fact, the same phenomenon is witnessed in dew-
drops and in jets of water — in short, wherever sunlight passes into drops
of water under a certain angife.

The appearance and the extent of the rainbow depend on the position of
the observer, and on the height of the sun above the horizon ; hence only
some of the rays refracted by the raindrops, and reflected in their concavity
to the eye of the spectator, are adapted to produce the phenomenon. Those
which do so are called effective rays.

To explain this let n (fig. 979) be a drop of water, into which a solar ray
S a penetrates. At a point of incidence, a, part of the light is reflected from

(he surface of the liquid ; another, entering it, is decomposed and traverses
the drop in the direction a b. Arrived at b, part of the light emerges from

-1003] Raijibozv. 1029

the raindrop, the other part is reflected from the concave surface, and tends
to emerge at^. At this point the hght is again partially reflected ; the re-
mainder emerges in a direction ^O, which forms with the incident ray, S a,
an angle called the angle of deviation. It is such rays as gO, proceeding
from the side next the observer, which produce on the retina the sensation
of colours, provided the light is sufficiently intense.

It csok be shown mathematically that in the case of a series of rays which
impinge on the same drop, and only undergo a reflection in the interior, the
angle of deviation increases from the ray S"//, for which it is zero, up to a
certain limit, beyond which it decreases, and that near this limit rays passing
parallel into a drop of rain also emerge parallel. From this parallelism a
beam of light is produced sufficiently intense to impress the retina ; these
are the rays which emerge parallel and are efficient.

As the ditfercnt colours which compose white light are unequally refran-
gible, the maximum angle of deviation is not the same for all. For red rays
the angle of deviation corresponding to the active rays is 42° 2', and for
violet rays it is 40° 17'. Hence, for all drops placed so that rays proceeding
from the sun to the drop make, with those proceeding from the drop to the
eye, an angle of 42° 2', this organ will receive the sensation of red light ;
this will be the case with all drops situated on the circumference of the
base of a cone, the summit of which is the spectator's eye ; the axis of
this cone is parallel to the sun's rays, and the angle formed by the two
opposed generating lines is 84° 4'. This explains the formation of the red
band in the rainbow ; the angle of the cone in the case of the violet band
is 80° 34'.

The cones corresponding to each band have a common axis called the
visual axis. As this right line is parallel to the rays of the sun, it follows
that when this axis is on the horizon, the visual axis is itself horizontal, and
the rainbow appears as a semicircle. If the sun rises, the visual axis sinks,
and with it the rainbow. Lastly, when the sun is at a height of 42° 2', the
arc disappears entirely below the horizon. Hence the phenomenon of the
rainbow never takes place except in the morning and evening.

What has been said refers to the interior arc. The secondary bow is
formed by rays which have undergone two reflections, as shown by the ray
^'idfeO, in the drop p. The angle STO formed by the emergent and
incident rays is called the angle of deviation. The angle is no longer suscep-
tible of a maximum, but of a minimum, which varies for each kind of rays,
and to which also efficient rays correspond. It is calculated that the mini-
mum angle from violet rays is 54° 7', and for red rays only 50° 57'; hence it
is that the red bow is here on the inside, and the violet arc on the outside.
There is a loss of light for every internal reflection in the drop of rain, and
therefore the colours of the secondary bow are always feebler than those of
the internal one. The secondary bow ceases to be visible when the sun is
54° above the horizon.

The moon sometimes produces rainbows like the sun, but they are veiy
pale.

1003. Aurora borealis. — The aurora borealis^ or northern light, or more
Y^xo'^&xXy polar aurora^ is a remarkable luminous phenomenon which is fre-
quently seen in the atmosphere at the two terrestrial poles. The following

1030 Meteorology. [1003-

is a description of an aurora borealis observed at Bossekop, in Lapland, lat.
70°, in the winter of 1838-39 : —

In the evening, between 4 and 8 o'clock, the upper part of the fog which
usually prevails to the north of Bossekop became coloured. This light
became more regular, and formed an indistinct arc of a pale yellow, with its
concave side turned towards the earth, while its summit was in the magnetic
meridian.

Blackish rays soon separated the luminous parts of the arc. Luminous
rays formed, becoming alternately rapidly and slowly longer and shorter,
their lustre suddenly increasing and diminishing. The bottom of these rays
always showed the brightest light, and formed a more or less regular arc.
The length of the rays was very variable, but they always converged towards
the same point of the horizon, which was in the prolongation of the north
end of the dipping-needle ; sometimes the rays were prolonged as far as
their point of meeting, and thus appeared like a fragment of an immense
cupola.

The arc continued to rise in an undulatory motion towards the zenith.
Sometimes one of its feet or even both left the horizon ; the folds became
more distinct and more numerous ; the arc was now nothing more than a
long band of rays convoluted in very graceful shapes, forming what is called
the boreal crown. The lustre of the rays varied suddenly in intensity, and
attained that of stars of the first magnitude ; the rays darted with rapidity,
the curves formed and re-formed like the folds of a serpent, or like a flag
moved by the wind (fig. 9S0), the base was red, the middle green, while the

Fig. 980.

remainder retained its bright yellow colour. Lastly, the lustre diminished,
the colours disappeared ; everything became feebler or suddenly went out.

Plate III. represents a very beautiful aurora observed by Lemstrom on
tlie north coast of Norway. The work of this author {IjAurorc Bor^ale^
(iauthicr Villars, Paris) is a storehouse of information on this subject.

-1003] Aurora Borealis. 103 1

A French scientific commission to the North observed 150 auror^e
boreales in 200 days ; it appears that at the poles, nights without an aurora
boreahs are quite exceptional, so that it may be assumed that they take place
every night, though with varying intensity. They are visible at a consider-
able distance from the poles, and over an immense area. Sometimes the same
aurora borealis has been seen at the same time at places so widely apart as
Moscow, Warsaw, Rome, and Cadiz. It seems difficult to assign a higher
limit for the occurrence of the aurora ; this is probably lower than has gene-
rally been stated. Lemstrom holds that from 22 to 44 miles is a close
approximation to the truth ; and it may be regarded as certain that even in
more southern latitudes the aurora is often seen much lower — at a height of
two or three miles, for instance. In polar countries certain forms of aurora,
more especially those of weak flames, are seen to proceed from the ground
on the tops of certain mountains. They are most frequent at the equinoxes,
and least so at the solstices. The number differs in different years, attain-
ing a maximum every 11 years at the same time as the sun-spots, and
like these a minimum which is about 5 or 6 years from the maximum.
The years 1844, 1855, i860, and 1877 are poor in the appearance of the
aurora.

There is, moreover, a period of about 60 years ; for the years 1728, 1780,
and 1842 have been remarkable for the prevalence of the aurora. The last
two periods are also remarkable for the occurrence of disturbances in the
earth's magnetism.

Numerous hypotheses have been devised to account for the aurorse
boreales. As they share the rotation of the earth, they must have an atmo-
spheric origin. Their direction, which is always parallel to that of the dipping
needle, and their action on the magnetic needle (702), seem, however, to
prove that they ought to be attributed to electric currents in the higher
regions of the atmosphere. In high latitudes the aurora borealis acts power-
fully on the wires of the electric telegraph ; the alarums are for a long time
violently rung, and telegraphic messages frequently interrupted by the
spontaneous abnormal working of the apparatus. In the lower discharges
a crackling sound has been heard, and during balloon ascents a strong
smell of ozone has been perceived when the balloon was among the luminous
rays.

The spectrum of the aurora borealis has been found to consist of several
lines in the green, and of an indistinct line in the blue ; to which must be
added a red line due to the red protuberances ; these lines are the same as
those of nitrogen, greatly rarefied and at a low temperature ; one line be-
tween the green and the yellow, and called the yellow line, is so charac-
teristic of the aurora that it is visible even when the eye can discern no other
trace of this light.

De la Rive held that auroras boreales were due to electric discharges
■which take place in polar regions between the positive electricity of the
atmosphere and the negative electricity of the earth. The positively elec-
trified aqueous vapours are supposed to be carried by the equatorial current
in the higher regions of the atmosphere to the poles, where the neutralisa-
tion takes place. These discharges produce luminous appearances of the
same kind as are observed in Geissler's tubes ; and De la Rive showed by

I032 Meteorology. [1003-

means of an apparatus specially devised for the purpose (fig. 917) that the
forms of the luminous phenomena are in accordance with this theory.

By direct experiments Lemstrom has been able to imitate and reproduce
a peculiar form of aurora observed in winter as a flame-like appearance on
the tops of two mountains 800 and 1,100 metres in height, and to show
that it is of electrical origin. He erected on the summit of a hill a system
of Dointcd rods extending over a surface of nearly 4,000 square feet ; each
rod was carefully insulated from the earth by means of a Mascart's insulator
ffig. 67o\ but was connected with the rest, and an insulated wire led down
from this system into the valley where it Avas connected with one ter-
minal of a galvanometer, the other being put to earth. The existence of
a positive current from the air to the earth was observed, and at the same
time yellowish-white columns of light, reaching to a height of 120 metres,
were observed to issue from the points. Observed Avith the spectroscope
it gave the characteristic lines between D and E.

The recent investigations of Exner relative to the fall of atmospheric
electrical potential lend a further support to the view that the aurora is due
to electricity. In the polar regions the fall of potential is 13 times greater
in summer, and 18 times o-reater in winter than at the equator. Hence an
electrical phenomenon which depends on the magnitude of this fall of
potential mu/t be more intense in winter and in high latitudes, than in
summer and in the torrid zones.

The occurrence of irregular currents of electricity which manifest them-
selves by abnormal disturbances of telegraphic communications is not in-
frequent : such currents have received the name of earth currents. Sabine
found that these magnetic disturbances are due to a peculiar action of
the sun, and probably independently of its radiant heat and light. It has
also been ascertained that the aurora borealis as well as earth currents in-
variably -^iccompanies these magnetic disturbances. According to the late
Balfour Stewart, aurora; and earth currents are to be regarded as secondary
currents due to small but rapid chansjes in the earth's magnetism : he likened
the body of the earth to the magnetic core of a Ruhmkoi-fif's machine (905) ;
the lower strata of the atmosphere forming the insulator, while the upper
and rarer, and therefore electrically conducting strata, may be considered
as the secondaiy coil.

On this analoev the sun may perhaps be likened to the primary current
which performs the part of producing changes in the magnetic state of the
core. Now in Ruhmkorff's machine the energy of the secondary current is
derived from that of the priman' current. Thus, if the analogy be correct,
the energy of the aurora borealis may in like manner come from the sun ;
but until we know more of the connection between the sun and terrestrial
magnetism, these ideas are to be accepted with some reserve.

S . J /! * 3 ji = _- » ^'1 r, t

-1005] . Climate. 1033

CLIMATOLOGY.

1004. Mean temperature. — The inciui daily teviperatiire., or simply tem-
pcra/ufc, is that obtained by adding together 24 hourly observations, and
dividing by 24. A very close approximation to the mean temperature is
obtained by taking the mean of the highest and lowest temperatures of the
day and of tne night, which are determined by means of the maximum and
minimum thermometers. These ought to be protected from the sun's rays,
to be raised above the ground, and far from all objects which might influence
them by their radiation.

The temperature of a month is the mean of those of 30 days, and the
temperature of the year is the mean of those of 12 months. Finally, the
temperature of a place is the mean of its annual temperature for a great
sei'ies of years. The mean temperature of London is 8 -28° C, or 46 -9° F.
The temperatures in all cases are those of the air, and not those of the
ground.

1005. Causes whicli modify the temperature of the air. — The principal
causes which modify the temperature of the air are the latitude of a place, its
height, the direction of the winds, and proximity of seas.

Influence of the latitude. — The influence of the latitude arises from the
greater or less obliquity of the solar rays, for as the quantity of heat absorbed
is greater the more perpendicular are the rays (414), the heat absorbed de-
creases from the equator to the poles, for the rays are then more oblique.
This loss is, however, in summer, in the temperate and arctic zones, partially
compensated by the length of the days. Under the equator, where the
length of the days is constant, the temperature is almost invariable ; in the
latitude of London, and in more northerly countries, where the days are
very unequal, the temperature varies greatly ; but in summer it sometimes
rises almost as high as under the equator. The lowering of the temperature
produced by the latitude is small : thus, in a latitude 1 1 5 miles north of
France, the temperature is only 1° C. lower.

hiflitence of height. — The height of a place has a much more consider-
able influence on the temperature than its latitude. In the temperate
zone a diminution of i^ C. corresponds in the mean to an ascent of 180
yards.

The cooling on ascending in the atmosphere has been observed in
balloon ascents, and a proof of it has been seen in the perpetual snows
which cover the highest mountains. It is due in part to the greater rarefac-
tion of the air, which necessarily diminishes its absorbing power ; besides
which the air is at a greater distance from the ground, which heats it by
contact ; and finally, dry air is very diathermanous.

The law of the diminution of temperature corresponding to greater
heights in the atmosphere has not been made out, in consequence of the
numerous disturbing causes which modify it, such as the prevalent winds,
the hygrometric state, the time of day, the season of the year, &c. The
difference between the temperatures of two places at unequal heights is not
proportional to the difference of level, but for moderate heights an approxi-
mation to the law may be made. As the mean of a series of very careful

I034 Meteorology. [1005-

observations made during balloon ascents, a diminution of i° C. corresponded
to an increase in height of 232 yards.

It will thus be seen that at a certain height above the ground, there must
be a surface or layer where the temperature is uniformly zero. The height
of this isothermal surface (1007) will vary materially with the time of the year,
being lower in the cold months ; it varies also with the time of day, rising
rapidly about mid-day. In summer this height may be taken at from 3,400
to 3,700 metres above the sea-level.

Directio7t of winds. — As winds share the temperature of the countries
which they have traversed, their direction exercises great influence on the
air in any place. In Paris, the hottest winds are the south ; then come the
south-east, the south-west, the west, the east, the north-west, north, and,
lastly, the north-east, which is the coldest. The character of the wind
changes with the seasons ; the east wind, which is cold in winter, is warm in
summer.

Proximity of the sea. — The neighbourhood of the sea tends to raise the
temperature of the air, and to render it uniform. The average temperature
of the sea in equatorial and polar countries is always higher than that of the
atmosphere. With reference to the uniformity of the temperature, it has
been found that in temperate regions— that is, from 25° to 50° of latitude —
the difference between the highest and lowest temperature of a day does not
exceed, on the sea, 2° to 3° ; while upon the Continent this amounts to from
12° to 15°.. In islands the uniformity of temperature is very perceptible, even
during the greatest heats. In continents, on the contrary, the winters for
the same latitudes become colder, and the difference between the tempera-
ture of summer and winter becomes greater.

1006. Gulf Stream. — A similar influence to that of the winds is exerted
by currents of warm water. To one of these, the Gulf Stream, the mildness
of the climate in the north-west of Europe is mainly due. This great body
of water, taking its origin in equatorial regions, flows through the Gulf of
Mexico, whence it derives its name ; passing by the southern shores of
North America, it makes its way in a north-westerly direction across the
Atlantic, and finally washes the coast of Ireland and the north-west of Europe
generally. Its temperature in the Gulf is about 28° C. ; and it is usually a
little more than 5° C. higher than the rest of the ocean on which it floats,
owing to its lower specific gravity. To its influence is due the milder climate
of West Europe as comj^ared with that of the opposite coast of America ; thus
the river Hudson, in the latitude of Rome, is frozen over three months in the
year. It also causes the polar regions to be separated from the coasts of
Europe by a girdle of open sea ; and thus the harbour of Hammerfest is
open the year round. Besides its influence in thus moderating cHmate, the
Gulf Stream is an important help to navigators.

1007. Isothermal lines When on a map all the points whose tempera-
ture is known to be the same are joined, curves are obtained which Hum-
Ijoldt first noticed, and which he called isothermal lines. If the temperature .
of a place only varied with the obliquity of the sun's rays— that is, with the
latitude— isothermal lines would all be parallel to the equator ; but as the
temperature is influenced by many local causes, especially by the height, the
isothermal lines are always more or less curved. On the sea, however, they

-1009J Distribution of Temperature. 1035

are almost parallel. Maps 4, 5, and 6 represent these lines for the Year,
for January and for July.

A distinction is made between isothermal lines, isotheral lines, and isO'
cJiime7ial lines, where the ineati general, the meafi summer, and the mean
winter temperatures are respectively constant. An isothermal zotie is the
space comprised between two isothermal lines. Kupfifer also distinguishes
isogeothermic lines where the mean temperature of the soil is constant.

1008. Climate. — By the climate of a place is understood the whole of the
meteorological conditions to which a place is subjected ; its mean annual
temperature, summer and winter temperatures, and the extremes within
which these are comprised. Some writers distinguish seven classes of
climates, according to their mean annual temperature : a hot climate from
30° to 25° C. ; a inarm climate from 25° to 20° C. ; a mild climate from 20°
to 15° C. ; a temperate climate from 15*^ to 10° C. ; a cold climate from 10° to
5° C. ; a very cold climate from 5° to zero C. ; and an arctic climate Avhere
the temperature is below zero.

Those climates, again, are classed as constant climates, where the dif-
ference between the mean and summer and winter temperature does not
exceed 6° to 8° ; variable climates, where the difference amounts to from
16° to 20° ; and extreme climates, where the difference is greater than 30°.
The climates of Paris and London are variable ; those of Pekin and New
York are extreme. Island climates are generally little variable, as the
temperature of the sea is constant ; and hence the distinction between land
and sea climates. Marine climates arc characterised by the fact that the
difference between the temperature of summer and winter is always less
than in the case of continental climates. But the temperature is by no
means the only character which influences climates ; there are, in addition,
the moisture of the air, the quantity and frequency of the rains, the number
of storms, the direction and intensity of the winds, and the nature of the
soil.

1009. Distribution of temperature on the surface of tbe ^lobe. — The
temperature of the air on the surface of the globe decreases from the equator
to the poles ; but it is subject to perturbing causes so numerous and so
purely local, that its decrease cannot be expressed by any law. It has
hitherto not been possible to do more than obtain by numerous observations
the mean temperature of each place, or the maximum and minimum tempera-
tures. The following table gives a general idea of the distribution of heat in
the Northern Hemisphere : —

Mean temperature at diffcrc/it latitudes.

Abyssinia

. 31-0° c.

Cairo .

. 22-4=

Calcutta.

. 28-5

Constantine

. 17-2

Jamaica.

. 26-1

Naples .

. . 167

Senegal .

. 24-6

Mexico.

. i6-6

Rio de Janeiro

. 23-1

Marseilles

. 14-1

Constantinople

. 137

London

. . 8-3

Pekin .

. 127

Stockholm

. . 5-6

Paris .

. IO-8

Moscow

• 5-6

1036 Meteorology. [1009-

Brussels . . . io-2° C. St. Petersburg . . 3-5° C.

Strasburg . . .9-8 St. Gothard . . . -ro

Geneva . . . -97 Greenland . . • -77

Boston .... 9-3 Melville Island . . -187

These are mean yearly temperatures. The highest temperature which
has been observed on the surface of the globe is 47*4° at Esne, in Egypt,
and the lov^^est is —75° in the Arctic Expedition of 1876; which gives a
difference of 122° between the extreme temperatures observed on the surface
of the globe.

The highest temperature observed at Paris was 38-4° on July 8, 1793,
and the lowest —23-5° on December 26, 1798. The highest observed at
Greenwich was 35° C. in 1808, and the lowest -20° C. in 1838.

No arctic voyagers have succeeded in reaching the poles, in consequence
of these seas being completely frozen, and hence the temperature is not
known. In our hemisphere the existence of a single glacial pole — that is, a
place where there was the maximum cold — has been long assumed. But
the bendings which the isothermal linespresent in the Northern Hemisphere
have shown that in this hemisphere there are two cold poles — one in Asia,
to the north of Gulf Taymour ; and the other in America, north of Barrow's
Straits, about 15° from the earth's north pole. The mean temperature of
the first of these poles has been estimated at — 17°, and that of the second
at — 19°. With respect to the austral hemispheres, the observations are
not sufficiently numerous to tell whether there are one or two poles of
greatest cold, or to determine their position.

loio. Temperature of lakes, seas, and sprlngrs. — In the tropics the
temperature of the sea is generally the same as that of the air ; in polar
regions the sea is always warmer than the atmosphere.

The temperature of the sea under the torrid zone is always about 26° to
27° at the surface : it diminishes as the depth increases, and in temperate
as well as in tropical regions the temperature of the sea at great depths is
between 2-5° and 3*5°. The temperature of the lower layers is caused by
submarine currents which carry the cold water of the polar seas towards the
equator.

The variations in the temperature of lakes are more considerable ; their
surface, which becomes frozen in winter, may become heated to 20° or 25° in
summer. The temperature of the bottom, on the contrary, is virtually 4°,
which is that of the maximum density of water.

Springs, which arise from rain water which has penetrated into the crust
of the globe to a greater or less depth, necessarily tend to assume the tempe-
rature of the terrestrial layers which they traverse. Hence, when they reach
the surface their temperature deperrds on the depth which they have attained.
If this depth is. that of the layer of invariable temperature, the springs ha\-e
a temperature of 10° or 1 1° in this country, for this is the temperature of this
layer, or about the mean annual temperature. If the sjirings are not very
copious, their temperature is raised in summer and cooled in winter by that.-
of the layers which they traverse in passing from the invariable layer to the
surface. But if they come from below the layer o( inxariable temperature
their temperature may considerably exceed t}ie n\ean temperature of the

-1011]

Distribution of Land and Water. 1037

The following list gives

place, and they are then called thermal springs.
the temperature of some of them : —

Wildbad ....... 37-5° C.

Vichy . . . . . . .40

Bath . . . . . . .46

Ems . . . . . . .46

Baden-Baden ...... 67-5

Chaudes-Aigues . . . . . ,88

Trincheras . . . . . . -67

Great C^eyser, in Iceland, at a depth of 66 feet. . . 124

From their high temperature they have the property of dissolving many
mineral substances which they traverse in their passage, and hence form
mineral zvatcrs. The temperature of mineral waters is not modified in
g-eneral by the abundance of rain or of dryness ; but it is by earthquakes,
after which they have sometimes been found to rise and at others to sink.

loil. Distribution of land and water. — The distribution of water on
the surface of the earth exercises great influence on climate. The area
covered by water is considerably greater than that of the dry land ; and the
distribution is unequal in the two hemispheres. The entire surface of the
globe occupies about 200 millions of square miles, nearly three-fourths of
which are covered by water ; that is, the extent of the water is nearly three
times as great as that of the land. The surface of the sea in the Southern
Hemisphere is to that in the Northern in about the ratio of 13 to 9.

The depth of the open sea is very variable ; the lead generally reaches
the bottom at about 300 to 450 yards ; in the ocean it is often 1,300 yards,
and instances are known in which a bottom has not been reached at a depth
of 4,500. It has been computed that the total mass of the water does not
-exceed that of a liquid layer surrounding the earth with a depth of about
1,100 yards.

PROBLEMS AND EXAMPLES
IN PHYSICS.

I. EQUILIBRIUM.

1. A body being placed successively in the two pans of a balance, requires i8o-
grammes to hold it in equilibrium in one pan, and i8i grammes in the other; required
the weight of the body to a milligramme.

From the formula x= s/p p, we have

X = -\/i8o X iSi = 1808', 499.

2. What resistance does a nut offer when placed in a pair of nutcrackers at a
distance of 4 of an inch from the joint, if a pressure of 5 pounds applied at a distance
of 4 inches from the joint is just sufficient to crack it? Ans. 26^ pounds.

3. What force is required to raise a cask weighing 6 cwt. into a cart o'S metre
high along a ladder 275 metres in length ? Ans. 195A pounds.

4. If a horse can move 30 cwt. along a level road, what can it move along a road
the inchnation of which is i in 80, the coefficient of friction on each road being ^ ?

Ans. 265 cwt.

5. The piston of a force-pump has a diameter of 8 centimetres, and the arms of
the lever by which it is worked are respectively 12 and 96 centimetres in length ; what
force must be exerted at the longer arm if a pressure of 12-36 pounds on a square cen-
timetre is to be applied? Ans. 77*69 pounds.

II. GRAVITATION.

6. A stone is thrown from a balloon with a velocity of 50 metres in a second. How
soon will the velocity amount to 99 metres in a second, and through what distance
will the stone have fallen ?

To find the time requisite for the body to have acquired the velocity of 99 metres in
a second, we have

V = V -^ gt;
in which V is the initial velocity, g the acceleration of gravity, which, with sufficient
approximation, is equal to 9'8 metres in a second, and / the time. Substituting these
values, we have

/ = 99 -is ^49^ 5 seconds.
9-8 9-8

For the space traversed we have

s = Vt -^ i^/2 _ ^o X 5 + 4-9 X 25 =372-5 metres.

7. A projectile was thrown vertically upwards to a height of 5io'"'22. Disregard-
ing the resistance of the air, what was the initial velocity of the body ?

The velocity is the same as that which the body would have acquired on falling
from a height of 510-22 metres.

From the formula v = \/2gs we get

V = ^/2 X 98 X 5io'22 = \/ioooo = 100 metres,

8. A stone is thrown vertically upwards with an initial velocity of 100 metres.
After what time would it return to its original position.

1 040 Problems and Examples in Physics.

The time of rising and falling is the same, but the time of falling is - (from the

formula v=gt) or — =io"2, which is half the time required ; therefore ^=20'4 sec.
9-8

9. A stone is thrown vertically upwards with an initial velocity of 100 metres ; after
X seconds a second stone is thrown with the same velocity. The second stone is rising
87 seconds before it meets the first. What interval separated the throws?

The rising stone will have the velocity v = V — gt, whence v = 100 — 9"8 x S'/.
On the other hand, the falling stone, at the moment the stones meet, will have the velocity
given by the equation v = gt' in which t' is the time during which the stone falls

before it meets the second one. This time is equal to 87 seconds + x — ^~. Hence

9'8
its velocity is ^ ^^^v

, = ,.8(8,.,--).

Equating the two values of v and reducing, we obtain x = ■^ seconds.

10. A body moving with a uniformly accelerated motion traverses a space of 1000
metres in 10 seconds. What would be the space traversed during the eighteenth
second if the motion continued in the same manner ?

The formula J = ^ ^g^/ 2 gjyes for the accelerating force ^ = 20 metres per second.
The space traversed during the eighteenth second will be equal to the difference of
the space traversed in 18 seconds and that traversed at the end of the seventeenth.

20 X 18^ 20 X 17^
^ _ ^u _ J./ _ ^^^ metres.

2 2

11. A cannon-ball has been shot vertically upwards with a velocity of 250 metres in
a second. After what interval of time would its velocity have been reduced to 54 metres
under the retarding influence of gravity, and what space would have been traversed by
the ball at the end of this time ?

If t be the time, then at the end of each second the initial velocity would be dimi-
nished by 9™ -8. Hence we shall have

54 = 250 — ^ X 9'8, whence t =■ 10 seconds ;

and for the space traversed

q"8 X 20-
= 250 X 20 — ■'- = 3040 metres.

12. Required the time in which a body would fall through a height of 2000 metres,
■neglecting the resistance of the air.

From s = \ gt- and substituting the values, we ha\-e

9-8

t~, whence t = 2o'2 seconds.

13. A body falls in air from a height of 4000 metres. Required the time of its fall
and its velocity when it strikes the ground.

From the formula j = ^gfi we have for the time / = / ^ ; and, on the other

V g

hand, from the formula for velocity v = gt we have / = =~ =20*4.

g 98

Hence ^ = /— , from which y = Vs -f^, and substituting the values for 5 and
g ^ g
g, V = 280 metres.

14. A stone is thrown into a pit 150 metres deep and reaches the bottom in 4
■ conds. With what velocity was it thrown, and what velocity had it acquired on

r'-aching the ground? Ans. The stone was thrown with a velocity of ly-g, and on
reaching the ground had acquired the velocity S7'i.

15. A stone is thrown downwards from a height of 150 metres with a velocity of 10
metres per second. How long will it require to fall ?

The distance through which the stone falls is cciual to the sum of the distances

Gravitation. 104 1

through which it would fall in virtue of its initial impulse and of that which it would

traverse under the influence of gravity alone ; that is, 150 = 10 ^ + ^^ ^ .

2
Taking the positive value only we get t = 4-61 seconds.

16. How far will a heavy body fall in vacuo during the time in which its velocity
increases from 40"25 feet per second to 88"55 feet per second ?

A /IS. Taking the value of ^ at 32-2 feet, the body falls through 96-6 feet.

17. Required the time of oscillation of a single pendulum whose length is o"9938,
and in a place where the intensity of gravity is g'Si.

From the general formula/" = w / , in which / expresses the time of one

oscillation, /the length of the pendulum, and ^ the intensity of gravity, we have

/ = 3-1416 /°^^ = I second.
V 9-81

18. Wliat is the intensity of gravity in a place in which the length of the seconds
pendulum is o™'99i ?

In this case/ = n / ,; and also / = n /^ I and therefore ^' = I , from
which g' = ?—. Substituting in this latter equation the values of g' , I and /', we
have ^' = 9™ 782.

19. In a place at which the length of the seconds pendulum is 0-99384, it is required
to know the length of a pendulum which makes one oscillation in 5 seconds.

In the present case, as g remains the same in the general formula, and t varies, the
length / must vary also. We shall have, then,

V ^ • ^s/ §>

from which, reducing and introducing the values, we have
/' = 52 X 0-99384 = 24-846.

20. A pendulum, the length of which is i"-9S, makes 61,682 oscillations in a day.
Required the length of the seconds pendulum. Atis. 0-99385 metre.

21. A pendulum clock loses 5 seconds in a day. By how much must it be
shortened to keep correct time }

Let s = the number of seconds in one day, and s' the number indicated by the
clock, then s : s' = n : n' = f- 1= s/ 1' ■ sj I .'. 86400: 86395=1 : \i^xx.-.x=-ggg8S^43.
Hence i — ^^ = 0-0001157 Ans.

22. What is the normal acceleration of a body which traverses a circle of 4-2
metres diameter with a rectangular velocity of 3 metres ? Ans. 4-286 metres.

23. An iron ball falls from a height of 68 cm. on a horizontal iron plate, and
rebounds to a height of 27 cm. Required the coefficient of elasticity of the iron.

If an imperfectly elastic ball with the velocity v strikes against a plate, it rebounds
with the velocity v, = — kv, from which, disregarding the sign, k = -'. Now we

have the velocity f, = Vz g/i, and v = oj 2 g/i, horn which A =Y"'- Suhstitut-
ing the corresponding values, we get i — 0-63.

24. Two inelastic bodies, weighing respectively 100 and 200 pounds, strike against
each other with velocities of 50 and 20 feet ; what is their common velocity, after the
impact? Ans. 30, or 3-3, according as they move in the same or in opposite directions
before impact.

3.x

1042 Problems and Examples in Physics.

III. ON LIQUIDS AND GASES.

25. The force with which a hydraulic press is worked is 20 pounds ; the arm of the
lever on which this force acts is 5 times as long as that of the resistance ; lastly, the
area of the large piston is 70 times that of the smaller one. Required the pressure
transmitted to the large piston.

If F be the power, and p the pressure transmitted to the smaller piston, we have
from the principle of the lever/ x i = /^ x 5. Moreover, from the principle of the
equality of pressure

jPxi=/x7o = 5X2ox7o = 7000 pounds.

26. Tlie force with which a hydraulic press is worked being 30 kilos, and the arm
of the lever by which this force is applied being 10 times as long as that of the resist-
ance, and the diameter of the small piston being two centimetres ; find the diameter of
the large piston, in order that a pressure of 2000 kilos, may be produced.

Ans. 5 "164 centimetres.

27. One of the limbs of a U-shaped glass tube contains mercury, to a height of
om-jy^ ; the other contains a different liquid to a height of o™'42 ; the two columns-
being in equilibrium, required the density of the second liquid with reference to mer-
cury and to water.

If d is the density of the liquid as compared with mercury, and d^ the density com-
pared with water, then i x 0-175 = 0-42 x d; and 13-6 x o'i75 = 0-42 x d/,
whence d = o'4i6 and d^ = 5 '66.

28. What force would be necessary to support a cubic decimetre of platinum in
mercury at zero ? Density of mercury i3'6 and that of platinum 21 '5.

From the formula P = VD the weight of a cubic decimetre of platinum is
I X 21-5 = 2i''-5 and that of a cubic decimetre of mercury is i x 13-6 = i3'''6.
From the principle of Archimedes, the immersed platinum loses part of its weight
equal to that of the mercury which it displaces. Its weight in tlie liquid is therefore
21 "5 — i3'6 = 7 '9. and this represents the force required.

29. Given a body ^ which weighs 7'S5 grammes in air, 5-17 gr. in water, and
5-35 gr. in another liquid, B ; required from these data the density of the body A and
that of the liquid B.

The weight of the body A loses in water 7-55 — 5'i7 = 2-38 grammes ; this repre-
sents the weight of the displaced water. In the liquid B it loses 7-55 - 6-35 = 1-2 gr. ;
this is the weight of the same volume of the body B, as that of A and of the displaced
water. The specific gravity of A is therefore

755 _ 0-172, and that of 5 " = 0-504.
238 ^ ' 238 ^ ^

30. A cube of lead, the side of which is 4 cm., is to be supported in water by
being suspended to a sphere of cork. What must be the diameter of the latter, the
specific gravity of cork being 0-24, and that of lead 11 "35 ?

The volume of the lead is 64 cubic centimetres ; its weiglit in air is therefore
64 X 1 1 '35, and its weight in water 64 x 11-35 — 64 = 662-4 gr.

If r be the radius of the sphere in centimetres, its volume in cubic centimetres will

be '^ '^ - , and its weight in grammes is '^-~ ><_o24 j^r^^^, ^.^^ jj^^ weight of the

3 3

displaced water is obviously '^ -n r^ in grammes, there will be an upward buoyancy

3
represented by4'^'^_4T'^x 0-24 ^ 4 "^ ';' x 0-76 ^^,^;^.,^ ^^^^^^ ^^ ^^^^^ ^^ ^,^^

3 3

11-85.

iight of thclead ; that is, 4" ^_S 7^ = 662-5, from which r = 5''™-925 and the

Oil Liquids and Gases. 1043

31. A cylindrical steel magnet 15 cm. in length and i'2 mm. in diameter, is loaded
at one end with a cylinder of platinum of the same diameter and of such a length that
when the solid thus formed is in mercury, the free end of the steel projects 10 mm.
above the surface. Required the length of this platinum, specific gravity of steel
being 7-8 and of platinum 21-5.

The weight of the steel in grammes will be 15 w r- x 7'8 and of the platinum
r r2 X 21-5.

These are together equal to the weight of the displaced mercury, which is
T r^ (14 + x) iy6, from which x = 9-29 cm.

32. A cylindrical silver wire o«»-ooi5 in diameter weighs 3"2875 grammes ; it is to
be covered w^th a layer of gold o"'ooo2 in thickness. Required the weight of the gold,
the specific gravity of silver being io"47 ^"^ ^^^^ ^^ Sol*^ i9'26.

If r is the radius of the silver wire and H its radius when covered with gold, then
r = 0= '075 and y? = o"=09S. The volume of the silver wire will be ^ r^ I and its
weight n r^ I io'47, from which / = i7«768.

The volume of the layer of gold is

IT (/?2 _ ^2) 17768,

and its weight

■K (o'0952 — o'075-) X 17768 X i9'26 = 3'656 nearly.

33. A kilogramme of copper is to be drawn into wire having a diameter of o"i6
centimetre. What length will it yield ? Specific gravity of copper 8-88.

The wire produced represents a cylinder / cm. in length, the weight of which is
T r^ /8"88, and this is equal to 1000 grammes. Hence / = 56™'oo85.

34. The specific gravity of cast copper being 879, and that of copper wire being
8 '88, what change of volume does a kilogramme of cast copper undergo in being

drawn into wire? Ans. __ —

86617

35. Determine the volumes of two liquids, the densities of which are respectively
1-3 and 07, and which produce a mi.\ture of three volumes having the density 0-9.

If .r and y be the volumes, then from P = VD, i'3:r + o7_>' = 3 x 09 and
a: + J = 3, from which * = i and y = i.

36. The specific gravity of zinc being 7 and that of copper 9, what weight of each
metal must be taken to form 50 grammes of an alloy ha\ing the specific gravity 8*2, it
being assumed that the volume of the alloy is exactly the sum of the alloyed metals ?

Let X = the weight of the zinc, and y that of the copper, then x + y = ^o, and

p
from the formula P = VD, which gives ^ = ^. the volumes of the two metals and of

the alloy are respectively _+-'' = ^° . From these two equations we get x = 17-07

and J = 32 •93.

37. A platinum sphere 3 cm. in diameter is suspended to the beam of a very ac-
curate balance, and is completely immersed in mercury. It is exactly counterbalanced
by a copper cylinder of the same diameter completely immersed in water. Required
the height of the cylinder. Specific gravity of mercury 13-6, of copper 8-8, and of
platinum 21-5. Atis. 2-025 centimetres.

38. To balance an ingot of platinum 27 grammes of brass are placed in the other
pan of the balance. What weight would have been necessary if the weighing had been
effected in vacuo? The density of platinum is 21-5, that of brass 8-3, and air under
a pressure of 760 mm. and at the temperature 0° has — the density of water.

The weight of brass in air is not 27 grammes, but this weight minus the weight of
a volume of air equal to its own.

Since P = VD .■ . V = and the weight of the air is - - = ?? .

D Z) X 770 8-3 X 770

By similar considerations, if x is the weight of platinum in vacuo, its weight in air

3x2

1 044 Problems and Examples in Phy.

will be X minus the weight of air displaced, that is ^ — , and this weight

21-5 X 770

is equal to that of the true weight of the brass ; and we have

X — — — 2j — ?Z ; from which x = 26 •996.

21-5 X 770 8-3 X 770

39. A body loses in carbonic acid 1-15 gr. of its weight. What woiJd be its loss
of weight in air and in hydrogen respectively?

Since a litre of air at 0° and 760 mm. weighs 1-293 gramme, the same volume of
carbonic acid weighs I -293 x i'524 = 1-97 gramme. We shall, therefore, obtain the
volume of carbonic acid corresponding to I'lS gr. by dividing this number by 1-97,
which gives o'5837 litre. This being then the volume of the body, it displaces that
volume of air, and therefore its loss of weight inairiso"s837X i'293 = 07547 grammes,
and in hydrogen 0-5837 x 1-293 x 0-069 = 0-052076.

40. Calculate the ascensional force of a spherical balloon of oiled silk which, when
empty, weighs 62-5 kilos, and which is filled with impure hydrogen, the density of

whicli is i that of air. The oiled silk weighs 0-250 kilo, the square metre.
13

The surface of the balloon is ^^-A _ 250 square metres. This surface being that of
0-25

a sphere, is equal to 4 n- Ji"^, whence j,nR~ = 250 and R = 4-459 ; therefore V = "^-'^

= 371 "52 cubic metres.

The weight of air displaced is 371-52 x 1-293 kilo = 480-375 kilos ; the weight of
the hydrogen is 36 -88 kilos, and therefore the ascensional force is
480-375 - (36-88 + 62-5) = 380-995.

41. A b.illoon 4 metres in diameter is made of the same material and filled with
the same hydrogen as above. How much hydrogen is required to fill it, and what
weight can it support ?

Thevohime is 4 „■ 7?3 = 33-5 1 cubic metres, and the surface 477.^- = 50-265 square
3
metres. The weight of the air displaced is 33-51 x 1-293 = 43'328 kilos, and that of
the hydrogen is from the above data 3-333 kilos, while the weight of the material is 12-566
kilos. Hence the weight which the balloon can support is

43-328 - (12-566 + 3-333) = 27-429 kil.

42. Under the receiver of an air-pump is placed a balance, to which are suspended
t>vo cubes; one of these is 3 centimetres in the side.and weighs 26-324 gr. ; and the other
is 5 centimetres in the side, and weighs 26-2597 grammes. When a partial vacuum is
made these cubes just balance each other. What is the pressure? Ans. o'"-374.

43. A soap-bubble 8 centimetres in diameter was filled with a mixture of one
volume of hydrogen gas and 15 volumes air. The bubble just floated in the air ; re-
quired the thickness of the film.

The weight of the volume of air displaced is '^ rr /^ ^ 0-001293 gramme, and that

of the mixture of gases '^ ■" r^ x 0-001293 x ■^ — 22 . j,j^jj ^]^^ difference of

3 16

these will equal the weight of the soap-bubble.

This weight is that of a spherical shell, which, since its thickness / is very
small, is with sufficient accuracy 4 t r- i s in grammes, where s is the specific gravity
= 1-1. Hence

"^ TT r^ r -001293 - 001293 X 15 oo93\ _ ^ ^ ^2 / j.j^

Dividing each side by "^ n r", and putting r = 4, we get

4 X -001293 (^i - ^^^°5^^)=3'3'

Oti Liquids and Gases. 1045

•001293 X .23^7 _ 3-3 / ;

4
whence/ = ■00009116629 cm.

44. In a vessel whose capacity is 3 litres, there are introduced 2 litres of hydrogen
under the pressure of 5 atmospheres ; 3 litres of nitrogen under the pressure of half an
atmosphere, and 4 litres of carbonic acid under the pressure of 4 atmospheres. What
is the final pressure of the gas, the temperature being supposed constant during the
experiment ?

The pressure of the hydrogen, from Dalton's law, will be ^ ^~^, that of the nitro-

3
gen will remain unchanged, and that of the carbonic acid will be ^^ ^, Hence the
total pressure will be

— +--+ — = 9J atmospheres.
323

45. A vessel containing 10 litres of water is first exposed in contact with oxygen
under a pressure of 78 cm. until the water is completely saturated. It is then placed
in a confined space containing 100 litres of carbonic acid under a pressure of 72 cm.
Required the volumes of the two gases when equilibrium is established. The coeffi-
cient of absorption of oxygen is o'042, and that of carbonic acid unity.

The volume of oxygen dissolved is 0-42. Being placed in carbonic acid it will
act as if it alone occupied the space of the carbonic acid, and its pressure will be

78 X — i — = o'326 cm.
10042
Similarly the 10 litres of water will dissolve 10 litres of carbonic acid gas, the total
volume of which will be no, of which 100 are in the gaseous state and 10 are dissolved.

Its pressure is therefore 72 X = 65 '454 cm.

no
Hence the total pressure when equilibrium is established is
0-326 + 65-454 = 65-78 cm. ;
and the volume of the oxygen dissolved reduced to the pressure 65-78 is

o"'*42 X ^^ = o"'-oo2o8, and that of the carbonic acid 10 x -^ 45't = q-qc.
^ 65-78 65-78

46. In a barometer which is immersed in a deep bath the mercury stands 743
mm. above the level of the bath. The tube is lowered until the barometric space,
which contains air, is reduced to one-third, and the mercury is then at a height of 701
mm. Required the atmospheric pressure at the time of observation. Ans. = 764""' .

47. ^^'hat is the pressure on the piston of a steam boiler of 8 decimetres diameter
if the pressure in the boiler is 3 atmospheres? Ans. 1038585 kilos.

48. What is the pressure of the atmosphere at that height at which an ascent of 21
metres corresponds to a diminution of i"™ in the barometric height? Ans. ^yS-g'"'".

49. What would be the heiglU of the atmosphere if its density were everywhere
uniform ? Ans. 7954-1 metres, or nearly 5 miles.

50. How high must we ascend at the sea-level to produce a depression of i mm.
in the height of the barometer?

Ans. Taking mercury as 10,500 times as heavy as air, the height will be 10-5 metres.

51. Mercury is poured into a barometer tube so that it contains 15 cc. of air under
the ordinary atmospheric pressure. The tube is then inverted in a mercury bath and
the air then occupies a space of 25 cc. ; the mercury occupying a height of 302 mm.
What is the pressure of the atmosphere ?

Let X be the amount of this pressure, the air in the upper part of the tube will have

a pressure represented by -^, and this, together with the height of the mercurial

25
column 302, will be the pressure exerted in the interior of the tube on the level of the

1046

Problems and Examples in Physics.

mercury in

the bath, which is equal to the atmospheric pressure

that is -?- + 302

= X, from which x = 755 mm.

52. What effort is necessary to support a cylindrical bell-jar full of mercury
immersed in mercury ; its internal diameter being 6 centimetres, its height ol above
the surface of the mercury (fig. 1)18 centimetres, and the pressure of the atmosphere
077 centimetre?

The bell-jar supports on the outside a pressure equal to that of a column of mercury
the section of whose base is cd, and the height that of the barometer. This pressure is
equal to

TT R'^ X 077 X I3'6.
The pressure on the inside is that of the atmosphere less the weight of a column
of mercury whose base is tfl? and height iJiJ. Thisisequal ton- /?^ x (077 — o"i8) x i3'6 ;
and the effort necessary is the difference of these two pres-
sures. Making i? = 3 cm., this is found to be 69 '216 kilo-
grammes.

53. A barometer is placed within a tube which is after-
ds hermetically closed. At the moment of closing, the
perature is 15° and the pressure 750 mm. The ax-
ial space is then heated to 30°. What will be the height
he barometer ?
The effect of the increase of temperature would be to

e the mercury in the tube in the ratio i + ^° to i +

5550
, and the height h would therefore be

V 5550/

I +

5550

and since in the closed space the elastic force of the air increases in the ratio
I +• 30 a : I + 15 a. we shall have finally A = 30174 mm.

54. The heights of two barometers A and B have been obser%'ed at — 10^ and
■V 15° respectively, to be ^ = 737 and B = 763. Required their corrected heights

ato=. ^"^- ^ = 738 'SS- B = 760-94.

55. A voltaic current gives in an hour S.p cubic centimetres of detonating gas
under a pressure of 760 and at the temperature i2°-5 ; a second voltaic current gives
in the same time 960 cubic centimetres under a pressure of 755 and at the temperature
t5°-5. Compare the quantities of gas given by the two currents. Atts. i : 1-129.

56. The volume of air in the pressure gauge of an

iparatus for compressing gases is equal to 152 parts.

I'.y the working of the machine this is reduced to

7 parts, and the mercury is raised through 0-48

UK'tre. W'liat is the pressure of the gas ?

IIere^5 = 152, AC = 37 parts, and BC = o^'^S.
The pressure of air therefore in ^Cis, from Boyle's

152
37

,.tm-io8 =

tig. 2.

■ pressure in the receiver is therefore

3-122 + 048 = 3'"-6o2,
ch is equal to 4-74 atmospheres.
57. An airtight bladder holding two litres of
at the standard pressure and temperature is
iiersed in sea-water to a depth of 100 metres,
•re tlie temperature is 4°. Required the volume
of tlie gas.

i83

o*i8568 litre.

A ir Pump. 1 047

The specific gravity of sea-water being i '026, the depth of 100 metres will repre-
sent a column of pure water 102 6 metres in height. As the pressure of an atmo-
sphere is equal to a pressure of io'33 metres of pure water, the pressure of this column

= ^°=:6? = 9.94 atm.
10-33
Hence, adding the atmospheric pressure, the bladder is now under a pressure of io'94

atmosphersB, and its volume being inversely as the pressure will be - = o'lS? litre,

1094
if the temperaiure be unaltered. But the temperature is increased by 4°, and therefore
the volume is increased in the ratio 277 to 273, and becomes

277

273

58. To what height will water be raised in the tube of a pump by the first stroke of the
piston, thelength of stroke of which is o'5m., the height of the tube 6 metres, and its section
t",; that of the piston? At starting the air in the tube is under a pressure of 10 metres.

If we take the section of the tube as unity, that of the body of the pump is 10 ; and
the volumes of the tube and of the body of the pump are in the ratio of 6 to 5. Then
if X is the height to which the water is raised in the pipe, the volumes of air in the
pump before and after the working of the pump are 6 at the pressure 10, and 5 + 6 — jr
at the pressure 10 — x.

Forming an equation from these terms, and solving, we have two values, x' = 18" 26
and xf' = 274. The first of these must be rejected as being physically impossible ;
and the true height is ^ = 275 metres.

59. A receiver with a capacity of 10 litres contains air under the pressure 76 cm.
It is closed by a valve, the section of w-hich is 32 square centimetres, and is weighted
with 25 kilogrammes. The temperature of the air is 30° ; its density at o® and 76 cm.
pressure is that of water. The coefficient of the expansion of gases is o '00366.

Required the weight of air which must be admitted to raise the valve.

The air already present need not be taken into account as it is under the pressure
of the atmosphere. Let x be the pressure in centimetres of mercury of that which is

X X 136

will represent in kilogrammes its pressure on a square centi-

57 44 _ 8 '8055 grammes.
76*00

admitted,

metre ; and therefore the internal pressure on the valve, and which is equal to the ex-
ternal pressure of 25 kilogrammes, is -^LJi ^3 ^ 32 _ ^^ jj From which x = 57*44.

For the weight we shall have

p _ 10 X 0001293
I + o'oo366 X 30

60. A bell-jar contains 3-17 litres of air ; a pressure gauge connected with it mark.<;
zero when in contact with the air (fig. 3). The jar is
closed and the machine worked ; the mercury rises
to 65 cm. A second barometer stands at 76 cm.
during the experiment. Required the weight of air
withdrawn from the bell-jar and the weight of that
which remains.

At 0° and 76 cm. the weight of air in the bell-jar is

1-293 ^ 3'^7 — 4-09881.
At 0° and under the pressure 76 — 65 the weight
of the residual air is

4-09881 X II _^^

'*^ = 0-5932,

and therefore the weight of that which is withdrawn is

4-0988 - 0-5932 = 3 5056 gr.

61. The capacity of the receiver of an air-pumi^

1048 Problems and Examples in Physics.

is 7 "53 ; it is full of air under the ordinary atmospheric pressure and at 0°. Re-
quired the weight of air when the pressure is reduced to 0-21 ; the weight with-
drawn by the piston ; and the weight which would be left at 15°.

The weight of 7-53 litres of air under the ordinary conditions is 9736 grammes.

Under a pressure of o'2i it will be 2-69 grammes, and at the temperature 15° it will

be ?^^?- , = 0-2S5 gramme.

I + 000366 X i5

62. In a theoretically perfect air-pump, how great is the rarefaction after 10 strokes,
if the volumes of the barrel and the receiver are respectively 2 and 3 ?

Ans. = 4'59"'™ ; or about of an atmosphere.
166

63. What must be the capacity of the barrel of an air-pump if the air in a re-
ceiver of 4 litres is to be reduced to i the density in two strokes ? Ans. 2g.

64. The reservoir of an air-gun, the capacity of which is 40 cubic inches, contains
air whose density is 8 times that of the mean atmospheric pressure. A shot is fired
when the atmospheric pressure is 741 mm. and the gas which escapes occupies a volume of
80 cubic inches. What is the elastic force of the residual air? Ans. 6 '05 atmospheres.

65. Suppose that at the limit of the atmosphere the pressure of the attenuated

air is the ^^ of a millimetre of mercury and the temperature — 135°, and that in a

1000
place at the sea-level, in latitude 45°, the pressure of the atmosphere is 760™™ and its
temperature 15° C. Determine from these data the height of the atmosphere.

From the formula 18400 1 1 + o '002 j T + / [ | log , we get for the height in metres
82237, which is equal to 51-1 miles.

66. If water is continually flowing through an aperture of 3 square inches with a
velocity of 10 feet, how many cubic feet will flow out in an hour? Ans. 750 cubic feet.

67. With what velocity does water issue from an aperture of 3 square inches, if
37-5 cubic feet flow out every minute ? Ans. 30 feet.

68. What is the ratio of the pressure in the above two cases? Ans. i : 9.

69. What is the theoretical velocity of water from an aperture which is 9 feet
below the surface of water ? Ans. 24 feet.

70. In a cylinder, water stands 2 feet above the aperture and is loaded by a piston
which presses with a force of 6 pounds on the square inch. Required the velocity of
the effluent water. Ans. 32 feet.

71. How deep must the aperture of the longer leg of a syphon, which has a sec-
tion of 4 square centimetres, be below the surface of the water in order that 25 litres
may flow out in a minute? Ans. 5'535 cm.

72. Through a circular aperture having an area of 0-196 square cm. in the bottom
of a reservoir of water which was kept at a constant level, 55 cm. above the bottom,
it was found that 98-5 grammes of water flowed in 22 seconds. Required the coeffi-
cient of efflux.

Since the velocity of efflux through an aperture in the bottom of a vessel is given by
the formula v = sj^gh, it will readily be seen that the weight in grammes of water
which flows in a given time,/, will be given by the formula iv = a a ts/zgh, where (Z is
the area in square centimetres, a the coefficient of efflux, / the time m seconds, and h
the height in centimetres. Hence in this case o = 0-699.

73. Similarly through a square a])orture, the area of which was almost exactly the
same as the above, and at the same depth, 104 '4 grammes flowed out in 21 '6 seconds.
In this case « = 073.

Sound. 1049

IV. ON SOUND.

74. A stone is dropped into a well, and 4 seconds afterwards the report of its
striking the water is heard. Required the depth, knowing that the temperature of the
air in the pit was 10° 74.

From the formula v = 333 \/ 1 + at we get for the velocity of sound at the tem-
perature in question 339 -05 metres.

Let / be the time which the stone occupies in falling ; then Igfl = x will represent
the depth of the well ; on the other hand, the time occupied by the report will be 4 — /,
and the distance will hQ [^ — t) v = x (i) ; thus [^ — t) v = i^/2 (ii), from which,
substituting the values,

(4 - t) 339-S = 4-9 i""
^ = 3793 seconds, and substituting this value in either of the equations (i) or (ii),
we have the depth = 72-6 metres nearly.

75. A bullet is fired from a rifie withavelocity of 414 metres, and is heard to strike
a target 4 seconds afterwards. Required the distance of the target from the marks-
man, the temperature being assumed to be zero.

X ^ X „

+ = ^- X = 738 '2.

414 333

76. At what distance is an observer from an echo which repeats a sound after 3
seconds, the temperature of the air being 10° ?

In these 3 seconds the sound traverses a distance of 3 x 339 = 1017 metres ; this
distance is twice that between the observer and the reflecting surface ; hence the dis-
tance is

££^7 = 508-5 metres.
2

77. Between a flash of lightning and the moment at which the corresponding
thunder is first heard, the interval is the same as that between two beats of the pulse.
Knowing that the pulse makes 80 beats in a minute, and assuming the temperature
of the air to be 15° C, what is the distance of the discharge? Ans. 454'! metres.

78. A stone is thrown into a well with a velocity of 12 metres, and is heard to
strike the water 4 seconds afterwards. Required the depth of the well.

Ai/s. About no metres.

79. What is the velocity of sound in coal gas at 0°, the density being o'5 ?

A/!s. 470'9 metres.

80. What must be the temperature of air in order that sound may travel in it with
the same velocity as in hydrogen at 0° ? Ans. About 3680° C.

81. What must be the temperature of air in order that the velocity of sound may
be the same as in carbonic acid at 0° ? Afis. — ios°S C.

82. Kendall, in a North Pole E.\pedition, found the velocity of sound at —40°
was 314 m. How closely does this agree with that calculated from the value we have
assumed for 0° ? Ans. 6 64 metres too much.

83. The report of a cannon is heard 15 seconds after the flash is seen. Required
the distance of the cannon, the temperature of the air being 22°.

From the formula for the velocity of sound we have

15 ^ 333 \/i + 0003665 X 22 = 5190 metres.

84. If a bell is struck immediately at the level of the sea, and its sound, reflected
from the bottom, is heard 3 seconds after, what is the depth of the sea ?

Ans. 7140 feet.

1050 Problems and Examples in Physics.

85. A person stands 150 feet on one side of the line of fire of a rifie range 450 feet
in length and at right angles to a point 150 feet in front of the target. What is the

velocity of the bullet if the person hears it strike the target of a second later than

9
the report of the gun? The temperature is assumed to be i6°-5. Ans. 2038 feet.

86. An echo repeats five syllables, each of which requires a quarter of a second to
pronounce, and half a second elapses between the time the last syllable is heard and
the first syllable is repeated. What is the distance of the echo, the temperature of
the air being 10° C. ? Ans. 297'47 metres.

87. The note given by a silver wire a millimetre in diameter and a metre in
length being the middle C, what is the tension of the wire? Density of silver 10-47.

Ans. 2267 kilogrammes.

88. The density of iron being 7-8 and that of copper 8 '8, what must be the
thickness of wires of these materials, of the same length and equally stretched, so that
they may give the same note ?

From the formula for the transverse vibration of strings we have for the number of

vibrations « = / — . As in the present case, the tensions, the length of the

rl Sf 7r d
strings, and the number of vibrations are the same, we have

rl \/ ivd r,ls/ ir d] r S/ d r^s/ d,

whence ^ = '^' = ^^ ; hence '' = /Sj? = 1-062.
r^ d 7-8 r, \/ 7-8

89. A wire stretched by a weight of 13 kilos, sounds a certain note. What must
be the stretching weight to produce the major third ?

The major third having ^ the number of vibrations of the fundamental note, and as,
4
all other things being the same, the numbers of vibrations are directly as the square
roots of the stretching weight, we shall have x — 20-312 kilos.

90. The diameters of two wires of the same length and material are 00015 and
0-0038 m. ; and their stretching weights 40oand 1600 grammes respectively. Required
the ratio of the numbers of their vibrations. Ans. n : n, = 1-266 : i.

91. A brass wire i metre in length stretched by a weight of 2 kilogrammes, and a
silver wire of the same diameter, but 3-165 metres in length, give the same number of
vibrations. What is the stretching weight in the latter case ?

Since the number of vibrations is equal, we shall have

1 /Z = 1 /Z;
rlW ivd rl.s/ ird,
from which, replacing the numbers, we get x = 25 kilos.

92. A brass and a silver wire of the same diameter are stretched by the weights of 2
and 25 kilogrammes respectively, and produce the same note. What are their lengths,
knowing that the density of brass is 8-39, and of silver 10-47 ?

Ans. The length of the silver wire is 3-16 times that of the brass.

93. A copper wire 1-25 mm. in diameter and a platinum one of 0-75 mm. are
stretched by equal weights. What is the ratio of their lengths, if, when the copper
wire gives the note C, the platinum gives F on the diatonic scale?;

Ans. The length of the copper is to the length of the platinum = 1-264 : i.

94. An organ pipe gives the note C at a temperature 0° ; at what temperature
will it yield the major third of this note? Ans. 153° C,

95. A brass wire a metre in length, and Stretched by a weight of a kilogramme,
yields the same note as a silver wire of the same diameter but 2-5 metres in length and
stretched by a weight of 7-5 kilogrammes. Required the specific gravity of the silver.

Ans. 10068.

96. How many beats are produced in a second by two notes, wliose rates of vibra-
tion are respectively 340 and 354 ? Ans. 14.

Heat.

1051

V. ON HEAT.

97. Two mercurial thermometers are constructed of the same glass ; the internal
diameter of one of the bulbs is 7"" "5 and of its tube 2-5 ; the bulb of the other is
62 in diameter and its tube 1-5. What is the ratio of the length of a degree of the
first thermometer to a degree of the second?

Let A and B be the two thermometers, D and D' the diameters of the bulbs, and
d and cH the diameters of the tubes. Let us imagine a third thermometer C with the
same bulb as B and the same tube as A, and let /, /', and /" denote the length of a
degree in each of the thermometers respectively. Since the stems of A and C
have the equal diameters, the lengths / and /" are directly as the volumes of the
tubes, or what is the same, as the cubes of their diameters ; and as B and C have
the same bulk, the lengths /' and /" are inversely proportionate to the sections of
the stems, or what amounts to the same, to the squares of their diameters. We
have then

f = m^^'^v = d^'

introducing the values and sohing, we have
/ = 0-638.

98. At what temperature is the number on the
Centigrade and Fahrenheit thermometers the same ?

Alls. — 40°.

99. The same question for the Fahrenheit and
Reaumur scales. Ans. — 25-6.

100. A capillary tube is divided into 180 parts
of equal capacity, 25 of which weigh 12 gramme.
What must be the radius of a spherical bulb to be
blown to it so that 180 divisions correspond to 150
degrees Centigrade?

Since 25 divisions of the tube contain i"2

gramme, 180 divisions contain =8 64.

U- ¥

/ li H

■)(>)(2

Fig.

And since these 180 divisions are to represent 150 degrees, the weight of mercury

corresponding to a single degree is ■^'^. But as the expansion corresponding to

8'6a
one degree is only the apparent expansion of mercury in glass, the weight __ - is ■

I ^o 0400

of the mercury in the reservoir, which is ^ ^R^. From this ^ = i "8755 centimetre.
3

101. By how much is the circumference of an iron wheel, whose diameter is 6 feet,
increased when its temperature is raised 400 degrees? Coefficient of expansion of
iron = 00000122. Ans. By 0092 foot.

102. What must be the length of a wire of this metal which for a temperature of
1° expands by one foot ? Ans. 81967 feet.

103. A pendulum consists of a platinum rod, on a flattening at the end of which
rests a spherical zinc bob. The length of the platinum is / at 0°. What must be the
diameter of the bob, so that its centre is always at the same distance from llie point of
suspension whatever be the temperature ? Coefficient of expansion of platinum
o 0000088 and of zinc 00000294.

Ans. The diameter of the bob must be g of the length of the platinum.

104. Two walls, which when perpendicular are 30 feet apart, have bulged out-
wards to the extent of 24 inches. They are to be made perpendicular by the contrac-

1052 Problems and Examples m Physics.

tion of an iron bar. By how much must its temperature be raised above that of the air,
which is taken at o°? Ans. 546-4.

105. An iron wire 4 sq. mm. in cross section is stretched — ? — of its length by a

81200
weight of I kilogramme. What weight must be applied to a bar 9 sq. mm. in cross
section, when it is heated from 0° to 20°, in order to prevent it from expanding?

Ans. 44 '5 kilo.

106. At the temperature zero a solid is immersed 0-975 of its total volume in
alcohol. At the temperature 25° the solid is wholly immersed. The coefficient of
expansion of the solid being o 000026, required the coefficient of expansion of the
alcohol. Afis. 0-001052.

107. Into a glass globe, the capacity of which at 0° is 250 cc, are introduced
25 cc. of air measured at 0° and 76 cm. The flask being closed and heated to 100",

required the internal pressure. Coefficient of cubical expansion of glass — ^^ —

38700

At 100'' the capacity of the flask is 250 ( i + — ^^ ) ; again at 100° the volume of
V 38700/
the free air under the pressure 76 is 25 (i + 100 x o'oo366). But its real volume is

2:;o X 3 — under a pressure A-. Hence
387 gg

76 : Jf = 250 X 2 : 25 X 1-366, from which x = 10-3548 cm.
387

108. The specific gravity of mercury at 0° being 13-6, required the volume of 3
kilogrammes at 85°. Coefficient of expansion .

The volume at 0° will be -^ and at 85° - 2- x(i + ^ ) = 0-2239 litres.
i3'6 136 V 5550^

109. A hollow copper sphere 20 cm. in diameter is filled with air at 0° under a
pressure of i^ atmosphere ; what is the total pressure on the interior surface when the
enclosed air is heated to a temperature of 600°? Ans. 6226-5 kilogrammes.

110. Between the limits of pressure 700 to 780mm. the boiling-point of water varies
o°-o375 C. for each mm. of pressure. Between what limits of temperature does the
boiling point vary, when the height of the barometer is between 735 and 755 mm. ?

A/IS. Between 99°-o625 and 99°-8i25.

111. Liquid phosphorus cooled down to 30°, is made to solidify at this tempera-
ture. Required to know if the soHdification will be complete, and if not, what weight
will remain melted ? The melting point of phosphorus is 44-2 ; its latent heat of fusion
5-4, and its specific heat 0-2.

Let X be the weight of phosphorus which solidifies ; in so doing it will give out a
quantity of heat = 5-4 ^ ; this is expended in raising the whole weight of the phos-
phorus from 30 to 44-2. Hence we have 5-4*" = i x (44-2 — 30) 0-2, from which

X =■ ^ = 0-526, so tliat 0-474 of phosphorus will remain liquid.
5 '4

112. A pound of ice at 0° is placed in two pounds of water at 0° ; required the
weight of steam at 100° which will melt the ice and raise the temperature of the mix-
ture to 30°. The latent heat of the liquefaction of ice is 79-2, and that of the vaporisa-
tion of water 536. A//s. -279 pound.

113. 65-5 grammes of ice at — 20"-" having been placed in x grammes of oil of
turpentine at 13-3°, the final temperature is found to be 3-1°. The specific heat of
turpentine is 0-4, and it is contained in a vessel weighing 25 grammes, whose specific
hiMt is o-i. The specific heat of ice is 0-5. Required the value of jr.

Arts. X = 147s grammes.

114. In what pro[)ortion must water at a temperature of 30° and linseed oil
(sp. heat = 0-5) at a temperature of 50° be mixed so that there are 20 kilogrammes of
the mixture at 40°? A»s. Water = 6-66 kilos, and linseed oil = 13-34.

Heat. 1053

115. By how much will mercury at 0° be raised by an equal volume of water at
1 00°? An5.bZ°-<)<Z.

116. The specific heat of gold being o '03244, what weight of it at 45° will raise a
kilogramme of water from 120-3 to i5°7?

Let X be the weight sought ; then x kilogrammes of gold in sinking from 45° to
i5«7 will give out a quantity of heat represented by x (450 - 15O7) 0-0324, and this is
equal to the heat gained by the water, that is to i (15-7 — 12-3) = 3-4, that is :r = 3-58.

117. fhe specific heat of sulphide of copper is 0-1212, and that of sulphide of silver
0-0746. 5 kilos, of a mi.xture of these two bodies at 40°, when immersed in 6 kilos, of
water at 7-669 degrees, raises its temperature to lo®. How much of each sulphuret did
the mi.\ture contain ?

The weight of the copper sulphuret = 2, and that of the silver sulphuret 3.

118. Into a mass of water at 0°, 100 grammes of ice at — 12° are introduced ; a
weight of 7-2 grammes of water at 0° freezes about the lump immersed, while its
temperatiu-e rises to zero. Required the specific heat of ice. Latent heat of water
79 ■2- Ans. 0-4752.

119. Four pounds of copper filings at 130° are placed in 20 pounds of water at 20°
the temperature of which is thereby raised 2 degrees. What is the specific heat, c, of
copper? Ans. c = 00926.

120. Two pieces of metal weighing 300 and 350 grammes, heated to a temperature
X, have been immersed, the former in 3351 -6 grammes of water at 10° and the latter in
1935-4 grammes at the same temperature. The temperature in the first case rises to
20'', and in the second to 30°. Required the original temperature and the specific heat
of the metal. Ans. x the temperature = 1000°; c the specific heat = 0-114.

121. In what proportions must a kilogramme of water at 50° be divided in order that
the heat which one portion gives out in cooling to ice at zero may be sufficient to change
the other into steam at 100° ? Ans. x = 0-8203.

122. Three mixtures are formed by mixing two and two together, equal quantities
of ice, salt, and water at 0°. Which of these mixtures will have the highest and which
the lowest temperature ? Ans. The mixture of ice and salt will produce the lowest
temperature, while that of ice and water will produce no lowering of temperature.

123. In 25-45 kilogrammes of water at i2°-5 are placed 6-17 kilos, of a body at a
temperature of 80° ; the mixture acquires the temperature i4°-i. Required the specific
heat of the body.

If <: is the specific heat required, then wc {t — 6) represents the heat lost by the body
in coobng from 80° to 14°-! ; and that absorbed by the water in rising from i2°-5 to
i4'^-i is m' (9 — /). These two values are equal. Substituting the numbers, we have
c = 0-10014.

124. Equal lengths of the same thin wire traversed by the same electrical current are
placed respectively in i kilogramme of water and in 3 kilogrammes of mercury. The
water is raised 10'^ in temperature, by how much will the mercury be raised ?

Ans. 100° -04.

125. How many cubic feet of air under constant pressure are heated through 1° C.
by one thermal unit ? Ans. 55*3 cubic feet.

126. Given two pieces of metal, one x weighing 2 kilos, heated to 80°, and the other
y weighing 3 kilos, and at the temperature 50°. To determine their specific heats
they are immersed in a kilogramme of water at lo'^, which is thereby raised to 26°-3.

The experiment is repeated, the two metals being at the temperature 100* and 40°
respectively, and, as before, they are placed in a kilogramme of water at 10°, which
this time is raised to 28°'4. Required the specific heats of the two metals.

Ans. x = 0-115;^ = 0-0555.

127. For high temperatures the specific heat of iron is 0-1053 "•■ 0000017 ^- ^^^lat
is the temperature of a red-hot iron ball weighing a kilogramme, which, plunged in 16

I054 Problems and Examples in Physics.

kilogrammes of water, raises its temperature from 12° to 24° ? What was the tempe-
rature of the iron?

(o'io53 + o'ooooiy/) [t — 24) = 16 (24 — 12),
or '000017 t- + "1048892 t — 2'5272 = 192 ;

transposing and dividing by the coefficient of f^, we get
/- + 6170 t = 11442776,
fi + 6170 i + (3085)2 = 20960001 ;
hence i + 3085 = 4578-3 nearly ; ,'. / = 1493-3.

128. A kilogramme of the vapour of alcohol at 80° passes tlirough a copper worm
placed in 10-8 kilogrammes of water at 12° the temperature of wliich is thereby raised
to 36°. The copper worm and copper vessel in which the water is contained weigh
together 3 kilogrammes. Required the latent heat of alcohol vapour. Ans. 238-77.

129. Determine the temperature of combustion of charcoal in burning to form car-
bonic acid.

We know from chemistry that one part by weight of carbon in burning unites
with 23 parts by weight of oxygen to form 3§ parts by weight of carbonic acid.
Again the number of thermal units produced by the combustion of a pound of charcoal
is 8080 ; the whole of this heat is contained in the 33 parts of carbonic acid produced,
and if its specific heat were the same as that of water, its temperature would be

_^— = 2204° C. ; but since the specific heat of carbonic acid is 0-2163 that of an equal
3§

weight of water, the temperature will be -- — t = 10189° C.

2204
0-2163

130. A glass globe measuring 60 cubic centimetres is found to weigh 19-515
grammes when filled with air under a pressure of 752-3™"" and at a temperature of 10° C.
Some ether is introduced and vaporised at a temperature of 60°, whereupon the flask
is sealed while quite full of vapour, the pressure being 753-4™". Its weight is now
found to be 19-6786 grammes. Required the density of the ether vapour compared
with that of hydrogen. Ans. 54-4.

131. Calculate the density of alcohol vapour as compared with air by Gay-Lussac's
method from the following data : —

Weight of alcohol 0-1047 grm.; vol. of vajiour at 110° C. =82-55 c.c. '< height of
mercury above the level in the bath, 98 mm. ; barometric height, 752-3 mm. ; tempera-
ture of the room, 15° C. Ans. 1-6.

132. In a determination of the vapour density by Gay-Lussac's method, 0-1163
gramme of substance was employed. The volume observed was 50-79 cc, the height
of the mercury above the level of that in the bath was 80-0™", the height of the oil
column reduced to miUimetres of mercury 16-9; the temperature 215° C, and the
height of the barometer at the time of observation 755-5"'". Required the specific
gravity of the vapour as compared with that of hydrogen. Ans. 50-1.

133. Through a U-tube containing pumice saturated with sulphuric acid a cubic
metre of air at 15° is passed, and the tube is found to weigh 3-95 gmmmes more.
Required the hygrometric state of the air.

The pressure of aqueous vapour at 15° is 12-699 '< hence the weight of a cubic
metre of aqueous vapour .saturated at 15° is ^^93 x 12 99 x 5 _ jg.^^ grammes,

(,4. :p 760x8

and the hygrometric state is ^^^ = 0-309.
12-79

134. The quantity of water given out by the lungs and skin may be taken at
30 ounces in 24 hours. How many cubic inches of air already half saturated at 10° will
be fully saturated by the moisture exlialed from the above two sources by one man ?
Tension of aqueous vapour at 10° in inches = 0-361. Pressure of tlie atmosphere = 30
inches. Arts. 6121 cubic feet.

Heat. 1 05 5

135. A mass of air extending over an area of 60,000 square metres to a height of
300 metres has the dew point at 15°, its temperature being 20°. How much rain will
fall if the temperature sinks to 10° ?

The weight of vapour condensed from one cubic metre under these circumstances
will be 3'i435 grammes, and therefore from 18,000,000 cubic metres it will be 56,583
kilogrammes, which is equal to a rainfall 00943 mm. in depth.

136. When 3 cubic metres of air at io° and 5 cubic metres at 18°, each saturated
with aqueous vapour at those temperatures, are mi.xed together, is any water precipi-
tated ? And if so, how much ?

The weight of water contained in the two masses under the given conditions are
respectively 28-i8and76'59grammes; the weight required to saturate the mixture at the
temperatureof 15° is 10239 grammes, and therefore 2'38 grammes will be precipitated.

137. The temperature of the air at sunset being 10°, what must be the lowest hygro-
metric state, in order that dew may be deposited, it being assumed that in conse-
quence of nocturnal radiation the temperature of the ground is 7° below that of the air ?

Ans. The hygrometric state must be at least o'62 of total saturation.

138. It is stated as a practical rule that when the tension of aqueous vapour present
in the atmosphere, as indicated by the dew point, is equal to x mm. of mercury, the
weight of water present in a cubic metre of that air is x grammes. What is the error
in this statement for a pressure of 10 mm. and the temperature 15° C. ?

Ans. 0-1J2 gr.

139. A raindrop falls to the ground from a height of a mile ; by how much would
its temperature be raised, assuming that it imparts no heat to the air or to the
ground? Arts. 30-8 C.

140. A lead bullet falls through a height of 10 metres ; by what amount will its
temperature have been raised when it reaches the ground, if all the heat is expended in
raising the temperature of the bullet ? Ans. 07515° C.

141. From what height must a lead bullet fall in order that its temperature may
beraised n degrees? — and what velocity will it have acquired? It is assumed that all the
heat is expended in raising the temperature of the bullet ; the specific heat of lead is
taken at 00314, and Joule's equivalent in metres at 424.

Ans. 13-31 X n metres ; v = 288 's/n.

142. How much heat is disengaged if a bullet weighing 50 grammes and having
a velocity of 50 metres strikes a target ?

Ans. Sufficient to raise one gramme of water through 1^ C.

143. How much heat is produced in the room of a manufactory in which i 2 horse-
power of the motor is consumed each second in overcoming the resistance of friction ?

Ans. A quantity sufficient to raise 102561 pounds of water one degree Centigrade.

144. What is the ratio between the quantities of heat which are respectively pro-
duced, when a bullet weighing 50 grammes and having a velocity of 500 metres,
and a cannon-ball weighing 40 kilogrammes with a velocity of 400 metres, strike a
target? Ans, i : 512.

145. The specific heat of lead is 0031, and its latent heat 5-37. What is the
mechanical equivalent of the heat necessary to raise 5 pounds of lead from a tempera-
ture of 270° C:. to its melting-point 335° C, and then to melt it ?

Ans. 51326 foot-pounds.

146. Assuming that the temperature at which heat leaves a perfect engine is 16° C,
at what temperature must it be taken in in order to obtain a theoretical useful effect of i ?

Ans. i6os° C.

147. Assuming that in a perfect engine heat is taken in at a temperature of 144°,
and is given out at a temperature of 36^ : what is the greatest theoretical useful effect?

Ans. o"259.

1056 Problems and Examples in Physics.

VI. ON LIGHT.

148. How many candles are required to produce at a distance of 2*5 metres, the
same illuminating effect as one candle at a distance of 0*45 m. ? Ans. 31.

149. Two sources of light whose intensities are as i : 2 are two metres apart. At
what position is a space between them equally illuminated ?

Ans. o'828 metre from the less intense light.

150. A candle sends its rays vertically against a plane surface. When the candle is
removed to thrice the distance and the surface makes an angle of 60° with the original

position, what is the ratio of the illuminations in the two cases? Atis. i : -

151. An observer, whose eye is 6 feet above the ground, stands at a distance of 18
feet from the near edge of a still pond, and sees there the image of the top of a tree,
the base of which is at a distance of 100 yards from the glace at which the image is
formed. Required the height of the tree. Aiis. 100 feet.

152. What is the height of a tower which casts a shadow 56 "4 m. in length when a
vertical rod 0*95 m. in height produces a shadow i'38 m. in length? Ans. 38 "8.

153. A minute hole is made in the shutter of a dark room, and at a distance of
2 "5 metres a screen is held. What is the size of the image of a tree which is 15 '3
metre's high and is at a distance of 40 metres? Ans. 0-95625 metre.

154. What is the length of the shadow of a tree 50 feet high when the sun is 30°
above the horizon? What when it is 45°, and 60°? Ans. 86-6 ; 50, and 28-867 feet.

155. Under what \'isual angle does a line of 30 feet appear at a distance of 18 feet ?

Ans. 79°"36.

156. The apparent diameter of the moon amounts to 31' 3". What is its real dia-
meter if its distance from the earth is taken at 239000 geographical miles?

Ans. 2166 geographical miles.

157. For an ordinary eye an object is visible with a moderate illumination and pure
air under a visual angle of 40 seconds. At what distance, therefore, can a black circle
(6 inches in diameter) be seen on a white ground ? Ans. 2578 feet.

158. At what distance from a circle with a diameter of one foot is the visual angle a
second? , Ans. 206265 feet.

159. At what distance would a circular disc i inch in diameter, of the same bright-
ness as the sun's surface, illuminate a given object to the same extent as a vertical sun
in the tropics, the light absorbed by the air being neglected ?

Ans. Taking the sun's angular diameter at 30', j: = 38 inches.

160. What is the minimum deviation for a glass prism (// = i -53), whose refracting
angle is 60° ? Ans. 39° 50'.

161. What is the minimum deviation for a prism of the same substance when the
refracting angle is 45° ? Ans. 63° 38'.

162. The refracting angle of a prism of silicate of lead has been found by measure-
ment to be 2r°T2, and the minimum deviation to be 24°-46. Required the refractive
index of the substance. Ans. 2-122.

163. Construct the path of a ray which falls on an e(|uiangular crown-glass prism
at an angle of 30° ; and find its deviation. Ans. 700-45.

164. What are the angles of refraction upon a ray which passes from air into glass
at an angle of 40° ; from air into water at an angle of 65° ; and from air into diamond
at an angle of 80°? Ans. 25O-20 ; 44^-5 ; 230-12.

165. The focal distance of a concave mirror is 8 metres. • What is the distance of
the image from the mirror when the object is at a distance of 12, 5, and 7 metres
respectively? Ans. 24; - 13-3 and - 56.

Light.

1057

166. An object at a distance of 10 feet produces a distinct image at a distance of 3
feet. What is the focal distance of the mirror? Ans. 2-3077 feet.

167. Required the focal distance of a crown-glass meniscus, the radius of curvature
of the concave face being 45 mm., and that of the convex face 30 mm. ; the inde.x of
refraction being 1-5. Ans. f = 180 mm.

168. What is the principal focal distance of a double-convex lens of diamond, the
radius of curvature of each of whose faces is 4 mm., and the refractive index of dia-
mond 2 •487^. Ans. 1-34 mm.

169. A watch-glass with ground edges, the curvature of which was 4-5 cm., was
tilled with water, and a glass plate slid over it. The focus of the plano-convex lens
thus formed was found to be i3'5 cm. Required the refractive index of the water.

Ans. n = I '33.

170. What is the focal distance of a double-convex lens when the distances of the
image and object are respectively 5 and 36 centimetres? Aus. 4-4 centimetres.

171. The radii of cun'ature of a double-convex lens of crown glass are six and
eight inches. What is the focal distance ? ^«^. 6'85 inches.

172. The focal distance of a double-convex lens is 4 inches ; the radius of cur-
vature of one of its faces is 3 inches. What is that of the second? A?is. 6 inches.

173. The radius of curvature of a plano-convex lens is 12 inches. Required its
focal distance. Ans. 24 inches.

174. If the focal distance of a double-convex lens is i centimetre, at what distance
must a luminous object be placed so that its image is formed at 2 centimetres dis-
tance from the lens ? A /is. 2 centimetres.

175. A candle at a distance of 120 centimetres from a lens forms an image on the
other side of the lens at a distance of 200 feet. Required the nature of the lens and
its focal distance. A/es. It is a convex lens, and its focal distance is 75 cm.

176. A plano-convex lens was found to produce at a distance of 62 cm. a sharp
image of an infinitely distant object. In front of the same lens, at a distance of 84 cm.,
a miUimetre scale was placed, and a sharp image was formed at a distance of 250 cm.
It was thus found that 10 millimetres in the object corresponded to 29 in the image.
From these observations determine the focal distance of the lens. Ans. The mean
of the results is 62 '4.

177. The image of a distant tree was sharply formed at a distance of 31 cm. from
the centre of a concave mirror.

In another case the image of an object 18 mm. in length at a distance of 405 mm.
from the mirror was formed at 1350 mm. from the mirror and had a length of 61 mm.
In another experiment the distances of object and image and the size of the image were
respectively 2200, 355, and 3 mm.

Deduce from these several data the focal distance of the mirror. Ans. 31-2 ; 30-5.

178. What must be the radii of curvature of the faces of a lens of best form made
of glass (« = i'5) if its focal distance is to be 6 inches? Ans. 3-5 inches and 21 inches.

179. A diffraction grating, with lines o'o5 mm. apart, is held in front of a Bunsen's
burner in which common salt is volatilised, and when viewed through a telescope it is
found that the angular distances of the first, second, fourth, and sixth bright bands from
the central one are respectively o^ 41', 1° 21', 2° 42', and 4° 3'. Required the wave-
length of sodium light.

The formula >. = '.1'" r"^ where K is the wave-length, <i> the angular distance of
n
any bright line of order n from the central one, gives as the mean of the 4 observa-
tions : Ans. o '00059088 mm.

1058 Problems and Examples in Physics.

VII. MAGNETISM AND FRICTIONAL ELECTRICITY.

180. A compass needle at the magnetic equator makes 15 oscillations in a minute ;
how many will it make in a place where the horizontal force of the earth's magnetism is

— as great? Ans. 12.

181. A compass needle makes 9 oscillations a minute under the influence of the
earth's magnetism alone ; how many will it make when re-magnetised so as to be
half as strong again as before? Ans. 11.

182. A small magnetic needle makes 100 oscillations in 7 min. 42 sees, under the
influence of the earth's force only ; when the south pole of a long bar magnet A is
placed 10 inches north of it, it makes 100 oscillations in 4 min. 3 sees. ; and with the
south pole of another magnet B in the same place, it makes 100 oscillations in 4 min.
48 sees. What are the relative strengths of the magnets A and B ?

Ans. A. ==■ I '404 B.

183. On a table where the earth's magnetism is counteracted, the north pole of a
compass needle makes 20 oscillations in a minute under the attraction of a south pole
4 inches distant ; how many will it make when the south pole is 3 inches distant ?

Ans. 26 '6.

184. If the oscillating magnet be re-magnetised so as to be twice as strong as
before, how many oscillations in a minute will it make in the two positions respectively?

Ans. 28'28 and 50*27.

185. At one end of a light glass thread, carefully balanced so as to oscillate in a
vertical plane, is a pith ball. Over this and in contact with it is a fixed pith ball of the
same dimensions. Both balls being charged with the same electricity it is found that
to keep them i'4 inch apart, a weight of "9 mgr. must be placed at the free end of the
glass thread. What weight must be placed there to keep the balls i"05 inch apart ?

Ans. I "6 mgr.

186. A small insulated sphere A charged with the quantity of + electricity 2 is
at a distance of 25 mm. from a second similar sphere B charged with the quantity 5 ;
the latter is momentarily touched with an unelectrified sphere b, of the same size, and
the distance altered to 20 mm. What is the ratio of the repulsive forces in the two
cases? Atis. 32 : 25.

187. Two insulated spheres A and B, whose diameters are respectively as 7 : 10,
have equal quantities of electricity imparted to them. In what ratio are their electrical
densities? Ans. 100 : 49.

188. Two such spheres whose diameters are as 3 : 5 contain respectively the
quantities of electricity 7 and 10, In what ratio are their densities ? Ans. 35 : 18.

189. Three insulated conducting spheres, A, B, and C, whose radii are respectively
I, 2, and 3, are charged with electricity, so that their respective potentials are as 3 : 2 : i,
and are then connected by wires, whose capacity may be neglected. What is the total
quantity and potential of the system? Ans. Q=io ; V=i'66.

190. Supposing each of the spheres discharged separately, what would be the total
work they would produce, as compared with that produced by the discharge of the
whole system ? Ans. 30 : 25.

Voltaic Electricity. io59

VIII. VOLTAIC ELECTRICITY.

191. A galvanometer offering no appreciable resistance is connected by short thick
wires with the poles of a cell, and deflects 20°. By how much will it be deflected if two
exactly similar cells are connected with the first side by side ? Aits. 47° '30.

192. By how much if the three cells are connected in series ? Ans. 20°.

193. Two cells each of i ohm resistance are connected in series by a wire the
resistance of which is also i ohm. If each of these when connected singly by short
thick wires to a galvanometer of no appreciable resistance deflects it 25°, how much
will the combination deflect it, the connections being made by short thick wires ?

Ans. 170-16.
A Siemens unit is equal to the resistance of a column of pure mercury a metre in
length and a square mm. in cross section. It is equal to o'9536ofan ohm or ba
unit; or a ba unit equals i'0485 Siemens unit, or equals a column of mercury i'0485
metre in length and a square mm. in cross section.

194. A single thermo-electric couple deflects a galvanometer of 100 ohms resist-
ance 0° 30'; how much will a series of 30 such couples deflect it, the connections being
made by short thick wires? Ans. 14° -40.

195. Suppose a sine galvanometer had been used in the last question, and the
first reading had been o°"3o', what would the second be? Ans. i5°'io.

196. The internal resistance of a cell is half an ohm ; when a tangent galvano-
meter of I ohm resistance is connected with it by short thick wires it is deflected 15° ;
by how much will it be deflected if for one of the thick wires a thm wire of i^ ohm
resistance is substituted ? Ans. 'j^'yj.

197. What will be the deflection if each of the wires is replaced by a thin wire of
i^ ohm resistance ? Ans. 6° 10'.

198. A cell of one-third of an ohm resistance deflects a tangent galvanometer of
unknown resistance 45°, the connection being made by two short thick wires. If a wire
of 3 ohms resistance be substituted for one of the short wires the deflection is 30°. What
is the resistance of the galvanometer? Ans. 375 ohms.

199. What would be the deflection if for the cell in the last question three exactly
similar cells in series were substituted [a] when the galvanometer alone is in circuit ;
{b) when both the galvanometer and the thin wire are in circuit ?

Ans. a 67° -48. b = 57° '41.

200. A galvanometer off'ering no sensible resistance is deflected 50° by a cell
connected with it by short thick wires. If a resistance of 3 ohms be put in the circuit,
the deflection is 20°. Find the internal resistance of the cell. Ans. 1-32.

201. Suppose the results in the last question were produced by two exactly similar
cells in series, find the internal resistance of each. Ans. o"659.

202. Suppose they were produced by two exactly similar cells placed side by side,
find the internal resistance of each. Ans. 2-639.

203. If the resistance of 130 yards of a particular copper wire ^ of an inch in

diameter is an ohm, express in that unit the resistance of 8242 yards of cojiper wire ~

12
of an inch in diameter. Ans. 35-66.

204. One form of fuse for firing mines by voltaic electricity consists of a platinum
wire f of an inch long, of which a yard weighs 2 grains. Required its resistance in
terms of a Siemens unit. Specific gravity of platinum 22, and its conducting power
11-25 that of mercury. Ans. 0-131.

205. Express in ohms the resistance of one mile of copper wire ^ of an inch in
diameter of the same quality as that referred to in 203. Am, 0-8461.

3 Y2

io6o Problems and Examples in Physics.

206. The whole resistance of a copper wire going round the earth (24800 miles) is
221650 ohms. Find its diameter in inches. Aiis. o'oj'^Z.

207. What length of platinum wire o'Oj of an inch in diameter must be taken to
get a resistance equal to i ohm, the specific resistance of platinum being taken at 5'55
that of copper ? ^«j. 14-25 metres.

208. 660 yards of iron wir^ o'o625 of an inch in diameter have the same electrical
resistance as a mile of copper wire 0-0416 of an inch in diameter. Find the specific
resistance of iron, that of copper being unity. Ans. 6-15.

209. Ten exactly similar cells in series produce a deflection of 45° in a tangent
galvanometer, the external resistance of the circuit being 10 ohms. If arranged so
that there is a series of 5 cells, of two abreast, a deflection of 33° '42 is produced ;
find the internal resistance of the cell. Ans. J ohm.

210. On the bobbins of the new Post Office pattern of a single needle instrument
are coiled 225 yards of No. 35 copper wire 0-0087 '"ch in diameter, the resistance of
which is about 92 ohms. Required the conductmg power of the wire in terms of
mercury. Afis. 46.

211. Ten exactly similar cells each of f of an ohm resistance give, when arranged
in five series of 2 each, a deflection of z-f'-^j ; but when arranged in 2 series of 5 each
a deflection of 33^-42. Required the external resistance of the circuit including that
of the galvanometer. Aiis. -i^.

1X1. A cell in a certain circuit deflects a tangent galvanometer 18° 26' ; two such
cells abreast in the same circuit deflect it 23° 57' ; two such cells in series in the same
circuit diminished by i ohm deflect it 29° -2. Find the internal resistance of one cell
and that of the circuit. A/is. R = r = i-66.

213. What is the best arrangement of 6 cells, each of § of an ohm resistance,
against an external resistance of 2 ohms ?

A71S. Indifferent whether in 6 cells of i each or in 3 cells of 2 each.

214. What is the best arrangement of 20 cells, each of o-8 ohm resistance, against
an external resistance of 4 ohms ? Ans. 10 cells of 2 each.

215. In a circuit containing a galvanometer and a voltameter, the current which
deflects the galvanometer 45° produces 10-32 cubic centimetres of mixed gas in a
minute. The electrodes are put farther apart, and the deflection is now 20° ; find
how much gas is now produced per minute. Ans. ^I'TSl cc

216. 100 inches of copperwire weighing 100 grains has a resistance of 0-1516 ohm.
Required the resistance of 50 inches weighing 200 grains. Ans. 0-01895.

217. A knot of nearly pure copper wire weighing one pound has a resistance of
1260 ohms at i5°-5 C. ; what is the resistance at the same temperature of a knot of the
same quality of wire weighing 125 pounds? Ans. 9-6 ohms.

218. Find the length in yards of a wire of the same diameter and 'quality as the
knot pound in 217, having a resistance of 2 ohms. Ans. 3-38 yards.

219. Find the length in yards of a wire of the same quality and total resistance as
the knot pound in 217, but of three times the diameter. Ans. 18261 yards.

220. The specific gravity of platinum is 2J times that of copper ; its resistance s|
as great. What length of platinum wire weighing 100 grains has the same resistance
as 100 inches of copper wire also weighing 100 grains? Ans. 27.

221. A cell with a resistance of an ohm is connected by very short tliick wires with the
binding screws of a tangent galvanometer, the resistance of which is lialf an ohm, and
the deflection is 45° ; if the screws of tlie galvanometer be also connected at the same -"
time by a wire of i ohm resistance, find the deflection. Ans. 36° 52'.

222. The resistance of a galvanometer is half an ohm, and the deflection when

Voltaic Electricity. 1 06 1

the current of a cell is passed through it is 30°. When a wire of 2 ohms resistance is
introduced into the circuit the deflection is 15° ; find the internal resistance of the cell.

Ans. 1-23.

223. When the current of a cell, the resistance of which is f of an ohm, is passed
through a galvanometer connected with it by very short thick wires, the deflection is
45° ; when the binding screws are also connected by a shunt having a resistance of i
the deflection is 33° "42. Find the resistance of the galvanometer. Ans. 2.

224. A cell whose internal resistance is 2 ohms has its copper pole connected with
the binding screw A of a galvanometer formed of a thick band of copper. From
the other screw B a wire of 20 ohms resistance passes to the zinc pole, and the deflection
read off is 7° -8. Find the deflection when B is at the same time connected with the
zinc pole by a second wire of 30 ohms resistance. Ans. ii°-8'.

225. What would be the deflection in 212 if the second wire instead of passing
from B to the zinc pole passed directly from the zinc pole to the copper pole ?

Ans. 2*437.

226. A Leclanch^ cell deflects a galvanometer 30° when 200 ohms resistance are
introduced into the circuit, 15° when 570 ohms are .introduced ; a standard Daniell
cell deflects it 30° when 100 ohms are in circuit, and 15° when 250 additional ohms are
introduced. Required the electromotive force of the Leclanch^ in terms of that of the
Daniell. Ans. 1-48.

227. A Bunsen and a Daniell cell are placed in the same circuit in the first case
so that the carbon of the first is united to the zinc of the Daniell ; and in the second
case so that their currents oppose each other. The currents are respectively 30°'2,
and in the second 10° '6. Required the electromotive force of the Bunsen in terms of
the Daniell. Ans. i^Sg.

228. A telegraph line constructed of copper wire, a kilometre of which weighs 30*5
kilogrammes, is to be replaced by iron wire a kilometre of which weighs 135 '6 kilo-
grammes. In what ratio does the resistance alter? Ans. The resistance of the iron
wire will be i*i8 times that of the copper wire for which it is substituted.

229. A telegraph line which has previously consisted of copper wire weighing 30*5
kilogrammes to the kilometre is to be replaced by an iron wire of the same diameter
which shall offer the same resistance. What must be the section of the latter, and
what its weight per kilometre?

Ans. The section of the copper wire is 3*4357 sq. mm., that of the iron by which
it is replaced is 206 sq. mm., and its weight per kilometre is 160 "4 kilogrammes.

230. When the poles of a voltaic cell are connected by a conductor of resist-
ance I, a current of strength i'32 is produced ; and when they are connected by a
conductor of resistance 5 the strength of the current is 0*33. Find from these data
the internal resistance and the electromotive force of the cell. Ahs. R = \ £ = 176.

231. A silver wire is joined end to end to an iron wire of the same length, but of
double the diameter, and six times the specific resistance ; the other ends are joined
to the battery, the current of which is transmitted for five minutes, during which time
a total quantity of 45 units of heat is generated in the two wires. How is it shared
between them ? Ans. Ag : Fe= 18 : 27.

232. A window casement of iron faces the south, and the hinges which support it
are on the east. What electrical phenomena are observed {a) when the window is
opened, and {b) when it is closed ?

233. Two points 135° apart in a uniform circular conducting ring are connected
with the opposite poles of a voltaic battery. Compare the strength of the current in
the two portions of the ring.

234. A mile of cable with a resistance of 3 '59 ohms was put in water, with the
end B insulated ; its core having been pricked with a needle the resistance tested from
the end A was found to be 2 'Si ohms. A being insulated, a test from B showed the
resistance to be 276. Required the distance from A to the injured spot.

Ans. 867 yards.

INDEX.

(THE NUMBERS KKFER TO TIIK ARTICLES.)

AV.K

ABEL'S electric fuse, 794
Aberration, chromatic, 5S3 ;
spherical, 533

Absolute electrical units, 963

Absolute expansion of mercury, 322

Absolute measure of electrical resistance,
954 ; temperature, 496

Absorbent power of aqueous vapour, 985

Absorbing power, 424

Absorption, electrical, 74S ; of gases by
solids, 193 ; of gases l3y liquids, 189 ;
of heat by liquids, 434 ; by vapours,
435 ; heat produced by, 4S2

Acceleration of a force, 27, 6ia, 77

Accidental haloes, 627 ; images, 626 ;
magnetic variations, 694

Accommodation (of the eye), 620

Accumulator, hydraulic, 151

Accumulators, 765

Achromatism, 584 ; of the microscope,
592

Achromatopsy, 632

Acidometer, 126

Acierage, 857

Aclinic lines, 698

Acoustics, 220-287

Acoustic foci, 237 ; attraction and repul-
sion, 290

Actinic rays, 433, 573

Action and reaction, 39

Adhesion, 86

Aerial meteors, 975 ; perspective, 618

Aerolites, 480

.^sculine, 582

Affinity, 85

After action, elastic, 91

Agents, 6

Agonic line, 692

Air, aspirating action of currents of, 207 ;
causes which modify temperature of,
974, 1006; heating by, 491 ; thermo-
meter, 334; resistance of, 48; trap,
167

ANN

Air-balloons, 196 ; chamber, 217
Air-brake, 209 ; pump, 200, 467 ; Bian-
chi's, 203 ; condensing, 209; Deleuil's,

204 ; gauges, 2Ci ; rarefaction in,
200 ; receiver of, 200 ; Sprengel's,

205 ; uses of, 2IO
Ajutage, 146
Alarum, electric, S97
Alcarrazas, 373

Alcoholic value of wines, 378

Alcoholometer, 128; Gay-Lussac's, 1285
centesimal, 128

Alcohol thermometer, 306

Allotropic states, 457

Alloys, 340

Alternate currents, 914

Amalgam, 754

Amalgamated zinc, 816

Amber, 723

Amici's camera lucida, 603

Ampere, 814

Ampere's inemoria tcclinica, S20 ; theory
of magnetism, 879 ;

Amplitude of vibration, 55

Analogous pole, 732

Analyser, 656

Analysis, spectral, 575 ; of solar light, 430

Anamorphoses, 534

Anelectrics, 724, 748

Anelectrotonus, 828

Anemometer, 974, 975

Aneroid barometer, 164, 187

Angle of deviation, 544, 1002 ; critical
540;. optic, 617; of polarisation, 654
of reflection and incidence, 511, 536
of repose, 39 ; of refraction, 536
visual, 617

Angular currents, laws of, 860 ; velocity,

Animal heat, 485
Anione, 842
Annealing, 90
Annual variations, 693

1064

Index.

ANO

Anode, 842

Anticyclone, 980

Antilogous pole, 732

Anvil, 922

Aperiodic galvanometer, 821

Aperture of a lens, 558

Aplanatic lenses, 558

Aqueous humour, 61 2

Aqueous vapour, its influence on climate,
985 ; tension of, 355-361

Arago's experiment, 181

Arbor Diana;, 853 ; Saturni, 853

Arc lamps, 838

Arc of vibration, 55 ; voltaic, 833

Archimedes' principle, 113; applied to
gases, 195

Area, unit of, 22

Armatures, 718 ; drums, 918 ; Siemens',
914

Arms of levers, 40

Armstrong's hydro-electric machine, 758

Artesian wells, ill

Artificial magnets, 680

Ascension, right, 600

Ascent of liquids in capillary tubes, 132 ;
between surfaces, 133

Aspirating action of air currents, 207

Astatic currents, 873 ; needle and system,
700 ; circuits, 873

Astronomical telescope, 595

Athermancy, 434

Atmolysis, 190

Atmosphere, its composition, 157; crush-
ing force of, 159 ; amount of, determi-
nation of, 163 ; electricity in the, 993,

994 ; moisture of, 400
Atmospheric electricity, causes of, 994,

995 ; pressure, 158, 163, 972
Atomic heat, 458 ; weight deduced from

specific heal, 458

Atoms, 3

Attraction, capillary, 134 ; and repulsion
produced by capillarity, 134; mole-
cular, 83 ; universal, 66

Attractions, magnetic, laws of, 703 ;
electrical, laws of, 734

Atwood's machine, 77

Audiometer, 932

Aura, 764

Aurora Ijorealis, 694, 1002

Aurum musivum, 754

Austral pole, 689

Avoirdupois, 23

Axis of crystal, 640 ; electric, 732 ;
lenses, 55 1 ; optic, 617 ; of a magnet,
681 ; of oscillation, 79

Azimuthal circle, 695

BAD conductors, 404
Bain's electro-chemical telegraph,.
895

Balance, 71 ; beam of, 72 ; compensat-
ing, 320 ; delicacy of, 73 ; hydrostatic,
120 ; induction, 932 ; knife-edge of,
71; pendulum, 320; physical and
chemical, 74 ; spring, 88 ; torsion, 89,
704, 733

Ballistic galvanometer, 821 ; pendulum,
81

Balloons, 195-199 ; construction and
management of, 197 ; Coxwell's, 96 j
Mcntgolfier, 196 ; weight raised by,
199

Bands of spectrum, 576

Barker's mill, 149

Barometers, 164; aneroid, 187; Bun-
ten's, 167; cistern, 165; corrections
in, 170 ; determination of heights by,
178; differential, 186; fixed, 175;
Fortin's, 166 ; Gay-Lussac's, 167 ;
glycerine, 176; precautions with, 168;
wheel, 174; variations of height of,
171

Barometric formula, Laplace's, 178 ;
gradients, 979 ; height of, corrected
for heat, 327 ; manometer, 186 ; va-
riations, 172

Baroscope, 195

Bassoon, 272

Battery, Bunsen's, Sio ; Callan's, 810;
chemical efi'ects of, S41 ; Daniell's,
808 ; electric, 774 ; floating, 865 ;
gas, 850 ; gravity, S12 ; Grove's, 809 ;
Leclanche's, 844 ; Leyden, constant,
807 ; charged by coil, 923 ; local,
877 ; luminous effects, 833 ; magnetic,
717 ; measurement of charge, 777 ;
mechanical oflects of, 839 ; Menotti's,
812 ; Marie Davy's, S12 ; postal, 877 ;
secondary, 849 ; Smee's, 811 ; sulphate
of mercury, S12 ; tension of, 815 ;
thermo-electric, 944 ; voltaic, 804,
S05 ; Walker's, 811 ; \Vollaston's, 805

Beam of a balance, 72 ; of a steam-
engine, 467

Beats, 262

Bcaume's hydrometer, 127

Becquerel's pyrometer, 949 ; thermo-
electric battery, 944 ; electrical ther-
mometer, 948

Bell of a trumpet, 237

Bell's telephone, 930 ; photophone, 936

Bellows, 243 ; hydrostatic, lOl ; water,
207

Bennett's clecUoscopc, 751

Index.

1065

BER

Berthollet's experiment, 188

Berlin's commutator, 870

Bianchi's air-pump, 203

Biaxial crystals, double refraction in,
644 ; optic axis of, 644 ; rings in,
667

Bifurcation, 639

Binnacle, 697

Binocular vision, 621

Biot's apparatus, 676

Biquartz, 677

Black's experiments on latent heat, 461

Bladder, swimming, liS

Block and tackle, 45

Blood-globules, 15

Blue cloud, 986

Bodies, properties of, 7, 122

Bohnenberger's electroscope, 818

Boiler, 466

Boiling, 350 ; by cooling, 367 ; laws of,
363

Boiling-point, influence of dissolved sub-
stances on, 365 ; of nature of vessel,
366 ; of pressure on, 367 ; in a ther-
mometer, 302 ; measurement of heights
by, 369

Bolometer, 960

Borda's method, 75

Boreal pole, 689

Bottomley's experiment, 990

Boutigny's experiments, 3S5

Boxes, resistance, 753

Boyle's law, 1S0-182

Boys's threads, 89

Brake, friction, 473 ; air, 209

Bramah's hydraulic press, 108

Branch currents, 961

Breaking weight, 91

Breezes, land and sea, 977

Breguet's thermometer, 309 ; magneto-
electrical machine, 912

Bridge, Wheatstone's, 956

British imperial yard, 22 ; and French
system of weights and measures, 125

Brittle bodies, 93

Browning's regulator, 836

Brush discharge, 787 ; dynamo-electrical
machine, 919

Bulbs, specific gravity, 123

Bull's eye, 591

Bunsen's filter-pump, 206 ; battery, 810;
burner, 576 ; ice calorimeter, 452 ;
photometer, 509

Bunsen and KirchhofPs researches, 578

Bunten's barometer, 167

Buoyancy of liquids, 100

Burning mirrors, 420

CHE

CABLE telegraph, 886
Caesium, 578

Cagniard-Latour's syren, 242 ; experi-
ments on formation of vapour, 370

Cailletet's and Pictet's researches, 382

Calibration. 298

Callans battery, 81 1

Calorcscence, 433

Caloric, 448

Calorific effects of electrical discharge,
790 ; of current electricity, 829, 830 ;
of Ruhmkorff's coil, 923 ; of the spec-
trum, 573

Calorimeter, 450; Bunsen's ice, 451;
Black's, 451 ; Favre and Silbermann's,
463 ; Lavoisier and Laplace's, 45 1

Calorimetry, 447

Camera lucida, 594 ; Amici's, 603 ; ob-
scura, 602; Porta's obscura, 514 ^
Wollaston's, 603

Campani's eyepiece, 592 ^

Capacity, error of barometric, 165 ; elec- y

trical, 739 ; specific inductive, 748

■Capillarity, 131 ; attraction and repulsion
produced by, 134 ; correction for, 169

Capillary phenomena, 131-138; electro-
meter, 840 ; tubes, 132 ; ascent and
depression in, 132; between parallel
or inclined surfaces, 133

Capsule, of the eye, 612

Carcel lamp, 849

Cardan's suspension, 166

Carre's mode of freezing, 374 ; dielectri-
cal machine, 760

Carriage lamps, 535

Carrier, electrical, 735

Cartesian diver, 116

Cascade, charging by, 776

Cataracts of a .^team engine, 467

Cathetometer, 88

Catoptric telescopes, 598

Caustics, 533, 534

Celsius' scale, 303

Centesimal alcoholometer, 128

Centigrade scale, 303

Centimetre, 125

Centre, optical, 555 ; of gravity, 68 ; of
parallel forces, 37 ; of pressure, 102

Centrifugal force, 53

Centripetal force, 53

Charge of a Leyden jar, penetration of>
773 ; measurement of, 787 ; laws of,
778 ; residual, 773

Charging by cascade, 776

Chatterlon's compound, 886

Chemical affinity, 85 ; combination, 483 ;
effects of the battery, 793 ; decomposi-

io66

Index.

CHE

tion, 841 ; of electrical discharge, 793;
of voltaic currents, 821 ; of Ruhmkorff's
coil, 923 ; harmonicon, 278 ; hygro-
meter, 394; properties of the spectrum,

573

Chemistry, i

Chevallier's microscope, 591

Cheval-vapeur, 473

Children's experiment, 830

Chimes, electrical, 763

Chimney, 487

Chladni's experiments, 284

Chlorophane, 635

Chlorophyl, 580

Chords, major and minor, 247 ; physical
constitution of, 264 ; tones dominant
and subdominant, 248 ; vocal, 259

Choroid, 612

Chromatic scale, 250 ; aberration, 583

Chromium, magnetic limit of, 720

Ciliary processes, 612

Circle, azimuthal, 695

Circular polarisation, 669

Cirrocumulus, 981

(Jirrostratus, 981

Cirrus, 981

Cistern barometer, 165

Clamond's thermo-electric battery, 945

Clarionet, 272

Clarke's magneto-electrical machine, 911

Cleavage, electricity produced by, 731

Clef, 252

Clement and Desorme's experiment, 207

Climate, 1008; constant, 1008; influence
of aqueous vapour on, 985

Climatology, 1004-1011

Clocks, 81 ; crutch of, 81 ; electrical, 898

Clouds, 981 ; electricity of, 996; forma-
tion of, 982

Coatings, 769 ; Lcydcn jar with movalile,
771

Cobalt, 720

Coercive force, 687

Coefficients of linear expansion, 313, 315,
316; conductivity, 404, 405; I'oisson's,
88

(.'ohesion, 84

(^oil, primary, 879 ; Ruhmkorff's, 914 ;
effects produced by, 914 ; resistance,
953 ; secondary, 879

Cold, apparent reflection of, 422 ; pro-
duced by evaporation, 373 ; ex])ansion
of gases, 494; by nocturnal radiation,
495 ; sources of, 493

Colladon and Sturm's exjicrimcnts, 234

Collecting plate, 779

Collimation, 595

CON

Collision of bodies, 58

Colloids, 140

Coloration produced by rotatory polari-
sation, 675

Colour, 7 ; of bodies, 592 ; of heat, 436;
of thin plates, 650

Colour discs, 570

Colour disease, 632

Co'ours, contrast of, 627 ; mixed, 570 ;
simple, 566 ; complementary, 570 ;
produced by polarised light, 662-668 ;
by compressed glass, 668

Combustion, 483 ; heat disengaged dur-
ing, 484

Comma, musical, 248

Common reservoir, 726

Communicator, 886

Commutator, 887, S89, 912, 922 ; Ber-
tin's, 870

Compass, correction of errors, 696 ; de-
clination, 695 ; mariner's, 697 ; incli-
nation, 698 ; sine, 824 ; tangent, 823

Compensating cube, 438

Comjicnsation, method of magnets, 719;
pendulum, 320 ; balance, 320 ; grid-
iron, 320; strips, 320

Complementary colours, 570

Component forces, 32

Composition of velocities, 52

Compound-wound microscope, 591 ; dy-
namo, 919^

Comjiressed glass, colours produced by,
668

Compressibility, 7, 16 ; of gases, 154,
180 ; of liiiuids, 97

Concave mirrors, 419, 528

Concert pitch, 251

Concordant tones, 247

Condensatii)!! of vapours, 375

Condensed gas, 193, 209; wave, 225

Condenser of an engine, 467, 759, 765 ;
electrical limits to charge of, 768 ; of
Ruhmkorff's coil, 922 ; Liebig's, 377

Condensing engine, 471 ; air-pump, 209 ;
force, calculation of, 767 ; electro-
scope, 779 ; plate, 799 ; hygrometers,
395

Conduction of heat, 403 ; of electricity,
725 ; lightning, I(X)I

Conducli\ity of bodies for heat, 404 ; co-
efficient of, 404, 405 ; of gases, 409 ;
of li(|uiils, 407 ; for electricity, 955, 958

Con<luclors, 725 ; equivalent, 956 ; good
and bad, 404; lightning, looi ; prime,
753 ; resistance of, 952

Congelation, 343

Conjugate mirrors, 420 ; focus, 525, 552

Index.

1067

CON

Connecting rod, 467

Conservation of energy, 65

Constant currents, 807

Contact theory of electricity, 799

Contractile force, 319

Contraction, coefficient of, S8

Convection, 40S ; currents, 445 ; electro-
lytic, 832

Convex meniscus, 131 ; mirrors, 526, 529

Cooling, method of, 455 ; Newton's law
of, 416

Corliss engine, 47 1

Cornea, 612

Cornish engine, 467

Corona, 981

Corpuscular theory, 499

Corti's fibres, 260

Cosine, law of the, 414, 508

Coulomb, 964

Coulomb's law, 703

Couple, 36 ; terrestrial magnetic, 690 ;
voltaic, 801 ; thermo-electric, 942

Couronne des tasses, 805

Cowper's writing telegraph, 890

Coxwell's balloon, 196

Crab, 42

Critical angle, 540 ; current, 920 ; tem-
perature, 370

Crookes's radiometer, 445 ; vacuum, 380,
446; experiments, 927

Cross-wire, 595

Crutch of a clock. Si

Cryohydrate, 348

Cryophorus, 373

Crystal, hemihedral, 732

Crj-stalline, 612

Crj'stallisation, 344

Cr)-stalloids, 140

Crystals, 343; expansion of, 315; doubly
refracting, 639, 652, 663 ; uniaxial,
642 ; positive and negative, 643

Cube, Leslie's, 423

Cumulostratus, 980

Cumulus, 980

Current electricity, 800

Currents, action on currents, 862, 863 ;
action of magnets, 866 ; action of
earth on, 872, 873 ; action on sole-
noids, S74, 879 ; constant, 807 ; di-
vided, 961 ; detection and measure-
ment of voltaic, 819; diaphragm, 839;
direct and inverse, 900, 901, 908;
effects of enfeeblement of, 806 ; energj' j
of, 920 ; extra, 907, 908 ; of inclina- ;
tion, 967 ; intensity of, 825 ; indue- 1
tion by, 900 ; laws of angular, 860 ;
laws of sinuous, 861 ; local, 816 ; |

magnetisation by, 871 ; motion and
sounds produced by, 884 ; muscular,
966 ; in active muscle, 969 ; in nerve,
970 ; rotation of magnets by, 856 ;
secondary, 806 ; terrestrial, 8S0 ; ther-
mal effects of, 830, 831 ; transmissions
by, 844

Curvature of liquid surfaces, 135 ; in-
fluence of, on capillary phenomena, 136

Curves, magnetic, 704

Cushions, 753

Cyanogen gas, 380

Cyclones, 979

Cylinder, 467 ; electrical machine, 757

Cymbal, 282

DAGUERREOTYPE, 608
Daltonism, 632

Dalton's laws on gases and vapours, 383;
method of determining the tension of
aqueous vapour, 356

Damper, 279, 905

Daniell's battery, 808 ; hygrometer, 396;
pyrometer, 311

Dark lines of the spectrum, 574 ; of
solar spectrum, 579

Davy's battery, 812

Davy's experiment, 421

Day, apparent, 21

Dead-beat galvanometer, 821 ; -point, 470

Decimetre, 24, 125

Declination compass, 695 ; errors of,
696; magnetic, 691 ; of needle, 691 ;
variations in, 691 ; of a star, 600

Decomposition, chemical, 841 ; of white
ligli^ 564 ; of salts, 843

Deilagrator, Hare's, 805, 829

Degrees of a thermometer, 303

De la Rive's floating battery, 867 ; ex-
periments, 928

De la Rue and Midler's experiments, 926

Deleuil's air-pump, 204

Delezenne's circle, 906

Delicacy of balance, 73 ; of thermo-
meter, 307

Densimeter, 130

Density, 24 ; of the earth, 67 ; electric,
736; gravimetrical, 185 ; oi gases, 335-
337; maximum of water, 330 ; of-
vapours, Gay-Lussac's method, 386 ;
Dumas's, 388 ; Deville and Troost's,
388 ; Ilofmann's, 387

Depolarisation, 665

Depolarising plate, 663

Depression of liquids in capillary tube,
132 ; between surfaces, 133

io68

Index.

Derived currents, 961
Descartes' laws of refraction, 537
Despretz's experiment, 404
Developer, 609
Deviation, angle of, 544
Deville and Troost's method, 388
Dew, 987 ; point, 395
Diabetic urine, analysis of, 678
Dial telegraphs, 888
Dialyser, 140
Dialysis, 140
Diamagnetism, 938
Diapason, 257
Diaphanous bodies, 500
Diaphragm, 591 ; currents, 839
Diathermancy, 434
Diatonic scale, 248
Dielectrical machine, Carre's, 760
Dielectric polarisation, 747
Dielectrics, 748
Differential barometer, 186
Differential galvanometer, 821 ; tl-ermo-
meter, Leslie's, j08 ; Matthiessen's,
308 ; tone, 263
Diffraction, 503 ; spectra, 648 ; fringes,

646
Diffusion of heat, 437; of liquids, 140
Digester, Papin's, 371
Dimensions of units, 6i«
Dionoea muscipula, 827
Dioptric telescopes, 598
Diosmose, 137
Diplopy, 631
Dip, magnetic, 698
Dipping needle, 698
Direct Vision Spectroscope, 511
Disc, Newton's, 567 ; Maxwell's colour,
570

Discharge, electrical, 766 ; effects of the,
783 ; lateral, looi ; silent, 793, slow
and instantaneous, 766 ; universal, 775

Discharging rod, 766

Dispersion, 544 ; abnormal, 581

Dispersive power, 564

Displacement, 46

Disruptive cischarge, 783

Dissipation of energy, 498

Dissociation, 389, 484, 845

Dissolving views, 604

Distance, estimation of, 618; adaptation
of eye to, 620

Distillation, 376

Distrilaition of free electricity, 735 ; of
magnetism, 722 ; of temperature,
1009 ; of land and water, loi I

Diurnal variations, 693

Diver, Cartesian, 116

EDE

Divided currents, 961

Dividing machine, 1 1

Divisibility, 7, 12

Dobereiner's lamp, 482

Dominant chords, 248

Doppler's principle, 233

Double-action steam-engine, 467, 468

Double refraction, 652

Double-weighing, 75

Doublet, Wollaston, 586

Dove's law of storms, 97S

Draught of fire-places, 48S

Dredging machines, 150

Driving wheels, 470

Drum armature, 918

Drummond's light, 606

Dry piles, 817 ; plates, 610

Duboscq's microscope, 606 ; regulator,^

835
Ductility, 7, 92

Duhamel's graphic method, 245
Dulong and Arago's experiments on
Boyle's law, 181 ; method of deter-
mining the tension of aqueous vapour,

357 , ,

Dulong and Petit's determmation of ab-
solute expansion of mercury, 322 ;
method of cooling, 455 ; law, 458
Dumas's method for vapour density,

388
Duplex telegraphy, 893
Duration of electric spark, 795
Dutroche's endosnn)nieter, 139
Dynamical theory of heat, 429
Dynamic radiation and absorption, 442
Dynamo-electrical machine, 916-918
Dynamo-magnetic machine, 916
Dynamometer, 90
Dyne, b\a

EAR, the, 7, 260
Ear trumpet, 239

Earnshaw on velocity of sound, 230

Earth, density of, 67 ; its action on
currents, 87 1-S73 ; action of solenoids,
878 ; current, 894 ; flattening of, by
rotation, 82 ; magnetic poles of the,
698 ; magnetisation by, 714

Earth's magnetism, 701

Ebullition, 350 ; laws of, 363

Eccentric, 467, 468

Eclielon lenses, 607

Echoes, 237 ; monosyllabic, Irisyilabic,-
mulliple, 237

Eddy currents, 929

Edehnann's hygrometer, 394

Index.

1069

EDI

Edison's Inmp, 838 ; phonograph, 291 ;
tasimeter, 933 ; telephone, 934

Efficiency of a machine, 451 ; of heat
engines, 454

Effluvium electrical, 793

Efflux, velocity of, 142 ; quantity of,
145 ; influence of tubes on, 146

Effusion of gases, 191

Elastic bodies, 58 ; after action, 91

Elastic force, 152; of vapours, 351

Elasticity, 7, 17 ; limit of, 17, 88; .of
traction, 88 ; modulus of, 88 ; of tor-
sion, 89 ; of flexure, 90

Electric alarum, 897 ; axis, 732 ; bat-
teries, 774, 789 ; candles, 838 ; charge,
778 ; chimes, 763 ; clocks, 898 ; den-
sity, 736 ; discharge, 783 ; egg, 788 ;
fish, 971 ; fuse, 794; glow, 787 ; lamp,
838 ; light, 831-833 ; stratification of
the, 924 ; lighting, 838 ; pendulum,
724 ; pistol, 793 ; poles, 732 ; residue,
773 ; shock, 770, 785 ; spark, 762 ;
telegraphs, 886-899 ; tension, 736 ;
whirl, 764 ; tube, 7S9

Electrical attractions and repulsions,
734 ; endosmose, 839 ; field, 738 ; po-
tential, 738 ; capacity, 739 ; measure-
ment of, 740 ; resistance, unit of, 954 ;
conductivity, 958 ; quantity, 7-33 ; units,

963

Electrical machines, 752-761 ; precau-
tions in, 754

Electricity, 6, 723 ; application of, to
medicine, 972 ; atmospheric, 992-
looi ; contact theory, 799 ; current,
800 ; communication of, 749 ; de-
velopment of, by friction, 724 ; by
jDressure and cleavage, 731 ; distribu-
tion of, 735 ; dynamical, 797-961 ;
disengagement of, in chemical actions,
793-799 ; frictional, 730 ; loss of,
743 ; mechanical effects, 792 ; power
of points, 742 ; produced by induction,
744 ; velocity of, 796 ; theories of,
728 ; work required for production of,
761

Electrified bodies, motion of, 729, 750

Electro-capillary phenomena, 840

Electrochemical equivalent, 844 ; tele-
graph, 895 ; series, 842

Electrodes, 803 ; polarisation of, 806

Electrodynamics, 858

Electrodynamometer, 962

Electro;;ilding, 855

Electrolysis, 842 ; laws of, 846

Electrolyte, 842

Electrolytic convection, 832

EXO

Electromagnetic force, 883 ; machines,
899 ; units, 963

Electromagnets, 880, 884

Electrometallurgy, 854, 855

Electrometer, 751; Lane's, 777; quad-
rant, 756 ; Thomson's, 780

Electromotive series, 801 ; force, 802,
814, 825, 959 ; determination of, 959 ;
force of elements, 814

Electromotor, 886

Electrophorus, 752

Electropyrometer, 949

Electroscope, 724 ; Bohnenberger's, 818;
Volta's condensing, 779 ; gold leaf, 751

Electrosilvering, 8 56

Electrostatic units, 963

Electrotonus, 828

Elements, electronegative and electro-
positive, 842

Elliptical polarisation, 672

Emergent rays, 542

Emission theory, 499

Emissive power, 425

Emulsions, 140; gelatine, 610

Endosmometer, 135

Endosmose, 139; electrical, 839; of
gases, 190

Endosmotic equivalent, 139

Endothermic reactions, 484

Energy, 62 ; conservation of, 65 ; dissi-
pation of, 498 ; transformations of, 64 ;
varieties of, 63

Engines, gas, 476 ; steam, 465 ; double-
action, 467 ; low and high pressure,
471 ; single action, 469 ; locomotive,
470 ; fire, 219 ; transformation of, 64;
Cornish, 467 ; horizontal, 468 ; work
of, 472 ; heat, 474 ; hot air, 475

Equator, 681 ; magnetic, 698

Equilibrium of forces, 35 ; of floating
bodies, 115 ; of heavy bodies, 69 ; of
liquids, 106, 107 ; mobile of tempera-
ture, 414 ; neutral, 70 ; stable, 70 ;
unstable, 70

Equivalent, electrochemical, 846 ; en-
dosmotic, 139 ; conductors, 955

Escapement, 81 ; wheel. Si

Ether, 429 ; luminiferous, 499

Eustachian tube, 260

Evaporation, 350 ; causes which accele-
rate it, 362 ; cold due to, 373 ; latent
heat of, 372

Evaporation and ebullition, 364

Exchanges, theory of, 415

Exhaustion, produced by air-pump, 203 ;

by Sprengel's pump, 205
Exosmose, 139

I070

Index.

EXO

Exothermic reactions, 484

Expanded wave, 225

Expansibility of gases, 147

Expansion, 296 ; apparent and real, 32 1 ;
al)SoIute, of mercury, 322 ; apparent,
of mercury, 323 ; of liquids, 326 ; of
solids, 313 ; of gases, 331-333 ; linear
and cubical, coefficients of, 313 ;
measurement of linear, 314 ; of crystals,
318; applications of, 319; force of,

329

Expansion of gases, cold produced by,
494 ; problems on, 332

Expansive force of ice, 346

Experiment, Berthollet's, 188; Frank-
lin's, 368 ; Florentine, 97 ; Pascal's,
162 ; Torricellian, 161

Extension, 7, 9

Extra current, 907, 908 ; direct, 90S ;
inverse, 908

Eye, 612 ; accommodation of, 620; not
achromatic, 628 ; refractive indices of
media of, 613; path of rays in, 615;
dimensions of various parts of, 614

Eye-glass, 544, 630 ; lens, 592 ; piece,
583, 590, 592 ; Campani's, 592

FAHRENHEIT'S hydrometer, 123 ;
scale, 303

Falling bodies, laws of, 76

Falsetto notes, 259

Farad, 964

Faraday's experiments, 745 ; wheel, 625 ;
theory of induction, 747 ; voltameter,
846

Favre and Silljermann's calorimeter,
463 ; determination of heat of com-
bustion, 483

Fibres, Corti's, 260

Field lens and glass, 592

Field magnets, 915

Field of a microscope, 591 ; of view,
593 ; magnetic, 707

Figures, Lichtenberg's, 772

Filter-pump, 206

Filters, 15

Finder, 595

Fire-engine, 219; -places, 487 ; -works,
149 ; -ball, 997

Fish, electrical, 971

Fishes, swimming bladder of, 117

Fizcau's experiments, '3'^') 5'-'7

Flag signals, 887

Flame, 483

Flame, 483 ; sensitive, 278

Flask, specific gravity, 121

Flattening of the earth, 82

Flexure, elasticity of, 90

Float, 466

Floating bodies, 115

Florentine experiment, 13, 97

Fluid, 4 ; imponderable, 6 ; elastic, 152 ;
magnetic, 683

Fluidity, 7

Fluorescence, 582

Flute, 280

Fluxes, 340

Fly-wheel, 467

Focal distance, 419

Foci, acoustic, 237 ; magnetic, 701 ; of
convex mirrors, 526 ; in double convex
lenses, 552

Focus, 419, 525 ; of a parabola, 143 ; con-
jugate, determination of the principle,
527 ; of a spherical concave mirror>
525> 552

Focussing the microscope, 587, 591

Fog-signal, 242

Fogs, 980

Foot, 22

Foot-pound, 61, 473

Force, 26 ; acceleration of, 77 ; centri-
i fiigal) 53 ; conservation of, 65 ; coer-
' cive, 687 ; direction of, 30 ; elastic,
of gases, 152 ; Unes of magnetic, 707 ;
of expansion and contraction, 319;
electromotive, 802, 814 ; representation
of, 30 ; parallelogram of, 33 ; of liquids,
329 ; portative, 719

Foices, 6; along the same line, 31;
equilibrium of, 38 ; impulsive, 60 ;
magnetic, 708 ; molecular, S3 ; mo-
ments of, 38 ; polygon of, 35 ; triangle
of, 35

Formula; for expansion, 318 ; barome-
tric, 178 ; for sound, 231 ; for splieri-
cal mirrors, 530, 531 ; for lenses,
559

Fortin's barometer, 166

Foucault's currents, 929 ; determination
of velocity of light, 506 ; experiment,
834. 929

Fountain in vacuo, 210 ; at Giggleswick,
214 ; intermittent, 212 ; Hero's, 21 1

Fovea centralis, 612

Franklin's experiment, 368, 992 ; plale,
769 ; theory of electricity, 728

Fraunhofer's lines, 574, 575

Freezing, apparatus for, 374

Freezing mixtures, 347, 34S ; point in a^
thermometer, 302

French weights and measures, 123 ;
boiler, 466

Index.

1071

FRE

Fresnel's experimentum crucis, 645 ;
rhomb, 671

Friction, 26, 44, 47 ; heat of, 477 ; hy-
ciraulic, 146 ; internal, of Hquids, 48,
147 ; of gases, 446 ; development of elec-
tricity by, 720

Friction wheels, 77

Frigorilic rays, 422

Fringes, 646

Frog, rheoscopic, 968

Frost, 987

Frozen mercury, 373, 380, 384

Fulcrum, 44

Fulgurites, 999

Fulminating pane, 769

Furnace, electrical, 821

Fuse, Abel's, 794 ; Chatham, S29, 830
, Fusing point, 338

Fusion, laws of, 338 ; vitreous, 338
latent heat of, 461 ; of ice, 450

GALILEAN telescope, 597
Galleries, whispering, 237

Gallium, 578

Gallon, 125

Galvani's experiment, 797

Galvanometer, 821 ; differential, 821 ;
Sir W. Thomson's, 822

Galvanoscope, 821

Galvano-thermometer, 830

Gas battery, 850 ; engines, 476

Gases, absorption of, by liquids, 189 ;
by solids, 193 ; by vapours, 435 ;
appHcation of Archimedes' principle
to, 195 ; cold produced by expansion
of, 494; compressibility of, 154, iSo ;
condensed, 193, 209 ; conductivity of,
409 ; diamagnetism of, 937 ; density
of, 335-337 ; dynamical theory of,
293; expansion of, 153, 331-334;
endosmose of, 190 ; effusion, 191 ;
transpiration of, 192 ; Gay-Lussac's
method, 331 ; index of refraction of,
550 ; laws of mixture of, 188 ; and
vapours, mixtures of, 383 ; permanent,
380 ; problems in, 332, 3S3 ; lique-
faction of, 380 ; physical properties of,
152 ; pressure exerted by, 156 ; radia-
tion of, 441 ; Regnault's method, 336 ;
specific heat of, 460 ; velocity of sound
in, 230, 231, 232 ; viscosity of, 446 ;
weight of, 155

Gaseous state, 4

Gassiott's battery. Si 5

Gauge, air-pump, 201 ; rain, 983

Gay-Lussac's alcoholometer, 128 ; baro-

meter, 167 ; determination and expan-
sion of gases, 331 ; of vapour-density,
385 ; stopcock, 382

Geissler's tubes, 205, 578, 925

Generating plate, Soi

Geographical meridian, 691

Geometrical shadows, 503

Giffard's injector, 207

Gilding metal, 855

Gimbals, 697

Glacial pole, 1009

Glaciers, 991

Glashier's balloon ascents, 196 ; factors,
398

Glass, compressed, 668 ; expansion of,
325 ; magnifying, 583 ; object, 590 ;
opera, 597 ; unannealed, 668

Glasses, periscopic, 629 ; weather, 174

Globe lightning, 997

Glow, electrical, 787 ; worm, 635

Glycerine barometer, 176

Gold-leaf electroscope, 751

Goldschmid's aneroid, 182

Gong, 282

Goniometers, 534

Good conductors, 404

Governor, 468

Gradient, barometric, 978

Gramme, 24, 125

Gramme's magneto-electrical machine,9i 7

Graphic method, Duhamel's, 245 ; Fos-
ter's, 831

Graphite, 810

Gratings, 647

Cirave harmonic, 263

(jravesand's ring, 295

Gravimetrical density, 185

Gravitation, 6, 82 ; terrestrial, 67 ; ac-
celerative effect of, 27

Gravity, battery, 812

Gravity, centre of, 68 ; Jolly's determina-
tion of constant of, 75

Gregorian telescope, 599

Gridiron pendulum, 320

Grimaldi's experiment, 645

Grotthiiss' hypothesis, 845

Grove's battery, 809 ; gas, 850

Guericke's air-pump, 200

Guide-blades, 150

Guitar, 279

Gulf Stream, 1006

Guthrie's researches, 348

HADLEY'S reflecting sextant, 521
Hail, 9S9,
Hair hygrometer, 399

lo/:

Index.

Haldat's apparatus, loi

Hall's experiment, 88 1

Hallstrom's experiments, 329

Haloes, 627, 646, 981

Hammer, 279, 921

Hardening, 90

Hardness, 7 ; scale of, 93

Hare's deflagrator, 805, S29, 830

Harmonicon, chemical, 278

Harmonics, 254, 273

Harmonic triad, 247 ; grave, 263

Harp, 279 ; Marloye's, 281

Harris's unit jar, 778

Heat, 292 ; animal, 485 ; absorption of,
by vapours, &c., 435, 439 ; atomic,
458 ; conduction of, 403 ; diffusion of,
437 ; developed by induction, 929 ;
dynamical theory of, 429 ; hypothesis
on, 292 ; influence of the nature of,
435 ; latent, 341 ; mechanical equi-
valent of, 497 ; polarisation of, 679 ;
produced by absorption and imbibi-
tion, 482 ; radiated, 403 ; radiant,
411, 4.46a; reflection of, 418; scat-
tered, 424; sources of, 477-496;
specific, 448, 454-460 ; transmission
of, 403 ; terrestrial, 481

Heaters, 466

Heating, 486 ; by steam, 490 ; by hot
air, 491 ; by hot water, 492

Height of barometer, 165 ; variations
in, 171

Heights of places, determination of, by
barometer, 178, 179 ; by Ijoiling point,

369

Heliograph, 523

Heliostat, 534

Helix, 45, 8S2

Helmholtz's analysis of sound, 255 ; re-
searches, 258

Hemihedral crystal, 732

Hemispheres, Magdeburg, 160

Henley's electrometer, 756 ; discharger,
792

Henry's experiment, 909

1 fcrepath's salt, 656

Hero's fountain, 211

Ilerschelian rays, 430 ; telescope, 601

Ilirn's experiments, 474

I loar-frost, 9S7

llofmann's density of vapours, 387

Holmes's magneto-electrical machine, 913

I loltz's electrical machine, 759

Homogeneous light, 572 ; medium, 502

I lope's experiments, 330

I Ic^rizontal line, 67 ; plane, 67

Horse-power, 61, 472

Hot-air engines, 475, 491

Hotness, 297

Hot-water, heating by, 492

Hour, 21

Howard's nomenclature of clouds, 981

Hughes's microphone, 931 ; induction
balance, 932

Humour, aqueous, 612

Huyghen's barometer, 177

Hyaloid membrane, 612

Hydraulic press, 108 ; engine, 151 ; fric-
tion, 146 ; lift, loS ; ram, 150; tourni-
quet, 149

Hydraulics, 95

Hydrodynamics, 141

Hydro-electric machine, 758 ; currents,
939

Hydrometers, 119; Nicholson's, 120;
Fahrenheit's, 123 ; with variable
volume, 126; Beaume's, 127; of con-
stant volume, 126 ; specific gravities,
119 ; uses of tables of, 125

Hydrostatic bellows, loi ; paradox, 103 ;
balance, 120

Hydrostfitics, 95 -98

Hygrometers, 393 ; of absorption, 399 ;
chemical, 394 ; condensing, 395 ;
Daniell's, 396 ; wet -bulb, 398; Mason's,
398 ; Regnault's, 397

Hygrometric stale, 392 ; substances, 391

Hj'grometry, 391 ; problem on, 401

Hygroscope, 399

Hypothesis, 5

Hypsometer, 369

ICE, 990 ; method of fusion of, 450
Ice calorimeter, 450 ; Bunsen's,
451; expansive force of, 346; ma-
chine, 494

Iceland spar, 659

Idioelectrics, 724

Image and object, magnitudes of, 561

Images, accidental, 626 ; condition of
distinctness of, 587 ; formation of, in
concave mirrors, 528 ; in convex mir-
rors, 529; in plane mirrors, 513; of
multiple, 516; magnitude of, 532;
produced by small apertures, 504 ;
virtual and real, 514 ; inversion of, 616

Imbibition, 193 ; heat produceil by, 4S2

Impenetrability, 7

Imperial British yard, 22

Imponderable matter, 6

Impulsive forces, 57

Incandesceni lamps, 83S

Inch, 125

Index.

1073

INC

Incident ray, 536

Inclination, 708 ; compass, 698

Inclined plane, 43 ; motion on, 50

Index of refraction, 538 ; measurement
of, in solids, 548 ; in liquids, 549 ; in
gases, 550

Indicator, 473, 886, 888, 889

Indices, refractive, table of, 550

Indium, 57S

Induced currents, 900-911

Induction, apparatus founded on, 911 ;
balance, 932 ; by the earth, 905 ; liy
currents, 900 ; of a current on itself,
907 ; electrical, 744 ; in telegraph
cables, 891 ; limit to, 746 ; Faraday's
theory of, 747 ; heat developed by,
929 ; by magnets, 904 ; magnetic, 686 ;
vertical, 715

Inductive capacity, specific, 748

Inductorium, 921

Inelastic bodies, 58

Inertia, 19 ; applications of, 20

Influence, magnetic, 686 ; electrical, 744

Ingenhaus's experiment, 404

Injector, Giffard's, 207

Insects, sounds produced by, 242

Insolation, 635, 636

Instruments, optical, 585 ; polarising,
656 ; mouth, 271 ; reed, 272 ;
stringed, 279 ; wind, 270, 280

Insulating bodies, 726 ; stool, 762

Insulators, 725

Intensity of the current, 825 ; of the
electric light, 837 ; illumination, 508 ;
of reflected light, 519; of a musical
tone, 246 ; of radiant heat, 414 ; of
sound, causes which influence, 226 ;
of terrestrial magnetism, 701 ; of ter-
restrial gravity, 82

Interference of light, 645; of sound, 261

Intermittent fountain, 212 ; springs, 214 ;
syphon, 214

Interpolar, 825

Intervals, musical, 247

Intrapolar region, 828

Inversion of images, 616

I ones, 842

Iris, 612

Iron, passive state of, 851 ; electrical
deposition of, 857

Iron ships, magnetism of, 715

Irradiation, 627

Irregular reflection, 518

Isobars, 979

Isochimenal line, 1007

Isoclinic lines, 698

Isodynamic lines, 701

Isogeothermic lines, 1007

Isogonic lines, 692

Isothcral lines, 1007

Isothermal lines, 466, 1007 ; zone, 1007

T ABLOCIIKOFF candle, 838
I Jacobi's unit, 846, 952
Jar, Leyden, 770-780

Jar, luminous, 785 ; Harris's unit, 778

Tet, lateral, 143 ; height of, 144 ; form
of, 148

Jew's harp, 272

Jolly's spring balance, 88 ; air thermo-
meter, 334

Jordan's barometer, 176

Joule's experiment on heat and work,
497 ; equivalent, 497

Jupiter, 505

Jurin's laws of capillarity, 132

KALEIDOPHONE, 625
Kaleidoscope, 516
Kamsin, 977
Kater's pendulum, 82
Kathelectrotonus, 828
Kathode, 842
Katione, 842
Keepers, 718

Kerr's electro-optical experiments, 937
Key, 887, 906, 912, 922 ; note, 249
Kienmayer's amalgam, 754
Kilogramme, 24, 125
Kilogrammetre, 472
Kinetic energy^ 62
Kinnersley's thermometer, 792
Kirk's ice machine, 494
Knife-edge, 71
Kbnig's apparatus, 256 ; manometric

flames, 288
Kravogl's machine, 899
Kiilp's method of compensation, 719
Kundt's velocity of sound, 277

LABYRINTH of the ear, 260
Lactometer, 129
Ladd's dynamo-electrical machine, 916
Lambert's method, 570
Lamps, incandescent, 836; Dobereiner,

482
Land and water, ion
Lane's electrometer, 777
Lantern, magic, 604
Laplace's barometric formula, 178
Laryngoscope, 563

I074

Index.

Larynx, 259

Latent heat, 341 ; of fusion, 461 ; oi

vapours, 372, 462
Lateral jet, 143
Latitude, magnetic, 698 ; influence of on

the air, 1005 ; parallel of, 82
Lavoisier and Laplace's calorimeter, 450 ;
method of determining linear expan-
sion, 314
Law, 5

Laws of mixture of gases and liquids, 383
Lead tree, 853

Leclanche's elements, 813, 814
Ledger lines, 252
Leidenfrost's phenomenon, 385
Lemniscate, 667

Length, unit of, 22 ; of undulation, 225
Lens, axis of, 551

Lenses, 551-559; achromatic, 582;
aplanatic, 558 ; centres of curvature,
551; combination of, 560; echelon,
607 ; foci in double convex, 552 ; in
double concave, 553 ; formation of
images in double convex, 556 ; in
double concave, 557 ; formulas relat-
ing to, 559 ; lighthouse, 607 ; optical
centre, secondary axis of, 555
Lenz's law, 901
Leslie's cube, 423 ; experiment, 373 ;

thermometer, 308
Level, water, 109; spirit, no
Level surface, 67
Levelling staff, 109
Lever, 40

Leyden discharge, inductive action of, 903
Leyden jars, 770-780 ; charged by
Ruhmkorffs coil, 923 ; potential of,
782 ; work by, 784
Lichlenberg's figures, 772
Liebig's condenser, 377
Lift, hydraulic, 108
Ligament, suspensory, 6l2
Light, 499 ; diffraction of, 646 ; homo
gencous, 569, 572 ; intensity of, 508 ;
interference of, 645 ; laws of reflection
of, 511 ; medium, 502 ; oxyhydrogen,
606 ; polarisation of, 652 ; relative
intensities of, 510 ; sources of, 634
theory of polarised light, 661 ; un-
dulatory theory of, 499, 637 ; velocity
of, 505-507
Lighthouse lenses, 607
Lighting, electric, 838
Lightning, 999 ; ascending, 997; effects
of, 997 ; conductor, lOOl ; globe, 999;
heat, 997 ; brusli, 997 ; flashes, 997 ;
zigzrig. 997

]NL\G

Limit of elasticity, 17; magnetic, 720;

to induction, 746 ; of perceptible

sounds, 244
Line, aclinic, 698 ; of collimation, 595 ;

isoclinic, 698 ; agonic, 692 ; isogenic,

692 ; isodynamic, 701 ; of sight,

595
I^inear expansion, coefficients of, 313,

Lines of magnetic force, 707 ; of elec-
trical force, 738

Lippmann's capillary electrometer, 840

Liquefaction of gases, 380, 381 ; of
vapours, 375

Liquids, 99 ; active and inactive, 667 ;
buoyancy of, lOO ; compressibility of,
97 ; conductivity of, 407 ; calculation
of density of, 107 ; diffusion of, 140 ;
diamagnetism of, 93S ; expansion of,
321 ; equilibrium of, 104; manner in
which they are heated, 408 ; pressure
on sides of vessel, 102 ; refraction of,
549 ; rotatory power of, 676 ; sphe-
roidal form of, 84 ; spheroidal state of,
385 ; specific heat of, 456 ; volatile
and fixed, 349 ; tensions of vapours of,
359 ; of mixed liquids, 360

Lissajous's experiments, 284-2S6

Lithium, 578

Litre, 24, 125

Local action, 806 ; attraction, 715 ; bat-
tery, 889 ; currents, 816

Locatelli's lamp, 428

Locomotives, 470, 471

Lodestone, 680

Long sight, 629

Loops and nodes, 269

Loss of electricity, 743 ; of weight in air,
correction for, 402

Loudness of a musical tone, 246

Lullin's experiment, 792

Luminifcrous other, 499

Luminous bodies, 500 ; effects of the
electric discharge, 773, 833 ; of the
electric current, 923 ; of Ruhmkorfl 's
coil, 923 ; heat, 434 ; jar, 790 ; me
teors, 993 ; paint, 636 ; pane, 789 ;
pencil, 501 ; radiation, 432; ray, 501 ;
lul)e, 789 ; square, and bottle, 789

MACIIINK, Atwood's, 77; elec-
trical, 752-760 ; \'on Ebner's,
794 ; electro-magnetic, 886
Mackerel-sky, 981
Macleod's gauge, 206
Magazine, 717

Index.

1075

Magdeburg hemispheres, 160

Magic lantern, 604

Magnetic attractions and repulsions, 702 ;
battery, 717; couple, 690; curves,
706; declination, 691; dip, 698;
effects of the electrical discharge, 791 ;
equator, 69S ; field, 707, 963 ; fluids,
683 ; induction, 686 ; influence, 686 ;
limit, 720; meridian, 691; needle,
691, 692 ; oscillations of, 705 ; obser-
vatories, 702 ; poles, 698 ; saturation,
716 ; storms, 694

Magnetisation, 710 ; by the action of the
earth, 714; by currents, 882; single
touch, 711

Magnetism, 6, 700 ; determination of,
in absolute pressure, 709 ; earth's, 701 ;
of iron ships, 715 ; Ampere's theory
of, 879 ; remanent, 883 ; theory of,
683 ; terrestrial distribution of free, 721

Magneto and dynamo-electrical machines,
918-920

Magneto-electrical apparatus, 911 ;
Gramme's, 917 ; machines, 913-916

Magnetometer, 949

Magnets, artificial and natural, 680 ;
broken, 685 ; action of earth on, 689 ;
equator of, 68 1 ; floating, 722 ; heat
developed by, 929 ; meter, 949 ; north
and south poles of, 682 ; portative force
of, 719 ; saturation of, 716 ; influence
of heat, 720 ; induction by, 904 ; in-
ductive action on moving bodies, 905 ;
action on currents, 867 ; on solenoids,
877 ; rotation of induced currents by,
928; optical effects of, 935 ; total action
of two, 708

Magnification, linear and superficial, 88 ;
measure of, 589 ; of a telescope, 55, 64

Magnifying power, 594

Magnitude, 9 ; apparent, of an object,
588 ; of images in mirrors, 587

Major chord, 247 ; triads, 248

Malleability, 859

Mance's heliograph, 523 ; method, 957

Manganese, magnetic limit of, 720

Manhole, 466

Manipulator, 888

Manometer, 97, 183 ; open-air, 183 ;
with compressed air, 184 ; Regnault's
barometric, 186

Manometric flames, 288

Mares' tails, 981

Marie-Davy battery, 812

Marine barometer, 165 ; engines, 466 ;
galvanometer, 822

Mariner's card, 975 ; compass, 697

MIC

Mariotte and Boyle's law, 180

Mariotte's tube, 180

Marloye's harp, 281

Maskelyne's experiment, 67

Mason's hygrometer, 398

Mass, measure of, 23 ; unit of, 23

Matter, 2

Matteucci's experiment, 903

Matthiessen's thermometer, 308 ; table of
electromotive forces, 940 ; electrical
conductivity, 958

Maxim's lamp, 838

Maximum current, conditions of, 826

Maximum and minimum thermometers,
310 ; of tension, 755

Maxwell's electromagnetic theory of light,
748, 965 ; colour discs, 570

Mayer's floating magnets, 722

Mean temperature, 1004

Measure of force, 29 ; of work, 60

Measure of magnification, 589, 594 ; of
mass, 23 ; of space, 22 ; of time, 21 ;
of velocity, 25

Measurement of small angles by reflec-
tion, 522

Mechanical equivalent of heat, 497 ;
effects of electrical discharge, 792 ;
battery, 839

Megascope, 606

Melloni's researches, 429 ; thermomul-
tiplier, 412, 946

Melting point, influence of pressure on,
339

Membranes, vibrations of, 283

Memoria technica, 820

Meniscus, 132 ; convex, 131 ; in baro-
meter, 169 ; Sagitta of, 169

Mercury, frozen, 373, 381, 384 ; pendu-
lum, 320 ; coefficient of expansion,
323 ; expansion of, 322 ; pump, 208 ;
purification of, 168

Meridian, 21 ; geographical and mag-
netic, 691

Meriten's machine, 913

Metacentre, 115

Metal, Rose's and Wood's fusible,
340

Metals, conductivity of, 955

Meteoric stones, 480

Meteorograph, 974

Meteorology, 973

Meteors, aerial, 964

Metre, 22, 125

Mica, 664

Microfarad, 964
' Micrometer lines, 594 ; screw, 1 1
I Microphone, 931

1076

Index.

Microscope, 12 ; achromatism of, 592 ;
Duboscq's, 606 ; compound, 591 ; field
of, 591 ; focussing, 587 ; magnifying
powers of, 594 ; photo-electric, 606 ;
simple, 586 ; solar, 605

Microspectroscope, 580

Mill, Barker's, 194

Milliampere, 964

Millimetre, 125

Mineral waters, 1000

Mines, firing by electricity, 795, 829

Minimum thermometer, 310 ; deviation,

547

Minor chord, 247

Minotto's battery, 812

Minute, 21

Mirage, 541

Mirrors, 512 ; applications of, 534; burn-
ing, 420; concave, 419, 528; conju-
gate, 420; convex, 526-529; glass,
515; parabolic, 535; rotating, 520,
795 ; spherical, 524

Mists, 980

Mixture of gases, 188 ; of gases and
liquids, 189 ; laws of, 383

Mixtures, freezing, 347 ; method of, 452

Mobile equilibrium, 415

Mobility, 7, 18

Modulus of elasticity, 88

Moisture of the atmosphere, 400

Molecular forces, 3 ; attraction, 83 ;
state of bodies, 4; velocity, 294

Molecular state, relation of absorption to,

443

Molecules, 3

Moments of forces, 38

Momentum, 28

Monochord, 266

Monochromatic light, 569

Monosyllabic echo, 237

Montgolfier's balloon, 196; ram, 150

Moon, 510

Morgagni's humour, 610

Morin's apparatus, 78

Morrcn's mercury pump, 208

Morse's telegraph, 889

Moscr's images, 193

Motion, 18; on an inclined i)lane, 50;
curvilinear, 25 ; in a circle, 53, 54 ;
rectilinear, 25 ; resistance to, in a
iluid, 48 ; uniformly accelerated rec-
tilinear, 48 ; cjuantity of, 29 ; of a
pendulum, 55; of ])rojectilc, 51

Mouth instrument, 271

Multiple battery, 826

Multiple echoes, 237; images formeil by
mirrors, 515, 516, 517

OBS

Multiplication, method of, 906
Multiplier, 821

Muscular currents, 966, 967, 968
Music, 220 ; physical theory of, 246-264
Musical boxes, 279 ; comnia, 248 ;
intervals, 247 ; scale, 248 ; tempera-
ment, 250 ; tones, properties of, 246 ,
intensity, notation, 252 ; pitch and
timbre, 246 ; sound, 223 ; range, 252
Myopy, 619, 629

NAIRNE'S electrical machine, 757
Nascent state, 84
Natterer's apparatus, 381
Natural magnets, 680
Naumann's law, 458
Needle, declination of, 691 ; dipping,

698 ; astatic, 700 ; magnetic, 691
Negative plate, 801
Negatives on glass, 609
Nerve-currents, 970
Neutral line, 744; equilibrium, 70;

point, 744 ; temperature, 940
Newtonian telescope, 600
Newton's disc, 567 ; law of cooling, 416

rings, 650, 651; theory of light, 568
Niaudet's element, 812
Nicholson's hydrometer, 120
Nickel, electrical deposition of, 857 ;

magnetic limit of, 720
Nicol's prism, 660
Nimbus, 981
Nobert's lines, 594
Nobili's battery, 943 ; rings, 852 ; ther-

momultipliers, 945 ; thermo-electric

pile, 428, 431, 943
Nocturnal radiation, 495
Nodal points, 271, 645
Nodes and loops, 269 ; of an organ pipe,

274 ; explanation of, 276
Noises, 221
Nonconductors, 725
Norremberg's apparatus, 657
Northern light, 1003
Norwegian stove, 410
Notation, musical, 252
Notes in music, 247 ; musical, of women

and l)oys, 259 ; wave-length of, 253
Nut of a screw, 45

OBJECT-GLASS, 590
Objective, 590
Oboe, 272

Obscure radiation, 432 ; rays, 433
transmutation of, 433

Index.

1077

OBS

Observatories, magnetic, 702

Occlusion of gases, 194

Occultation, 505

Octave, 249

Oersted's experiment, S20

Ohms, 987

Ohm's law, 825

Opaque bodies, 500

Opera-glasses, 597

Ophthalmoscope, 633

Optic axis, 617 ; axis of biaxial crystals,
644; angle, 607; nerve, 612

Optical centre, 555 ; effects of magnets,
926 ; instruments, 585 ; electrical ex-
periments, 937

Optics, 499

Optometer, 619

Organ, 280 ; pipes, 274 ; nodes and loops
of, 274

Orrery, electrical, 764

Orthochromatic plates, 611

Oscillations, 55; axis of, 79; method of,
705

Oscillating discharges, 783

Otto's gas engine, 476

Otto von Guericke's air-pump, 200

Outcrop, III

Overshot wheels, 150

Oxyhydrogen light, 606

Ozone, 793, 999

PACINOTTI'S ring, 917
Paddles of steam vessels, 150
Paint, luminous, 636
Pallet, 81

Pane, fulminating, 769 ; luminous, 790
Papin's digester, 371
Parabola, 51, 143

Paraliolic mirrors, 535 ; curve, 60, 143
Parachute, 198
Paradox, hydrostatic, 103
Parallel of latitude, 82 ; forces, 36 ;

centre of, 27
Parallel rays, 501
Parallelogram offerees, 33
Paramagnetic bodies, 938
Partial current, 961
Pascal's law of equality of pressures, 96 ;

experiments, 162
Passage tint, 677
Passive state of iron, 851
Path, mean of molecules, 273
Pedal, 279

Peltier's cross, 950 ; effect, 950
Pendulum, 55 ; application to clocks,

81 ; ballistic, 81 ; compensation, 320;

PLU

electrical, 724; gridiron, 320; mer-
curial, 320 ; length of compound, 79 ;
reversible, 79 ; verification of laws of,
80

Penetration of a telescope, 596

Penumbra, 503

Percussion, heat due to, 479

Periscopic glasses, 629

Pennanent gases, 380

Persistence of impression on the retina,
625

Perspective, aerial, 618

Perturbations, magnetic, 692, 693

Phantasmagoria, 606

Phenakistoscope, 625

Phenomenon, 5

Phial of four elements, 106

Phonautograph, 287

Phonograph, Edison's, 291

Phosphorescence, 635, 636

Phosphorogenic rays, 573

Phosphoroscope, 636

Photo-electric microscope, 606

Photoelectricity, 732

Photogenic apparatus, 606

Photographs on paper, 609 ; on albu-
menised paper and glass, 61 1

Photography, 608-611

Photometers, 509, 511

Photophone, 936

Physical phenomena, 5 ; agents, 6 ;
properties of gases, 152; shadows, 503

Physics, object of, I

Physiological effects of the electric dis-
charge, 785 ; of the current, 827 ; of
RuhmkorfFs coil, 923

Piano, 279

Piezometer, 97

Pigment colours, 570

Pile, voltaic, 804-818

Pincette, tourmaline, 666

Pipes, organ, 274

Pisa, tower of, 69

Pistol, electric, 793

Piston of air-pump, 200 ; rod, 467

Pitch, concert, 251 ; of a note, 246 ;
a screw, 45

Plane, 45 ; electrical inclined, 764 ;
mirrors, 513 ; wave, 642

Plante's secondary battery, 849

Plants, absorption in, 193

Plate electrical machine, 753

Plates, colours of thin, 650 ; vibrations
of, 282 ; Chladni's, 282 ; photographic
dry, 610

Plumb line, 67

Pluviometer, 983

I078

Index.

Pneumatic syringe, 154, 479

Poggendorff's law, 793

Point, boiling, 366, 367

Points, action of, 742 ; nodal, 271, 645

Poisseuille's apparatus, 147

Poisson's coefficient, 88

Polar aurora, 1003

Polarisation, 848 ; angle of, 654 ; cur-
rent, 848 ; of electrodes, 806 ; by
double refraction, 652 ; by reflection,
653 ; by single refraction, 655 ; ellip-
tical and circular, 669, 670, 672 ; of
heat, 679 ; galvanic, 806, 848 ; light,
652 ; of the electric medium, 747 ;
plane of, 654 ; plate, 804 ; rotatory,
674

Polarised light, theory of, 661 ; colours
produced by the interference of, 662, j
668 ; rays, 662

Polariser, 656

Polarising instruments, 656

Polarity, 806 ; boreal, austral, 689

Pole, glacial, 997

Poles, 803 ; analogous and antilogous,
842 ; electric, 732 ; of the earth, 698 ;
magnetic, 698 ; of a magnet, 681 ;
mutual action of, 682 ; precise defini-
tion of, 684 ; austral and boreal, 689

Polygon of forces, 35

Polyorama, 606

Poly prism, 544

Ponderable matter, 6

Pores, 13

Porosity, 7, 13 ; application of, 15

Portative force, 719

Positive plate, 801 ; crystals, 643

Positives on glass, 610

Postal battery, S89

Potential energy, 62 ; of electricity, 738 ;
of a Leyden jar, 782 ; of a sphere, 741

Pound, 125; avoirdupois, 23, 29; foot, 59

Powders, radiation from, 443

Power of a lever, 40 ; of a microscope,
594; of points, 742

Presbytism, 619, 629

Press, hydraulic, 108

Pressure, centre of, 102 ; on a body in a
liquid, 112; atmospheric, 158 ; amount
of, on human body, 163 ; exi)eriment
illustrating, 210; influence on melting
point, 339 ; heat produced by, 479 ;
electricity produced by, 731
Pressures, equality of, 98 ; vertical down-
ward, 99 ; vertical upward, 100 ; in-
dependent of form of vessel, lOl ; on
the sides of vessels, 102 ; rate of trans-
mission of, 99

Prevost's theory of exchanges, 415

Primary coil, 893

Primitive current, 961

Principal current, 961

Principle of Archimedes, 113

Prisms, 543-547 ; double refracting, 659 ;

Nicol's, 660 ; with variable angle, 544
Problems on expansion of gases, 332 ;

on mixtures of gases and vapours, 384 ;

on hygrometry, 401
Projectile, motion of, 51
Prony's brake, 42, 473
Proof plane, 735
Propagation of light, 502
Protoplasm, 827
Protuberances, 579
Pulley, 41:
Pump, air, 200 ; condensing, 209 ; filter,

206
Pumping engine, 467
Pumps, different kinds of, 215 ; suction,

216 ; suction and force, 217
Punctum CKCum, 612
Pupil, 612

Psychrometer, 398, 974
Pyroelectricity, 732
Pyroheliometer, 480
Pyrometers, 311 ; electric, 949

UADRANTAL deviation, 715
Quadrant electrometer, 756

RADIANT heat, 411 ; detection and
^ measurement of, 412 ; causes
which modify the intensity of, 414 ;
Melloni's researches on, 428 ; relation
of gases and vapours to, 43S; relation
to sound, 446a

Radiated heat, 403, 411

Radiating power, 425 ; identity of ab-
sorbing and radiating, 426 ; causes
which modify, &c., 427 ; of gases, 441

Radiation, cold produced by, 495 ; from
powders, 443 ; of gases, luminous, and
ol)scure, 432; laws of, 413; solar,
480

Radiative power, 9S5

Radiometer, 445

Railway, electrical, 917 ; friction on
centrifugal, 53

Rain, 983 ; clouds, 983 ; bow, 1002 ; fall,
974) 9^3 ; g^"ge, 983 ; drop, veloctty
of, 48

Ram, hydraulic, 150; powder, 479

Ramsden's electrical machine, 753 •

Index.

1079

RAO

Raoult's researches, 343

Rarefaction in air-pump, 200 ; by Spren-
gel's pump, 205

Ray, incident, 536 ; luminous, 501 ;
ordinary and extraordinary, 641

Rays, actinic, or Ritteric, 433 ; diver-
gent and convergent, 501 ; frigorific,
422; of heat, 411, 429 ; Herschelian,
430 ; invisible, 429 ; obscure, 433 ;
path of, in eye, 615; phosphorogenic,
573 ; polarised, 662 ; transmutation of
thermal, 434

Reaction and action, 39

Real volume, 14 ; foci, 552 ; focus, 525 ;
image, 528, 556

Reaumur scale, 303

Receiver of air-pump, 200

Recomposition of white light, 567

Reed instruments, 272

Reeds, free and beating, 272

Reflected light, intensity of, 519

Reflecting power, 423 ; goniometer,
534 ; sextant, 521 ; stereoscope, 623 ;
telescope, 598

Reflection, apparent, of cold, 422 ; of
heat, 418 ; from concave mirrors, 419 ;
irregular, 518 ; laws of, 417 ; verifi-
cation of laws of, 420 ; in a vacuum,
421 ; of light, 511-541; of sound,
236

Refracting crystals, 639, 652, 663 ; stereo
scope, 624 ; telescope, 598

Refraction, 536-545 ; double, 639 ; po-
larisation by, 652 ; explanation of
single, 638 ; of sound, 238

Refractive index, 538 ; determination of,
562 ; of gases, 550 ; of liquids, 549 ;
of solids, 548 ; table of, 550 ; indices
of media of eye, 6 1 3

Refractory substances, 338

Refrangibility of light, alteration of, 5S2

Regelation, 990

Regnault's experiments, 229 ; determi-
nation of density of gases, 336 ; mano-
meter, 186 ; methods of determining
the expansion of gases, 333 ; of specific
heat, 454 ; of tension of aqueous va-
pour, 356, 358 ; hygrometer, 397

Regnier's electric lamp, 838

Regulator of the electric light, 835, 836

Reis's telephone, 885

Relay, 889

Remanent magnetism, 883

Repulsions, magnetic, 705 ; electrical
laws of, 731

Reservoir, common, 726

Residual charge, 748, 773

RUH

Residue, electric, 773

Resilience, 773

Resinous electricity, 727, 728

Resistance, limiting angle of, 43 ; of a

conductor, 825 ; boxes, 953 ; of an

element, 957
Resonance, 237 ; box, 251 ; globe, 255
Rest, 18

Resultant of forces, 32-34
Retina, 612 ; persistence of impression

on, 625
Return shock, 1000
Reversible pendulum, 79
Reversibility of Holtz's machine, 759
Reversion, method of, 696 ; spectroscope,

577
Rheometer, 821
Rheoscope, 821
Rheoscopic frog, 968
Rheostat, 951
Rhomb, Fresnel's, 671
Rhumbs, 697, 975
Richness, hygrometric, 392
Right ascension, 600
Rime, 987
Ring inductor, 919
Rings, coloured, 666 ; Gravesand's, 295 ;

in biaxial crystals, 667 ; Newton's, 650,

651 ; Nobili's, 852
Ritchie's experiment, 426
Ritteric rays, 433
Robinson's anemometer, 974
Rock salt, heat transmitted through,

437

Rods, vibrations of, 281

Roget's vibrating spiral, 859

Rose's fusible metal, 340

Rotary engine, 471

Rotating mirror, 520, 795

Rotation, electrodynamic and electro-
magnetic, of liquids, 869 ; winds, 978

Rotation of the earth, 80 ; of magnets
by currents, 912 ; of currents by mag-
nets, 868 ; of induced currents by
magnets, 928

Rotatory power of liquids, 676 ; polari-
sation, 673, 674; coloration produced
by, 675

Rousseau's densimeter, 130

Roy and Ramsden's measurement of
linear expansion, 361

Rubbers, 753

Rubidium, 578

Ruhlmann's barometric and thermome-
tric observations, 179

Ruhmkorffs coil, 921 ; effects produced
by, 923

io8o

Index.

Rumford's photometer, 509
Rutherford's thermometers, 310

SACCHARIMETER, 677
Saccharometer, 126

Safety-catch, 829 ; tuljc, 379 ; valve, 108,
371 ; whistle, 466

Sagitta of meniscus, 169

Salimeters, 129

Salts, decomposition of, 843

Saturation, degree of, 392 ; magnetic,
716 ; of colours, 570

Saussure's hygrometer, 399

Savart's toothed wheel, 241

Scale of hardness, 93

Scales in music, 248 ; chromatic, 250 ;
of a thermometer, 303 ; conversion of,
into one another, 303

Scattered heat, 424; light, 518

Schehallien experiment, 67

Scheiner's experinient, 619

Schwendler's platinum light standard, 838

Scintillation of stars, 541

Sciopticon, 604

Sclerotica, 612

Scott's phonautograph, 2S7

Scraping sound, 281

Scratching sound, 281

Screen, magnetic, 82 2

Screw, II, 45

Screw, magnetic, 822

Secchi's meteorograph, 974

Secondary axis, 555 ; batteries, 849 ;
currents, 806; coil, 893

Second of time, 21, 25

Seconds pendulum, 79

Secular magnetic variations, 692

Segments, ventral and nodal, 269

Segner's water-wheel, 149

Selenite, 664

Selenium, 951

Self-induction, 905

Semicircular deviation, 715

Semi-conductors, 725

Semiprism, 526

Semitones, 249

Senarmont's experiment, 406

Sensitive membrane, 229 ; -wound ma-
chine, 919a

Serein, 985

Series, thermo-electric, 940

Serum, 12

Sextant, 521

Shadows, 503

Shaft, 467

Shock, electiic, 770-785 ; return, 1000

SOU

Shooting stars, 480

Short circuit, 810 ; sight, 629

Shunt, 961 a ; -wound machine, 919 a

Siemens' armature, 914; dynamo-elec-
trical machine, 918 ; unit, 952 ; elec-
trical thermometer, 960

Sight, line of, 595

Silent discharge, 793

Silver, voltameter, 846

Simoom, 977

Sine compass, 824

Singing of liquids, 363

Sinuous currents, 861

Sirocco, 977

Size, estimation of, 618

Sky, 969

Sleet, 988

Slide valve, 469

Sling, 53

Smee's battery, 811

Snow, 988 ; line, 991

Soap-bubble, colours of, 650

Solar microscope, 605 ; light, thermal
analysis of, 430 ; radiation, 480 ;
spectrum, 564 ; properties of the, 573 ;
dark lines of, 574, 579 ; time, 21 ;
day, 21

Soleil's saccharimeter, 677

Solenoids, 874-878 ; action of currents
on, 875 ; of magnets and of earth on,
876, 877 ; on solenoids, 878

Solidification, 343 ; change of volume
on, 343, 346 ; retardation of, 345

Solidity, 4, 7

Solids, conductivity of, 404 ; index of
refraction in, 54S ; diamagnetism of,
938 ; linear and cubical expansion of,

3;4> 319

Solids, formula; of expansion, 31S

Solution, 342

Sondhauss's experiments, 23S

Sonometer, 266, 932

Sonorous body, 222

Sound, 221 ; cause of, 223 ; not propa-
gated in vacuo, 222 ; propagated in all
clastic bodies, 224 ; propagation of, in
air, 225 ; causes which influence inten-
sity of, 226 ; apparatus to strengthen,
227 ; interference of, 261 ; velocityof, in
air, 230 ; in gases, 231 -232 ; in liquids,
234 ; solids, 235 ; reflection of, 236 ;
refraction of, 237 ; relation of radiant
heat to, 446^ ; transmission of, 228 ;
waves, 229

Sound, ilelmholtz's analysis of, 255

Sound, Kiinig's apparatus, 255; Kundt's,
277

Index.

io8i

sou

Sounder, 896

Sounds, intensity of, 289 ; limit of per-
ceptible, 244 ; synthesis of, 257 ; per-
ceptions of, 260 ; produced by currents,
865

Space, meaSire of, 22

Spar, Iceland, 659

Spark and brush discharge, 7S7 ; elec-
trical, 762, 787 ; duration and velocity
of, 795

Speaking trumpet, 239; tubes, 228

Specific gravity, 24, 119, 124; bottle
hydrometer, 120, 121; of solids, 120;
of gases, 335 ; of liquids, 123 ; tables
of, 124, 125

Specific heat, 448-460; compound bo-
dies, 564 ; detei-mination of, by fusion
of ice, 450 ; by method of mixtures,
452 ; by Regnault's apparatus, 454 ;
of solids and liquids, 456, 457 ; of
gases, 460

Specific inductive capacity, 748

Spectacles, 630

Spectra, 648

Spectral analysis, 575 ; colours and pig-
ment, 571

Spectroscope, 576 ; direct vision, 577 ;
experiments with, 578 ; uses of the,
580

Spectrum, calorific, 573 ; chemical, 573

Spectrum, 430; colours of, 566; pure,
565 ; solar, 564, 577

Spectrum, dark lines of, 574

Spectrum, diffraction, 648

Spectrum, luminous properties of, 573

Spectmm of aurora boreahs, 1003 ; pro-
perties of, 573

Specular reflection, 518

Spherical aberration, 533, 558 ; mirrors,
524 ; focus of, 525 ; formulae for, 530,

Spheroidal form of liquids, 84 ; state,

385
Spherometer, 11

Spiral, 882 ; Roget's vibrating, 859
Spirit-level, no
Sprains, 17
Spray producer, 207
Sprengel's air-piimp, 205
Spring balance, 26
Springs, loio ; intermittent, 214
Stable equilibrium, 70
Stars, declination of, 600; spectral analysis

of, 582
Staubbach, 76
Stave, 252
VSteam-engines, 465 ; boiler, 466 ; double

TEL

action, or Watt's, 467 ; horn, 242 ;
pipe, 207 ; various kinds of, 472 ;
work of, 473 ; heating by, 490 ; vessels,

150
Steel, 467
Steeling, 857
Stereoscopes, 622-624
Sterometer, 185
Stethoscope, 240
Stills, 376

Stool, insulating, 762
Stopcock, doubly exhausting, 202 ; Gay-

Lussac's, 382
Storage batteries, 849
Storms, magnetic, 694
Stoves, 489 ; Norwegian, 410
Stowage, 115

Stratification of electric light, 924
Stratus, 981

Stringed instruments, 279
Strings, 265 ; transverse vibration of,

26s
Subdominant chords, 248
Substance, i
Suction pump, 216 ; and force pump,

217; load which piston supports,

218
Sulphate of mercury battery, 812
Sun, 510 ; analysis of, 579; constitution

of, 579
Sun-spots, 701
Superfusion, 345
Surface level, 67 ; tension, 137 ;

coloured, 581
Suspension, axis of, 71 ; Cardan's, 160
Suspensory ligament, 612
Swan lamps, 838

Swimming, 118 ; -bladder of fishes, 117
Swing of a needle, 821
Switch, 932

Symmer's theory of electricity, 728
Synthesis of sounds, 257
Syphon, 213; barometer, 1 67 ; inter-
mittent, 214; recorder, 892
Syren, 242
Syringe, pneumatic, 154, 479

TAMTAM rnetal, 94
Tangent compass, or galvanometer,
823, 847
Tasimeter, 933
Tears of wine, 136

Telegraph, cables, Covvper's writing,
890; induction in, 891 ; electric, 886-
890 ; electrochemical, 892 ; dial,
888 ; Morse's, 889

4 A

io82

Index.

Telegraphy, duplex, 893

Telephone, 885, 930 ; Edison's, 934 ;
Reis's, 882 ; toy, 235

Telescopes, 595-601 ; astronomical, 595;
Galilean, 597 ; Gregorian, 599 ; Her-
schelian, 601 ; Newtonian, 600 ;' re-
flecting, Rosse's, 601

Telluric lines, 573

Telpherage, 920^

Temper, 94

Temperature, 297, 448 ; correction for,
in barometer, 170 ; critical, 370 ; of
a body, 297 ; determined by specific
heat, 457

Temperature, absolute zero of, 496 ; in-
fluence of, on specific gravity, 123 ;
mean, 1004 ; how modified, 1005 ;
distribution of, 1009 ; of lakes, seas,
and springs, loio

Temperatures, diff"erent remarkable, 312 ;
influence on expansion, 318

Tempering, 90, 94

Tenacity, 7, 91

Tension, 117, 736, 922 ; maximum of,
electrical machine, 755 ; maximum of,
vapours, 353 ; of aqueous vapour at
various temperatures, 355-361 ; of
vapours of different liquids, 359 ; of
mixed liquids in. two communicating
vessels, 361 ; free surface, 137

Terquem's experiment, 735

Terrestrial currents, 901 ; heat, 481 ;
magnetic couple, 690 ; magnetism, 721 ;
telescope, 596

Terrestrial gravitation, 67, 82

Terrestrial magnetic couple, 690

Tetanus, 827

Thallium, 578

Thaumatropc, 625

Theodolite, 10

Theory, 5 ; of induction, 747

Thermal analysis, 430 ; unit, 447, 484 ;
springs, lOio

Thermal effects of the current, 829, 830

Thermal rays, transmutation of, 434 ;:
unit, 447

Thermobarometer, 369

Thermochrose, 436

Thermo-dynamic efficiency, 454

Thermo-electric battery, 412, 944 ;
couples, 942 ; currents, 941, 943, 947,
pile, 412, 431, 943 ; series, 940

Thermo-electricity, 939

Thermo-element, 940

Thennometcr, electric, 792

Thermometers, 298 ; liecquerel's elec-
trical, 948 ; correction of readings, 328 ;

TUB

differential, 308 ; division tubes of in,
299 ; filling, 300 ; graduation of, 30X ;
determ.ination of fixed points of, 302 ;
scale of, 303 ; displacement of zero,
304 ; limits to use of, 305 ; alcohol,
306 ; conditions of delicacy of, 307 ;
Kinnersley's, 792 ; Leslie's, 308 ;
Matthiessen's, 308 ; Breguet's, 309 ;
rnaximumand minimum, 310 ; Siemens'
electrical, 960 ; weight, 323 ; air, 331,
334

Thermometry, 297-300

Thermo-multiplier, Melloni's, 412, 946

Thermomotive wheel, 476

Thennoscope, 308

Thomson's electrometers, 780, 781 ; gal-
vanometer, 822 ; apparatus for atmo-
spheric electricity, 993 »

Thread of a screw, 45

Threads, fine, 89

Throw of a needle, 82 1

Thunder, 998

Timbre, 246

Time, measure of, 21 , mean solar, 21

Tint, 570 ; transition, 677

Tones, combinational, 263 ; differential,
263

Tonic, 248

Toothed wheel, 241

Torricelli's experiment, 161 ; theorem,
142 ; vacuum, 168

Torsion, angle of 89 ; balance, 89, 704,
734 ; force of, 89

Total reflection, 540

Tourmaline, 658, 732 ; pincette. 666

Tourniquet, hydraulic, 149

Tower of Pisa, 69

Toy telephone, 235

Traction, elasticity of, 88

Trajectory, 25

Transformation of energ}-, 64

Transit, 21

Transition tint, 677

Translucent bodies, 500

Transmission of heat, 403 ; of light, 499,
542 ; by the current, 844

Transmission of sound, 228

Transmitter of photophone, 936

Transparency, 7, 500

Transparent media, 542-549

Transpiration of gases, 192

Triad, harmonic, 247 1

Triangle, 281 i

Triangle of forces, 35 ' (

Trumpet, speaking, car, 239 ,'

Tubes, Gcissler's, 205, 925 ; luminous. ♦
789 ; safety, 379 ; speaking, 22S

Inde

1083

TUN

Tuning-fork, 251, 281, 290
Turbines, 150
Twilight, 51S
Twinkling of stars, 541
Tympanum, 260

Tyndall's res(Sirches, 431, 446^, 986,
00 1

ULTRAGASEOUS state, 927
Unannealed glass, colours pro-
duced by, 668

Undershot wheels, 150

Undulation, length of, 225, 637

Undulatory theoiy, 499, 637

Uniaxial crj'stals, 640-643 ; double
refraction in, 642 ; positive and nega-
tive, 643

Unit jar, Harris's, 778 ; Jacobi's, 952 ;
Siemens', 952 ; thermal, 447

Unit of length, area and volume, 22 ;
heat, 447 ; of work, 61

Units, fundamental, 6irt

Unstable equilibrium, 70

Urinometer, 129

VACUUM, application of, to con-
struction of air-pump, 200 ; extent
of, produced by air-pump, 201 ;
Crookes's, 446; fall of bodies in a,
76 ; formation of vapour in, 352 ; heat
radiated in, 413 ; reflection in a, 421 ;
Torricellian, 168

Valency, change of, 458

Valve, safety, 108, 371 ; chest, 466

Vane, electrical, 764

Vaporisation, 350 ; latent heat of, 372,
462

Vapour, aqueous, tension of, at various
temperatures, 357-361 ; formation of,
in closed tube, 370 ; latent heat of,
372

Vapours, 349 ; absorption of heat by,
435 ; absoqjtive powers of, 440 ;
density of, Gay-Lussac's method, 386 ;
Hofinann's, 387 ; densities of, 389 ;
determination of latent heat of, 372,
462 ; Dumas's method, 388 ; elastic
force of, 351 ; formation of, in vacuo,
352 ; saturated, 353 ; unsaturated,
354 ; tension of different liquids, 359 ;
of mixed liquids, 360 ; in communicat-
ing vessels, 361

Variations, annual, 693 ; accidental,
694 ; barometric, 171; causes of,
172; diurnal, 693; relation of, to

weather, 173 ; in magnetic declination,
691, 695

Varley unit, 952

Velocity, 25, 6ia, 153 ; direction of, 56 ;
of efflux, 142 ; of electricity, 795 ; of
light, 505-507 ; graphic representation
of changes of, 56 ; Kundt's method,
277; molecular, 294; of sound in air,
230 ; gases, 231, 232 ; formula for cal-
culating, 232; of winds, 975

Velocities, composition of, 52 ; examples
of, 25

Vena contracta, 145

Ventral and nodal segment, 269, 274

Verdel's constant, 935

Vernier, 10

Vertical line, 67

Vestibule of the ear, 260

Vibrating spiral, Roget's, 859

Vibration, 222; arc of, 55 ; produced by

currents, 884; of tuning-forks, 290
Vibrations, 262 ; formulje, 275 ; of
membranes, 283 ; laws of, 267 ; mea-
surement of number of, 241 ; number
of, producing each note, 251 ; of mu-
sical pipe, 275 ; of rods, 281 ; of
plates, 282 ; of strings, 265, 267, 270

Victoria Regia, 485

View, field of, 593

Vinometers, 129

Violin, 279

Virtual and real images, 514; focus,
525 ; velocity, 46

Viscosity, 96, 146, 147 ; of gases, 446

Vision, distance of distinct, 619; bino-
cular, 621

Visual angle, 617

Vis viva, 59, 448, 477 '

Vital fluid, 797

Vitreous body, 612; electricity, 727;
fusion, 338 ; humour, 612

Vocal chords, 259

Volatile liquids, 349

Volta's condensing electroscope, 779
. electi-ophoinis, 752; fundamental ex-
periment, 798

Voltaic arc, 833 ; couple, 801 ; currents,
819 ; induction, 900 ; pile and battery,
804, 805, 815, 832

Voltameter, silver, 846; Faraday's, 846

Volume, 22 ; unit of, 22, 24 ; determi-
nation of, 114; change of, on solidi-
fication, 346 ; of a liquid and that of
its vapour, relation between, 390

Volumometer, 185

Von Ebner's electrical machine, 794^

Voss's electrical machine, 759

io"4

Index.

WAL

ZON

WALKER'S battery, 8ii, 886
Water barometer, 1 76 ; bellows,
207 ; decomposition of, 123 ; hammer,
76 ; hot, heating by, 492 ; level,
109

Water, maximum density of, 330; spouts,
984 ; wheels, 150

Watt's engine, 467

Wave, condensed,- 225 ; expanded, 225 ;
lengths, 637, 649 ; plane, 642 ; of a
note, 253

W' eather, its influence on barometric ya-
riations, 171, 172; glasses, 174; charts,
979 ; forecasts, 979

Wedge, 44

Wedgwood's pyromete.r, 311

W^eighing, method of double, 75

Weight, 23, 82 ; relative, 43 ; of bodies
weighed in air, correction for loss
of, 402; of gases, 155; thermometer,
324

Weights and measures, 125

Wells, artesian, iii

Wells's theory of dew, 987

Werdermann"s electric lamp, 838

Wet-bulb hygrometer, 398

Wheatstone's bridge, 955 ; photometer,
509 ; rheostat, 95 1 ; rotating mirror,
795 ; and Cooke's telegraph, 887

Wlieel and axle, 42

Wheel barometer, 174; thermomotive,
476

Wheels, friction, 77; escapement, 81 ;
water, 150

Whirl, electrical, 764

Whispering galleries, 237

Whistle, safety, 466

White light, deoomposition of, 564 ; re-
composition of, 567

W^hite's pulley, 41

Wiedemann and Franz's tables of con-
ductivity, 404

Wiedemann's determination of electro-
motive force, 959

Wild's magneto-electrical machine, 915

Wimshurst's machine, 760

Winckler's cushions, 753

Wind chest, 272 ; instruments, 270, 280

Windhausen's ice machine, 494

Winds, causes of, 976 ; direction and
velocity of, 974, 975, 1005 ; law- of ro-
tation of, 978 ; periodical, regular, and
variable, 977

Wine, alcoholic value of, 378 ; tears of,
136

Wire telegraph, 886

Wollaston's battery, 805 ; camera lucida,
603 ; cryophorus, 373 ; doublet, 586

Wood, conductivity of, 404

Wood's fusible metal, 340

Work, 34, 59 ; measure of, 60 ; of an
engine, 472 ; rate of, 473 ; unit of, 61 ;
internal and external, of bodies, 295 ;
of a voltaic battery, 832 ; required for
the production of electricity, 761

Writing telegraphs, 8S9, 890

YARD, British, 22, 125
Yellow spot, 612
Young and Fresnel's experiment, 645
Young's modukis, 88

ZAMBONI'S pile, 817
Zero, absolute, 496 ; aqueous va-
pours below, 355 ; displacement of, 304
Zigzag lightning, 985
Zinc, amalgamated, 816 ; carbon battery,

810
Zither, 279
Zoetrope, 625
Zone, isothermal, 1007

Spottiswoolic &" Co. Printers, New-sirect Sgiiarc, Loudon.

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Full text of "Elementary treatise on physics experimental and applied for the use of colleges and schools"

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